ISSN 2188-5001
MATERIALS DESIGN AND
CHARACTERIZATION LABORATORYSUPERCOMPUTER CENTERACTIVITY REPORT

2019

INSTITUTE FOR SOLID STATE PHYSICSTHE UNIVERSITY OF TOKYOMaterials Design and Characterization Laboratory (MDCL)
The MDCL was established as the third research facility of the Institute for Solid
State Physics (ISSP) when the latter was reorganized in May 1996. Its aim is to promotematerial science with an emphasis on the “DSC cycle”, where DSC stands for design,synthesis and characterization, three processes for developing new materials.
The MDCL consists of two sections, Materials Design (MD) section and Materials
Synthesis and Characterization (MSC) section. The Supercomputer Center of the ISSP
(SCC-ISSP) is placed in the MD section, while in the MSC section there are seven laboratories for joint use; Materials Synthesis Laboratory, Chemical Analysis Laboratory, X-ray
Diffraction Laboratory, Electron Microscope Laboratory, Electromagnetic Measurement
Laboratory, Spectroscopy Laboratory, and High-Pressure Synthesis Laboratory.
Almost all the facilities of the MDCL are open to scientists in Japan through the User
Programs conducted by two steering committees of the MDCL. One is the steering committee of the SCC-ISSP, under which the Supercomputer Project Advisory Committee isplaced for reviewing proposals. The other is the steering committee of the MSC facilities.
More than half of the members of these committees are from the outside of ISSP.

COVER FIGURE
Crystal structures and phonon properties of thermoelectric clathrate Ba8 Ga16 Ge30 .
Adopted from T. Tadano and S. Tsuneyuki: Phys. Rev. Lett. 120 (2018) 105901.
See T. Tadano, Page 15–24, ”First-principles calculation of thermophysical properties ofsolids with strong phonon anharmonicity”.

iiActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

PREFACEThe Supercomputer Center (SCC) is a part of the Materials Design and Characterization
Laboratory (MDCL) of ISSP. Its mission is to serve the whole community of computationalcondensed-matter physics of Japan providing it with high performance computing environment.
In particular, the SCC selectively promotes and supports large-scale computations. For thispurpose, the SCC invites proposals for supercomputer-aided research projects and hosts theSteering Committee, as mentioned below, that evaluates the proposals.
The ISSP supercomputer system consists of two subsystems: System B, which is intended formore nodes with relatively loose connections. In July, 2015, the SCC replaced the two
supercomputer subsystems (SGI Altix ICE 8400EX and NEC SX-9) to one new system (System
B, SGI ICE XA/UV hybrid system). The system B consists of 1584 CPU nodes, 288 ACC
nodes, and 19 FAT nodes. The CPU node has 2 CPUs (Intel Xeon). The ACC node has 2CPUs(Intel Xeon) and 2GPUs (NVIDIA Tesla K40). The FAT node has 4CPUs (Intel Xeon) andlarge memory (1TB). The system B has totally 2.6 PFlops theoretical peak performance.
The new system C (HPE SGI 8600) was installed in January, 2018. It consists of 252 nodes, andeach node has 2 CPUs (Intel Xeon) and 192 GB of memory. The system C has totally 774
TFlops.
The hardware administration is not the only function of the SCC. Since 2015, the SCC has
started “Project for advancement of software usability in materials science”. In this project, forenhancing the usability of the ISSP supercomputer system, we perform some softwareadvancement activities such as implementing a new function to an existing code, releasing a
private code on Web, and writing manuals. Two target programs were selected in school year
2019 and developed software were released as abICS (proposal made by S. Kasamatsu(Yamagata Univ.)) and TeNeS (proposal made by N. Kawashima (ISSP)). The SCC has also
started a service for porting users’ materials science software to General Purpose GPUs
(GPGPU) since 2015. One program was selected for the GPGPU porting in school year 2019.
All staff members of university faculties or public research institutes in Japan are invited topropose research projects (called User Program). The proposals are evaluated by the Steering
Committee of SCC. Pre-reviewing is done by the Supercomputer Project Advisory Committee.
In school year 2019, totally 309 projects were approved. The total points applied and approved
are listed on Table. 1 below. Additionally, we supported post-K and other computational
materials science projects through Supercomputing Consortium for Computational Materials
Science (SCCMS).
The research projects are roughly classified into the following three (the number of projects
approved):
First-Principles Calculation of Materials Properties (145)
Strongly Correlated Quantum Systems (36)
Cooperative Phenomena in Complex, Macroscopic Systems (128)
All the three involve both methodology of computation and its applications. The results of the
projects are reported in 'Activity Report 2019' of the SCC. Every year 3-4 projects are selected
for “invited papers” and published at the beginning of the Activity Report. In the Activity
Report 2019, the following three invited papers are included:iii

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo"First-Principles Calculation of Thermophysical Properties of Solids with Strong Phonon
Anharmonicity",
Terumasa TADANO"Development of Open-Source Parallelized Tensor Network Softwares: mptensor and TeNeS",
Satoshi MORITA and Naoki KAWASHIMA"Disorder-Free Glass Transitions of Spins and Orbitals in a Frustrated Pyrochlore Magnet”,
Kota MITSUMOTO, Chisa HOTTA, and Hajime YOSHINO
June 1, 2020
Naoki Kawashima(Chairman of the steering committee, SCC, ISSP)

iv

CONTENTS
PREFACE
1 OUTLINE1

1.1 Supercomputer System
1.2 Project Proposals
1.3 Committees
1.4 Staff

1
1
3
7

2 STATISTICS (SCHOOL YEAR 2019)
2.1 System and User Statistics
2.2 Queue and Job Statistics
2.3 Project for Advancement of Software Usability
in Materials Science
2.4 GPGPU Support Service
3 RESEARCH REPORTS

7
7
8
10
10
14

3.1 Invited Articles
3.2 First-Principles Calculation of Material Properties
3.3 Strongly Correlated Quantum Systems
3.4 Cooperative Phenomena in Complex Macroscopic
Systems
3.5 SCCMS Projects
3.6 Software Advancement Projects, GPGPU
Implementation, and Workshop Support
4 PUBLICATION LIST

14
43
196
238
359
385

391

ISSP Joint Research Projects
SCCMS Projects
Doctor Theses
Master Theses

392
433
440
442

v

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1

OUTLINE

1.1

Supercomputer System

In SY2019, the ISSP supercomputer center provided users with System B - SGI
ICE XA/UV hybrid system and System C - HPE SGI 8600 system. System B isa massively-parallel supercomputer with three types of compute nodes: 19 “Fat”
nodes, 1584 “CPU” nodes, and 288 “ACC” nodes. “Fat” nodes are each comprised of four Intel Xeon E5-4627v3 CPUs (10 cores/CPU) and 1 TB of memory.
“CPU” nodes have two Intel Xeon E5-2680v3 CPUs (12 cores/CPU) and 128 GBof memory. “ACC” nodes have two nVIDIA Tesla K40 GPUs in additon to two
Xeon E5-2680v3 CPUs and 128 GB of memory. System B achieves 2.6 PFLOPS
in theoretical peak performance with high power eﬃciency. The subsystem comprised of only CPU nodes ranks 61st on the November 2015 Top 500 List, which isa ranking based on total performance measured by the HPL benchmark. The subsystem of ACC nodes ranks 104th on the Top 500 List, and it also ranks 23rd on
the Green 500 List, which is a ranking based on performance per watt of electrical
power consumption. The compute nodes communicate to each other through FDR
Inﬁniband. The Fat nodes are interconnected in fat tree topology, while the CPU
and ACC nodes are connected in enhanced hypercube topology. System B enteredoﬃcial operation on Aug. 21, 2015. SY2019 was the ﬁfth year of the operation of
the current System B. System C is a massively-parallel supercomputer with 252“CPU” nodes, which have two Intel Xeon Gold 6148 CPUs (20 cores/CPU) and
192 GB of memory. System C achieves 774 TFLOPS in theoretical peak performance. SY2019 was the second year of the operation of the current System C. For
further details, please contact ISSP Supercomputer Center (SCC-ISSP).
[Correspondence: center@issp.u-tokyo.ac.jp]

1.2

Project Proposals

The ISSP supercomputer system provides computation resources for scientists
working on condensed matter sciences in Japan. All scientiﬁc staﬀ members (including post-docs) at universities or public research institutes in Japan can submit
proposals for projects related to research activities on materials and condensed
matter sciences. These proposals are peer-reviewed by the Advisory Committee
members (see Sec. 1.3), and then the computation resources are allocated basedon the review reports. The leader of an approved project can set up user accounts
for collaborators. Other types of scientists, including graduate students, may also
be added. Proposal submissions, peer-review processes, and user registration are
all managed via a web system.
The computation resources are distributed in a unit called “point”, determined
as a function of available CPU utilization time and consumed disk resources. There
were calls for six classes of research projects in SY 2019. The number of projects
and the total number of points that were applied for and approved in this school
year are listed in Table 1.

1

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1: Classes of research projects in SY 2019

Class

A
B
C
D
E
S
SCCMS
Total

Maximum
PointsSys–B Sys–C
100
100
1k
500
10k
2.5k
10k
2.5k
30k
2.5k
–
–

Application

# of
Proj.

any time
twice a year
twice a year
any time
twice a year
twice a year

17
88
182
5
17
0
36
345

Total points
AppliedApproved
Sys–B Sys–C
Sys–B Sys–C
1.7k
0.9k
1.7k
0.9k
83.8k
4.7k
58.3k
4.1k
1416.2k88.2k
608.0k
63.0k
26.9k
2.0k
26.9k
2.0k
475.0k
44.0k
253.0k
35.6k
0
0
0
0
253.0k
23.5k253.0k
23.5k2255.6k 163.2k 1200.9k 128.8k• Class A is for trial use by new users; proposals for Class A projects are accepted
throughout the year.
• Proposals for projects in Classes B (small), C (mid-size), E (large-scale), and S(exceptional) can be submitted twice a year. Approved projects in Classes A, B,
C, and E continue to the end of the school year.
• In Class D, projects can be proposed on rapidly-developing studies that need toperform urgent and relatively large calculations. An approved project continues
for 6 months from its approval.
• Class S is for projects that are considered extremely important for the ﬁeld ofcondensed matter physics and requires extremely large-scale computation. The
project may be carried out either by one research group or cooperatively by several
investigators at diﬀerent institutions. A project of this class should be applied withat least 10,000 points; there is no maximum. We require group leaders applying
for Class S to give a presentation on the proposal to the Steering Committee of
the SCC-ISSP. Class S projects are carried out within one year from its approval.
• Project leaders can apply for points so that the points for each system do not
exceed the maximum point shown in this table.

2

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

SGI ICE XA/3744 CPU + 576 GPU
2.62PFlops 240.4TB memory

SGI UV/
UV/76 CPU3
31.6TFlops
1
19TB memoryd array
disk
1.29 PB
Front-end WS
SGI Rackabe Standard-Depthe Server C2112-GP2

System B
System C

HPE SGI 8600
774TFlops 47.25TB memory

disk array 500TB

Front-end WS
HPE

YOU

Figure 1: Supercomputer System at the SCC-ISSP

In addition, from SY 2016, ISSP Supercomputer is providing 20% of its computational resources for Supercomputing Consortium for Computational Materials
Science (SCCMS), which aims at advancing parallel computations in condensed
matter, molecular, and materials sciences on the 10-PFlops K Computer and theexascale post-K project. Computational resources have also been allotted to Computational Materials Design (CMD) workshops, as well as for Science Camps heldin ISSP for undergraduate students.

1.3

Committees

In order to fairly manage the projects and to smoothly determine the system
operation policies, the Materials Design and Characterization Laboratory (MDCL)of the ISSP has organized the Steering Committee of the MDCL and the Steering
Committee of the SCC-ISSP, under which the Supercomputer Project Advisory
Committee (SPAC) is formed to review proposals. The members of the committees
in SY 2019 were as follows:

Steering Committee of the MDCLHIROI, Zenji

ISSP (Chair person)3

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoKAWASHIMA, Naoki
OZAKI, Taisuke
NOGUCHI, Hiroshi
UWATOKO, Yoshiya
SUGINO, Osamu
TOHYAMA, Takami
ONO, Tomoya
YAMAURA, Jun-ichi
TAKAHASHI, Hiroki
MOTOME, Yukitoshi
HOSHI, Takeo
KIMURA, Kaoru
HASEGAWA, Masashi
NAKATSUJI, Satoru

ISSP
ISSP
ISSP
ISSP
ISSP
Tokyo Univ. of Sci.
Kobe Univ.
Tokyo Tech.
Nihon Univ.
Univ. of Tokyo
Tottori Univ.
Univ. of Tokyo
Nagoya Univ.
ISSP

Steering Committee of the SCC-ISSP
KAWASHIMA, Naoki
NOGUCHI, Hiroshi
OZAKI, Taisuke
SUGINO, Osamu
TSUNETSUGU, Hirokazu
KATO, Takeo
KONDO, Takeshi
MORITA, Satoshi
HIGUCHI, Yuji
FUKUDA, Masahiro
KAWAMURA, Mitsuaki
NAKAJIMA, Kengo
TSUNEYUKI, Shinji
HATANO, Naomichi
MOTOME, Yukitoshi
ONO, Tomoya
TOHYAMA, Takami
YOSHINO, Hajime
SUZUKI, Takafumi
YOSHIMOTO, Yoshihide
OKUMURA, Hisashi
HOSHI, Takeo
YATA, Hiroyuki
FUKUDA, Takaki

ISSP (Chair person)
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
Univ. of Tokyo
Univ. of Tokyo
Univ. of Tokyo
Univ. of Tokyo
Kobe Univ.
Tokyo Univ. of Sci.
Osaka Univ.
Univ. of Hyogo
Univ. of Tokyo
NINS-RSCS
Tottori Univ.
ISSP
ISSP

Supercomputer Project Advisory Committee
KAWASHIMA, Naoki

ISSP (Chair person)4

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

NOGUCHI, Hiroshi
SUGINO, Osamu
OZAKI, Taisuke
TSUNETSUGU, Hirokazu
KATO, Takeo
KONDO, Takeshi
HIGUCHI, Yujihi
MORITA, Satoshi
FUKUDA, Masahiro
KAWAMURA, Mitsuaki
NAKAJIMA, Kengo
TSUNEYUKI, Shinji
IMADA, Masatoshi
HATANO, Naomichi
SUZUKI, Takafumi
YOSHIMOTO, Yoshihide
OKUMURA, Hisashi
HOSHI, Takeo
ONO, Tomoya
YOSHINO, Hajime
MOTOME, Yukitoshi
TOHYAMA, Takami
KITAO, Akio
ARITA, Ryotaro
IKUHARA, Yuichi
SHIBATA, Naokazu
AKAGI, Kazuto
YANASE, Yoichi
HATSUGAI, Yasuhiro
OKADA, Susumu
KOBAYASHI, Nobuhiko
NAKAYAMA, Takashi
HOTTA, Takashi
MATSUKAWA, Hiroshi
YAMAUCHI, Jun
HAGITA, Katsumi
KONTANI, Hiroshi
SAITO, Mineo
KAWAKAMI, Norio
YUKAWA, Satoshi
SUGA, Seiichiro
TATENO, Masaru
YASUDA, Chitoshi
OGATA, Masao
WATANABE, Satoshi

ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
ISSP
Univ. of Tokyo
Univ. of Tokyo
Toyota Riken/Waseda Univ.
Univ. of Tokyo
Univ. of Hyogo
Univ. of Tokyo
NINS-RSCS
Tottori Univ.
Univ. of Tsukuba
Osaka Univ.
Univ. of Tokyo
Tokyo Univ. of Sci.
Tokyo Tech.
Univ. of Tokyo
Univ. of Tokyo
Tohoku Univ.
Tohoku Univ.
Kyoto Univ.
Univ. of Tsukuba
Univ. of Tsukuba
Univ. of Tsukuba
Chiba Univ.
Tokyo Metropolitan Univ.
Aoyama Gakuin Univ.
Keio Univ.
National Defense Academy
Nagoya Univ.
Kanazawa Univ.
Kyoto Univ.
Osaka Univ.
Univ. of Hyogo
Univ. of Hyogo
Univ. of the Ryukyus
Univ. of Tokyo
Univ. of Tokyo

5

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

OKAMOTO, Yuko
HUKUSHIMA, Koji
NEMOTO, Koji
YABANA, Kazuhiro
HIDA, Kazuo
WATANABE, Kazuyuki
FURUKAWA, Nobuo
KUROKI, Kazuhiko
TAKANO, Hiroshi
YASUOKA, Kenji
TANAKA, Yukio
MASUBUCHI, Yuichi
KAWAMURA, Hikaru
KUSAKABE, Koichi
SHIRAI, Koun
SAKAI, Toru
ISHIBASHI, ShojiOTANI, Minoru
TOMITA, Yusuke
MIYASHITA, Seiji
SHIRAISHI, Kenji
OGUCHI, Tamio
KAWAKATSU, Toshihiro
KOBAYASHI, Kazuaki
TATEYAMA, Yoshitaka
KIM, KangOTSUKI, TomiMORIKAWA, Yoshitada
ODA, Tatsuki
OTSUKI, Junya
KOGA, Akihisa
SHIMOJO, Fuyuki
TAKETSUGU, Tetsuya
TSURUTA, Kenji
HAMAGUCHI, Satoshi
NISHIDATE, Kazume
KAGESHIMA, Hiroyuki
SATO, Tetsuya
ISHII, Fumiyuki
TATETSU, Yasutomi
YANAGISAWA, Susumu
SHUDO, Ken-ichi
OHMURA, Satoshi
NOGUCHI, Yoshifumi
NAKAMURA, Kazuma

Nagoya Univ.
Univ. of Tokyo
Hokkaido Univ.
Univ. of Tsukuba
Saitama Univ.
Tokyo Univ. of Sci.
Aoyama Gakuin Univ.
Osaka Univ.
Keio Univ.
Keio Univ.
Nagoya Univ.
Nagoya Univ.
Osaka Univ.
Osaka Univ.
Osaka Univ.
Univ. of Hyogo
AIST
AIST
Shibaura Inst. Tech.
JPS
Nagoya Univ.
Osaka Univ.
Tohoku Univ.
NIMS
NIMS
Osaka Univ.
Sophia Univ.
Osaka Univ.
Kanazawa Univ.
Okayama Univ.
Tokyo Tech.
Kumamoto Univ.
Hokkaido Univ.
Okayama Univ.
Osaka Univ.
Iwate Univ.
Shimane Univ.
Keio Univ.
Kanazawa Univ.
Meio Univ.
Univ. of the Ryukyus
Yokohama Natl. Univ.
Hiroshima Inst. Tech.
Shizuoka Univ.
Kyushu Inst. Tech.

6

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

GOHDA, Yoshihiro
HAMADA, Ikutaro
RAEBIGER, Hannes
WATANABE, Hiroshi
TADA, Tomofumi
TODO, Synge

1.4

Tokyo Tech.
Osaka Univ.
Yokohama Natl. Univ.
Keio Univ.
Tokyo Tech.
Univ. of Tokyo

Staﬀ

The following staﬀ members of the SCC-ISSP usually administrate the ISSP Supercomputer.
KAWASHIMA, Naoki
NOGUCHI, Hiroshi
OZAKI, Taisuke
SUGINO, Osamu
IDO, Kota
FUKUDA, Masahiro
HIGUCHI, Yuji
KAWAMURA, Mitsuaki
MORITA, Satoshi
YOSHIMI, Kazuyoshi
MOTOYAMA, Yuichi
YATA, Hiroyuki
FUKUDA, Takaki
ARAKI, Shigeyuki

Professor (Chair person)
Associate Professor
Professor
Professor
Research Associate
Research Associate
Research Associate
Research Associate
Research Associate
Project Researcher
Project Researcher
Technical Associate
Technical Associate
Technical Associate

2

STATISTICS (SCHOOL YEAR 2019)

2.1

System and User Statistics

In the following, we present statistics for operation time taken in the period from
April 2019 to March 2020 (SY 2019). In Table 2, we show general statistics ofthe supercomputer system in SY 2019. The total numbers of compute nodes in
System B and System C are 1891 and 252, respectively. Consumed disk points
amount to about 3% and 2% of the total consumed points in System B and SystemC, respectively.
In the left column of Fig. 2, availabilities, utilization rates, and consumed points
in Systems B and C are plotted for each month. Throughout the school year, theutilization rates were very high, exceeding 80% throughout most of the year.
The user statistics are shown in the right column of Fig. 2. The horizontal
axis shows the rank of the user/group arranged in the descending order of theexecution time (hour×nodes). The execution time of the user/group of the ﬁrst
rank is the longest. The vertical axis shows the sum of the execution time up to7

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 2: Overall statistics of SY 2019
System B System C
total service time (×10 node·hours)
16242
2165
number of executed jobs
75681751444
3
total consumed points (×10 point)656
59
CPU points (×103 point)635
58
3
disk points (×10 point)
21
1
3
total exec. time (×10 node·hours)
14529
1843
availability
98.04%
98.06%
utilization rate
89.39%
85.13%
3

the rank. From the saturation points of the graphs, the numbers of “active” users
of Systems B and C are around 400 and 100, respectively. The maximum ranks in
the graphs correspond to the number of the users/groups that submitted at least
one job.

2.2

Queue and Job Statistics

Queue structures of Systems B and C in SY2019 are shown in Table 3. In System
B, users can choose from three types of compute nodes; jobs submitted to queues
with “cpu”, “acc”, and “fat” at the end of their queue names are submitted toCPU, ACC, and Fat nodes, respectively, while only CPU nodes are available in
System C. See Sec. 1.1 for a description of each type of compute node. The user
then has to choose the queue according to the number of nodes to use and theduration of their calculation jobs. Queue names starting with “F” are for jobs
taking 24 hours or less, while those starting with “L” can run much longer up
to 120 hours. More nodes are allotted to “F” queues in order to maximize theturnaround time of user jobs. The queue names starting with “i” are used forinteractive debugging of user programs and the elapsed time limit is 30 minutes.
The number following “F”, “L”, or “i” correspond to the number of nodes that canbe used by one user job. Note that F/B72acc queue were abolished in November
2018.
To prevent overuse of the storage, points are charged also for usage of disk
quota in the three systems, as shown in Table 4. Disk points are revised often for
optimal usage of the resources by examining usage tendencies each year.
Although we do not mention here in detail, to promote utilization of themassively parallel supercomputer, background queues for system B (“B4cpu”,“B36cpu”, “B144cpu”, “B18acc”, and “B2fat”) and background queues for system C (“B4cpu”, “B9cpu”, “B36cpu”) which charge no points for the jobs havealso been open.
The number of jobs, average waiting time, and total execution time in each8Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

System B

14

106 node·hours

12
10
8
6
4
user exec. timegroup exec. time

2
0
0

100

200
300
400
Rank of user/group

500

600

System C

1.8
1.6

106 node·hours

1.4
1.2
1.0
0.8
0.6

user exec. timegroup exec. time

0.4
0.2

0

25

50
75
100
125
Rank of user/group

150

175

Figure 2: Left: Availabilities, utilization rates and point consumptions of eachmonth during SY 2019. Right: User statistics. The horizontal axis shows therank of the user/group arranged in the descending order of the execution time(hour×nodes). The vertical axis shows the sum of the execution time up to the
rank.

9

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

queue are shown in Table 5. In System B, a large portion of jobs have been executedin “F” queues. The largest amount of the execution time has been consumed in
the large-scale “F144cpu” queue, but substantial number of jobs were run in every
queue, suggesting that a wide variety of user needs are met by this queuing scheme.
In most of these queues, the queue settings meet the user’s tendencies in that thewaiting times are on the order of the elapsed-time limit.

2.3

Project for Advancement of Software Usability in Materials Science

From School Year 2015, the supercomputer center (SCC) has started “Project
for advancement of software usability in materials science”. In this project, forenhancing the usability of the supercomputer system in ISSP, we perform some
software-advancement activity such as implementing a new function to an existing
code, releasing a private code on Web, writing manuals. Target programs are
publicly oﬀered in December and selected in the review by the Steering Committeeof SCC. The projects are carried out by the software development team composedof three members in ISSP. In SY 2019, two projects were selected as listed inTable 6.

2.4

GPGPU Support Service

As noted in Sec. 1.1, ACC nodes with graphics processing units (GPU) were introduced in System B in School Year 2015. Since GPUs were introduced in the
ISSP Supercomputer center for the ﬁrst time, many programs developed or utilized by users of this center have not been programmed for GPU computing. To
help users take advantage of GPUs, the supercomputer center has started a service
for porting users’ materials science software to General Purpose GPUs (GPGPU).
After a call for proposals (which will usually be in December), target programs forthe next school year are selected by the Steering Committee of SCC. The porting
service is carried out on each program for about two months; the coding is performed by engineers from the computer vendor supplying the ISSP supercomputer
system, and ISSP staﬀ oversee the progress of the project and manage necessarycommunications with the proposer. Copyrights of the resulting software basicallybelong to the proposers, but the supported contents might be published underagreement with the proposer. In SY 2019, one project was selected as listed inTable 7.

Acknowledgments
The staﬀs would like to thank Prof. Takafumi Suzuki (now at University of Hyogo)
for developing WWW-based system (SCM: SuperComputer Management System)
for management of project proposals, peer-review reports by the SPAC committee,
and user accounts. We also thank Ms. Reiko Iwafune for creating and maintaining
a new WWW page of the ISSP Supercomputer Center.

10Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 3: Queue structures in SY 2019
System B
Memoryjob points
queue
Elapsed time # of nodes # of nodes
namelimit (hr)/job/queuelimit (GB)/(node·day)
F4cpu
24
1–4
216
120/node
1
L4cpu
120
1–4
108
120/node
1
24
5–36
288
120/node
1
F36cpuL36cpu120
5–36
144
120/node
1
F144cpu24
37–1441008
120/node 72(144)/(# of nodes)∗L144cpu120
37–144144
120/node 72(144)/(# of nodes)∗i18cpu0.5
1–18
72
120/node1
F18acc24
1–18
180120/node2
L18acc120
1–18
90120/node
2
i9acc
0.5
1–9
36
120/node
2
F2fat
24
1–2
17
1000/node
4
L2fat
120
1–2
6
1000/node
4
i1fat
0.5
1
2
1000/node
4∗

For F/L144cpu queue, the number of occupied node increases in increments of 72
nodes.

System C
queue Elapsed time # of nodes # of nodes
Memorynamelimit (hr)/job/queuelimit (GB)
F4cpu
24
1–4
54
170/node
L4cpu
120
1–4
18
170/node
1–4
18
170/node
i4cpu
0.5
F9cpu
24
5–9
36
170/node
L9cpu
120
5–9
18
170/node
F36cpu24
10–36
144
170/node
L36cpu120
10–36
36
170/node∗

job points/(node·day)
1
1
1
1
1
18(36)/(# of nodes)∗18(36)/(# of nodes)∗For F/L36cpu queue, the number of occupied node increases in increments of 18 nodes.

11Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 4: Disk points of Systems B and C

System B
System C∗∗

point/day/home
0.001 × θ(q − 300)
/work 0.0001 × θ(q − 3000)/home
0.001 × θ(q − 150)
/work 0.0001 × θ(q − 1500)

q is denoted in unit of GB.
θ(x) is equal to the Heaviside step function H(x) multiplied by x, i.e., xH(x).

Table 5: Number of jobs, average waiting time, total execution time, and average
number of used nodes per job in each queue.

queue# of Jobs

F4cpu
L4cpu
F36cpuL36cpuF144cpu
L144cpu
i18cpuF18acc
L18acc
i9acc
F2fat
L2fat
i1fat

169958
9051
26234
2295
9950
194
76809
201751
6661
6519
7310
753
3504

System B
Waiting Time
Exec. Time # of nodes(hour) (×103 node·hour)
12.85
1223.79
1.38
26.04
570.601.71
30.71
1342.06
8.54
64.56
812.259.57
33.30
7208.66
90.65
83.32
829.66109.860.52
106.568.74
3.93
831.48
3.07
3.28
11.86
536.87
0.15
2.31
3.94
24.27
75.56
1.28
30.50
26.75
1.37
0.22
0.54
1.00

System C
queue# of Jobs Waiting Time
Exec. Time # of nodes
3(hour) (×10 node·hour)
F4cpu
25640
12.06
268.51
1.54
L4cpu
1718
79.26
110.23
1.61
i4cpu
10297
0.06
2.86
2.63
F9cpu
2863
40.39
159.26
7.43
L9cpu
203
31.61
46.64
6.36
F36cpu2588
19.52
652.5824.94
L36cpu130
70.88
160.2424.37

12

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 6: List of Project for advancement of software usability in materials science
for SY 2019.
Project Proposer
Shusuke Kasamatsu
Yamagata University
Naoki Kawashima
The University of Tokyo

Project Name
Coupling of extended ensemble sampling
and ﬁrst-principles solvers
Tensor Network Solver
for Quantum Lattice Problems

Table 7: List of supported software and project proposers for the GPGPU support
service for SY 2019.
Project Proposer
Project Name
Junya Otsuki
GPU acceleration of matrix calculations
Okayama University in the solver of Bethe-Salpeter equation

13

3
3.1

RESEARCH REPORTS
Invited Articles

First-Principles Calculation of Thermophysical Propertiesof Solids with Strong Phonon Anharmonicity

15

Terumasa TADANO

Development of Open-Source Parallelized Tensor Network
Softwares: mptensor and TeNeS

25

Satoshi MORITA and Naoki KAWASHIMA

Disorder-Free Glass Transitions of Spins and Orbitals
in a Frustrated Pyrochlore Magnet
Kota MITSUMOTO, Chisa HOTTA, and Hajime YOSHINO

14

35

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation of thermophysical properties ofsolids with strong phonon anharmonicity
Terumasa TADANO
Research Center for Magnetic and Spintronic Materials,
National Institute for Materials Science (NIMS),
Sengen, Tsukuba, Ibaraki 305-0047

Abstract
Optimizing thermophysical properties of solids, including thermal expansion, thermal conductivity,
and thermodynamic stability is crucial for developing energy- or light-harvesting material that showsa high device performance at operating temperatures. To achieve a simulation-guided design ofsuch materials, lattice vibration (phonon excitation)needs to be modeled accurately beyond the quasiharmonic level. In recent years, several important theoretical and technical improvements havebeen made in the field of ab initio phonon calculation. These methods have overcome the limitation of the conventional phonon calculation method
and further strengthened the predictive power offirst-principles calculations based on density functional theory. In this report, we review some of
the new computational approaches and demonstrate
their validity through applications to a hydrogenrich superconductor and thermoelectric materials
in which phonons are strongly anharmonic.

1

Introduction

Predicting and understanding thermophysical properties of solids only from the crystal structure is
crucial for achieving a simulation-guided design ofhigh-performance energy- and light-harvesting materials including but not limited to thermoelectric,
photovoltaic, and superconducting materials. For
example, lattice thermal conductivity, κL , needs tobe reduced to achieve a high thermoelectric figure-of-merit ZT . Also, the critical temperature (Tc ) of
ferroelectric phase transition plays a crucial role inrealizing a giant dielectric constant of polar semiconductors at ambient temperature, as exemplified
by the commercially used BaTiO3 -based ceramics. Since these finite-temperature thermophysical properties are characterized by the thermal andquantum fluctuation of nuclei, it is necessary toconsider the excitation of phonons for achieving ameaningful prediction.
First-principles phonon calculation is performed
actively and routinely based on density functional
theory (DFT). In most cases, the harmonic approximation (HA) is adapted, assuming that theatomic displacements are much smaller than interatomic distances. While the HA gives reasonable phonon dispersion curves and thermodynamic
quantities for many semiconductors and metals, it
often becomes inaccurate and sometimes breaks
down completely for high-performance thermoelectric and dielectric materials where the atomic
displacements can be as large as 10% of an interatomic distance. Moreover, the HA obviously
fails to describe physical properties related to theanharmonicity of the potential, including phononphonon scattering and structural phase transition.
To solve these limitations of the HA, a more advanced phonon calculation method that can include
phonon anharmonicity is required.
In the last few decades, several new ab initio phonon calculation methods have been proposed as an efficient way to include anharmonic
effects [1–7]. Among them, the self-consistent15

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyophonon (SCP) based approaches [3–7] are particularly important because they enable us to access
finite-temperature phonon frequencies and polarization vectors as well as Tc values of structuralphase transition [8, 9]. Also, the recent advancesin thermal transport theory are noteworthy [10,11].
The advent of these new methods, as well as theirefficient implementations in open-source software,
have opened up a way to study complicated lattice dynamics in emergent materials and to predict
finite-temperature thermophysical properties thatcannot be reached by the conventional method.
In this short report, we introduce the basics of the
new phonon calculation methods and demonstrate
their validity through applications to a hydrogenrich superconductor, thermoelectric clathrate, andthermoelectric tetrahedrite.

2

Recent progress of ab initio
phonon calculation

Self-consistent phonon theory
The self-consistent phonon (SCP) theory, which
was originally developed by Hooton [12], aims tocalculate phonon frequencies and polarization vectors that are renormalized by anharmonicity of thepotential. In this theory, an existence of a welldefined effective one-body Hamiltonian


X
1
†
H0 =
~Ωqν bqν bqν +(1)2qν
is assumed. Here, q and ν are the momentum
and branch index of phonons, respectively, andb†qν (bqν ) is creation (annihilation) operator of thephonon qν. The frequency Ωqν is the effective
frequency that is renormalized by anharmonic effects; therefore, its value differs from the harmonicfrequency ωqν . In addition, since the effective polarization vectors {qν } are also different from theharmonic ones {eqν }, b† and b in Eq. (1) differ
from the creation and annihilation operators of theharmonic Hamiltonian H0 .
Now, let us consider how to determine Ωqν and{qν }. To this end, we introduce the exact Hamiltonian H and associated density operator ρH =e−βH /Tr(e−βH ), with β = 1/kT . The Hamiltonian H includes all anharmonic terms; therefore, it
may be written as H = H0 + U3 + U4 + . . . where
Un is the potential energy of the nth-order anharmonicity. By using H and ρH , the exact Helmholtz
free-energy is given as
FH = Tr(ρH H) +1
Tr(ρH ln ρH ).
β(2)Next, let us substitute a trial density matrix defined as ρH0 = e−βH0 /Tr(e−βH0 ) for ρH in
Eq. (2). We then obtain FH (H0 ) = Tr(ρH0 H) +1
β Tr(ρH0 ln ρH0 ). By using the Jensen’s inequality ehXi ≤ heX i, it is straightforward to show thefollowing Feynman–Gibbs–Bogoliubov inequality
holds:
FH ≤ FH (H0 ).
(3)
In the SCP theory, Ωqν and {qν } are determinedso that the right-hand side of Eq. (3) is minimized.
This is nothing but a mean-field approximation.
Indeed, the SCP theory is a phonon version of the
Hartree–Fock theory.
The minimization of FH (H0 ) can be performedby repeatedly calculating atomic forces in supercells with stochastically sampled atomic configurations and updating the variational parameters in
H0 [5]. An alternative approach we have developed
is to derive the SCP equation via the condition of∂FH (H0 )/∂Xi = 0, where Xi comprises all variational parameters including Ωqν and {qν }. For
the brevity of the explanation, let us assume that thepolarization vectors do not change by anharmonic
effects. Also, we consider the anharmonic terms
up to the fourth-order because fifth- and higherorder terms are less significant. We then obtain thefollowing SCP equation [6, 13]:2
Ω2qν = ωqν+1X
Φ(qν; −qν; q1 ν1 ; −q1 ν1 )
2q ν
1 1

×

~[1 + 2n(Ωq1 ν1 )]. (4)2Ωq1 ν1

The second term on the right-hand side is the renormalization term associated with the quartic anharmonicity, whose magnitude is proportional to themean-square displacement of normal coordinate

16

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyohQ∗qν Qqν i = ~[1 + 2n(Ωqν )]/2Ωqν with n(ω) being the Bose–Einstein distribution function. Sincen(ω) is temperature dependent, the effective frequency Ωqν also changes as a function of temperature.
We have shown that Eq. (4) gives phonon dispersion curves of cubic SrTiO3 that agree wellwith the results of inelastic neutron scattering
measurements. Once we compute all quartic
coefficients Φ(qν; −qν; q1 ν1 ; −q1 ν1 ) in Eq. (4),the effective frequencies at various temperatures
can be obtained quickly. To compute the quartic coefficients, we first calculate the real-space
fourth-order interatomic force constants (IFCs)
in a supercell. Then, the real-space IFCs aretransformed into the normal coordinate representation Φ(qν; −qν; q1 ν1 ; −q1 ν1 ). The computational complexity of this transformation isO(Nqirred. Nq1 Nν2 ), where Nqirred. is the numberof irreducible sets of q points, Nq1 is the number of q1 points, and Nν is the number of phonon
branches. When we consider the anharmonic mixing of polarization vectors, we also need to compute the off-diagonal elements of the quartic coefficients. In that case, the computational complexity becomes O(Nqirred. Nq1 Nν4 ). In our implementation of Eq. (4) in alamode [14], we use ahybrid parallelization of MPI and OpenMP. With
this implementation, the SCP calculation has beensuccessfully performed even for complex structures. For example, a SCP calculation of thermoelectric clathrate Ba8 Ga16 Ge30 (Nν = 162,
Nqirred. Nq1 = 1) with the polarization mixing finishes within 10 hours when we use 432 CPU coresof ISSP system B (sekirei).

Phonon scattering
While the SCP method can compute anharmonicphonon frequencies and polarization vectors efficiently, it is still based on a non-interacting picture [Eq. (1)]. Therefore, the phonon linewidth iszero, which leads to the unphysical result that thephonon lifetime and lattice thermal conductivity
are infinite. To solve this problem, phonon scattering processes must be considered. In bulk semi-

conductors, the most dominant source of phonon
scatterings is the phonon-phonon scattering associated with the lattice anharmonicity. In the lowtemperature region, other scattering processes, including phonon-impurity scattering and phononboundary scattering, also become relevant. However, ab initio treatment of these extrinsic phonon
scatterings is still challenging. Therefore, we will
focus on the intrinsic phonons scattering below.
The intrinsic scattering rate of phonons can beobtained by applying many-body perturbation theory to the anharmonic Hamiltonian. Here, thelowest-order perturbation term is the cubic anharmonicity U3 . The unperturbed Hamiltonian may
be the true harmonic Hamiltonian H0 , only if all
2 > 0), or thephonons are dynamically stable (ωqν
effective one-body Hamiltonian H0 obtained by an
SCP calculation. When we use H0 as the unperturbed Hamiltonian, the phonon self-energy ofthe bubble, which gives a first-order correction, isgiven as [15](B)Σqν (iωm ) =1 X X ~|Φ(−qν; q1 ν1 ; q2 ν2 )|2
16 q q ν νωqν ω1 ω2
1 2

1 2

× ∆(−q + q1 + q2 )f (1, 2, iωm ),(5)
X
1 + n1 + n2
f (1, 2, iωm ) =σiωm + σ(ω1 + ω2 )σ=±1
n1 − n2−, (6)iωm + σ(ω1 − ω2 )where ωm = 2πm/β~. Here, for the brevity of thenotation, we represent ωq1 ν1 as ω1 and n(ω1 ) as n1 .
The function ∆(q) in Eq. (5) becomes 1 when q is
an integral multiple of the reciprocal lattice vector
G and 0 otherwise. Therefore, the double loop
over q points in Eq. (5) can be reduced to a single
loop. After performing an analytic continuation to
the real axis, we obtain the phonon linewidth as(B)(B)Γqν = ImΣqν (ωqν ) and the phonon frequency(B)(B)
shift as ∆qν = −ReΣqν (ωqν ).
In many semiconductors, the linewidth calcu(B)lated from Γqν shows reasonable agreement withexperimental data, including its linear temperaturedependence in the high-temperature range. However, in some cases, the theoretical value may un-17

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

derestimate the experimental linewidth most likely
due to the presence of additional scattering channels of phonons, including phonon-impurity scattering and higher-order phonon-phonon scatterings. Recently, the self-energies of these additional
scattering processes have been evaluated based on
DFT for relatively simple systems and reported to
be important in correctly understanding the thermal transport behavior [16, 17], which is the main
topic of the next subsection.

Thermal transport
First-principles calculation of κL has been an active research topic in recent years because its active
control would lead to efficient energy conversion
and thermal management devices. In particular,significant effort has been placed on elucidating
the atomistic-level origin of ultralow thermal conductivity of efficient thermoelectric materials suchas intermetallic clathrates and SnSe. To computeκL from first principles, the semi-classical Peierls–
Boltzmann theory (PBT) is usually adopted. In the
PBT, we first assume that the heat flux is carriedby phonon quasiparticle; therefore, the heat flux
operator is approximated asXjph =~ωqν vqν b†qν bqν .
(7)qνHere, vqν = ∂ωqν /∂q is the group velocityof phonon, which is readily obtained from thephonon dispersion curves. Then, after introducing
the single-mode relaxation-time approximation, we
obtain the thermal conductivity tensorXκP =cqν vqν ⊗ vqν τqν ,(8)
qν

with cqν being the mode specific heat. The phonon
lifetime τqν can be obtained from the phonon
linewidth as τqν = ~/(2Γqν ). When we consider the dominant bubble self-energy for Γqν , thethermal conductivity shows the temperature dependence of κL ∝ T −1 in the high-temperature
range, in accord with many experimental observation. So far, the PBT-based calculations have been
performed for many thermoelectric materials andexplained their thermal transport behavior successfully.
While the PBT has been successful for many
crystalline solids, it fails to describe the temperature profile of κL observed in amorphous solids
and other disordered solids. In these systems, thethermal conductivity shows little temperature dependence and does not decrease even in the hightemperature region. To understand thermal transport physics in disordered solids, a beyond PBTtreatment would be necessary. One of the mostproblematic assumptions made within the PBT formalism is the approximation of Eq. (7). Morespecifically, when we express the harmonic heat
flux operator j (2) with the creation and annihilation
operators of phonons, we obtain the band diagonal
and off-diagonal terms as follows:j (2) =X ~(ωqν + ωqν 0 )qνν 0= jph +

2vqνν 0 b†qν bqν 0

X ~(ωqν + ωqν 0 )qν6=ν 02vqνν 0 b†qν bqν 0 .
(9)Here, vqνν 0 is the band off-diagonal extension of
the group velocity. In the PBT, the band offdiagonal terms of the heat flux operator is omitted. In the pioneering work by Allen and Feldman [18, 19], however, they showed that the offdiagonal contribution is dominant in the disorderedsolids and successfully explained the temperaturedependence of κL observed in amorphous silicon.
In the Allen–Feldman (AF) theory, however, the effect of phonon scattering is not considered. Therefore, their theory is still not suited for studying thermal transport in disordered solids that also show
strong anharmonicity.
Recently, a new thermal transport theory thatunifies the PBT and the AF theory has been developed [10]. According to their result, the thermal
conductivity is given asκL = κP + κC ,(10)

where κP is the Peierls term defined by Eq. (8), andκC is the coherent term associated with the interband components of the heat flux operator, which

18

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

So far, we have introduced the state-of-the-art
ab initio phonon calculation methods. To study
phonon-related properties by using these methods,
the harmonic, cubic, and quartic IFCs are necessary
as inputs. These IFCs can be estimated by repeatedly calculating atomic forces in a supercell withsuitably chosen atomic configurations. In the conventional supercell approach, only a few atoms in asupercell are displaced. For instance, the harmonic
IFC between atom i and j, Φij , is estimated as
Φij = −[Fj (ui = +h)−Fj (ui = −h)]/2h, where
Fj (ui = ±h) represents the atomic force acting on
the atom j when the atom i is displaced slightly(h ≈ 0.01 Å) from its equilibrium position. This
procedure needs to be repeated for all irreducible
ij pairs. To estimate the cubic IFC, Φijk , in thesame fashion, we need to consider, at most, four
displacement patterns for each element. Therefore,
the number of displacement patterns necessary toobtain all relevant IFCs increases rapidly for thehigher-order terms, and the calculation of quartic
IFCs would be infeasible or extremely expensive if
possible.
To mitigate this issue, we employ the compressive sensing approach [20, 21]. First, to increase
the information density obtained from a single DFT
calculation, we displace all atoms in a supercell in
random directions. For these sampled atomic configurations, we compute the atomic forces; these
displacement-force data sets will be served as training data sets of a linear model. Second, instead of105

conventional
LASSO

104

103

102

8G
a1
Cu 6 Ge
3
12
Sb 0
4S
1
Sn 3
Se
cSr
Ti
O
t-S 3
rT
iO
c3
Cs
Pb
B
t-C
r
sP 3
bB
oCs r3PbBr
3

Efficient calculation of force constants

Ba

While this new theory has been tested only for a
few systems so far, it is expected to improve theprediction accuracy of κL and help us deepen our
understanding of anomalous thermal transport instrongly anharmonic and/or disordered materials.

3Γqν + Γqν 0. (11)(ωqν − ωqν 0 )2 + (Γqν + Γqν 0 )2Tevqνν 0 ⊗ vqν 0 νF×ωqν + ωqν 0

Pb

q ν6=ν 0Si

X X cqν ωqν 0 + cqν 0 ωqν

Sc

κC =

calculating the IFC one by one by the central difference, we estimate all IFCs simultaneously by performing linear regression. Since the atomic forces
F can be expressed as a linear function of IFCs Φ
as F = AΦ with A being a sensing matrix comprising atomic displacements, we can estimate theparameter vector Φ by using ordinary least-squares
or other regression methods. In particular, the L1
penalized regression models such as LASSO areuseful because they select and compute physicallyimportant IFCs somewhat automatically and set theother irrelevant parameters exactly zero.
We have applied LASSO to various systems andtested its performance. As shown in Fig. 1, thenumber of static DFT calculations could be reduced dramatically from what would be required
if the conventional approach were used. In these
LASSO calculations, we gradually increased thetraining data sets and the cutoff radii of interaction until we obtained an accurate model that reproduces the DFT forces within ∼5% error. The
numbers shown for the conventional method are estimated by symmetry argument, where anharmonic
IFCs up to the fourth-order are considered within
the cutoff radii as the LASSO calculation. The efficient approach, which can be 100 times as efficientas the conventional one, enables us to perform the
SCP and PBT calculations of complex systems.

No. of static DFT calcs.

is given as

Figure 1: Number of displacement patterns thatwas used to extract IFCs by LASSO (cyan) compared with the estimated number of patterns required by the conventional approach (red).

19

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
Harmonic

SCP (T = 0 K)

300

Frequency (meV)

250
200
150
100
50
0
−50
Γ

X U|K

Γ

L

W

X

Figure 2: Phonon dispersion curves of F m3̄mLaH10 at 150 GPa calculated within the HA andthe SCP theory at T = 0 K.

3Applications

Quantum fluctuation in record superconductor LaH10
Recently, record superconductivity at ∼250 K has
been reported for LaH10 under the high pressure of
137–218 GPa [22, 23]. The possibility of the highTc superconductivity in LaH10 was first predicted
by DFT calculations [24,25] and subsequently confirmed experimentally. In the previous DFT predictions, a sodalite-like structure of LaH10 withspace group F m3̄m has been suggested as a crystal structure that realizes a high-Tc . However, if
the phase stability is evaluated based on enthalpy,
LaH10 is predicted to be thermodynamically unstable against decomposition below 200 GPa. Moreover, F m3̄m-LaH10 is predicted to be dynamically unstable over the whole pressure range wherea ∼250 K Tc has been observed experimentally.
These contradictions likely indicate the limitationof the conventional computational approaches.
To solve this puzzle, we have performed phonon
calculations of LaH10 with including anharmonic
effects [26]. Figure 2 shows the phonon dispersion of F m3̄m-LaH10 calculated within the HA
and the SCP theory at 150 GPa. The F m3̄mstructure is dynamically unstable when the HA isemployed, indicating the F m3̄m structure distorts
into a low-symmetry structure. Indeed, we haveconfirmed that the enthalpies of R3̄m- and C2LaH10 are lower than that of F m3̄m-LaH10 by∼50 meV per formula unit (f.u.) at 150 GPa. However, this conclusion changes when we consider thezero-point motion of hydrogen atoms. As shownin Fig. 2, the quartic anharmonicity renormalizes
phonon frequencies significantly and stabilizes thephonons in the entire Brillouin zone even at T = 0
K, which is possible due to the large zero-point
motion of hydrogen atoms. After obtaining the stable phonons, we have also estimated the zero-point
energy (ZPE) and evaluated the relative stabilityof the F m3̄m structure over the distorted phases
based on enthalpy+ZPE. As a result, the F m3̄mphase is found to be stable than the R3̄m structure by ∼ 110 meV / f.u., which agrees better withthe experimental observation. The inclusion of the
ZPE also changes the thermodynamic stability of
F m3̄m-LaH10 . For example, the formation enthalpy defined as∆H[LaH10 ] = H[LaH10 ]71− H[LaH11 ] − H[LaH3 ] (12)88is about 140 meV/f.u. at 200 GPa, indicating that
LaH10 decomposes into LaH3 (Cmcm) and LaH11(P 4/nmm). However, this conclusion changes
when we consider the ZPE additionally; the formation enthalpy becomes negative as ∆H +∆ZPE =−280 meV/f.u.
To summarize, our calculations have clearlyshown that the large quantum fluctuation of hydrogen nuclei plays a crucial role in stabilizing
the highly-symmetric F m3̄m-LaH10 over the wide
pressure range of 137–218 GPa. We have also
calculated the superconducting Tc based on the
Migdal–Eliashberg theory and obtained an excellent agreement with the experimental values obtained for LaH10 and LaD10 [26]. This agreement
further confirms that the F m3̄m phase of LaH10 isindeed responsible for the record superconductivity
at ∼250 K.

20

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

(a)

(b)

Harmonic(c)

SCP (300 K)

Lattice thermal conductivity (W/mK)

35

Frequency (meV)

30
25
20
15
10
5
0

°

X

M

°

R

3.0
∑P (based on HA)
2.5∑P (based on SCP)

2.0

∑C (based on SCP)
∑P + ∑C
Expt. (Sales et al.)Expt. (May et al.)

1.5
1.0
0.5

200

400

600

800

1000

(d)

(e) 50Harmonic(f)

SCP (300 K)

Frequency (meV)

40
30
20
10
0
°10

°

H

P

N

°

Lattice thermal conductivity (W/mK)

Temperature (K)
1.0
∑P
∑C

∑P + ∑C
Expt. (Suekuni et al.)

0.8

0.6

0.4

0.2

0.0

200

400

600

800

1000

Temperature (K)Figure 3: Crystal structures and phonon properties of thermoelectric clathrate Ba8 Ga16 Ge30 (BGG) andtetrahedrite Cu12 Sb4 S13 . (a) Crystal structures of (a) BGG, adopted from Ref. [27], and (d) tetrahedrite.
(b,e) Phonon dispersion curves of BGG and tetrahedrite, respectively, calculated within the HA (dottedlines) and the SCP method at 300 K (solid lines). (c,f) Thermal conductivities of BGG and tetrahedrite,
respectively, calculated by different methods. For comparison, the experimental values of Refs. [28–30]
are also shown.

Thermal conductivity in complex thermoelectric materials
The thermal transport in complex thermoelectricmaterials has attracted special attention not only
because their thermal conductivity is unusually
low but because they sometimes show a glasslike
temperature dependence even though they possess periodic crystal structures. In this report, we
will focus on the origin of the unusual temperature dependence of κL observed in type-I clathrate
Ba8 Ga16 Ge30 (BGG) and tetrahedrite Cu12 Sb4 S13 ,whose crystal structures are shown in Figs. 3 (a)and (d). In our previous study [31], we have shownthat the low-κL value of BGG can be attributed
to the strong phonon-phonon scattering inducedby the presence of low-frequency optical phonons.
We could successfully reproduce the experimental κL values up to ∼ 100 K by using Eq. (8).
However, the temperature dependence weaker thanκL ∝ T −1 could not be explained by the conventional PBT. In Cu12 Sb4 S13 , κL is almost tempera-ture independent, which cannot be explained by theconventional PBT. Actually, the HA yields imaginary phonons for Cu12 Sb4 S13 , which hinders a
direct application of Eq. (8).
To understand the origin of the unusual temperature dependence in BGG and tetrahedrite, wehave recently performed SCP calculations of thesecomplex materials. Also, the thermal conductivity
is evaluated based on Eq. (10) for which the SCP
eigenvalues and eigenvectors are used as inputs.
Figures 3 (b) and (e) show the calculated phonon
dispersion curves of BGG and tetrahedrite, respectively. The phonon dispersion curves calculated
within the HA and SCP theory are somewhat similar, particularly for the high-frequency phononmodes. In the low-frequency range, however, we
can see notable differences. In BGG, the frequencyof low-lying optical phonon modes around 4.5 meV
increases with heating. These phonon modes correspond to the collective vibration of Ba guest atoms
inside the large cavities made by the host frame-21

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

work, as indicated by the red arrows of Fig. 3 (a).
These phonon modes are often called “rattling“ motion. In tetrahedrite, the unstable phonon modes exist within the HA. These phonon modes correspondto the collective vibrations of Cu(2) atoms, which
are located on the triangle planes made by sulfur
atoms (see Fig. 3(d)). Since the displacement of theCu(2) atoms occur in the direction perpendicular
to the triangle planes, these characteristic phononmodes were named “planar rattling” [30]. In our
SCP calculations, the planar rattling modes werestabilized by anharmonic renormalization above ∼80 K.
Next, we have calculated κP and κC of Eq. (10)separately; the results are compared with available
experimental data in Figs. 3 (c) and (f). When we
employed the harmonic phonon dispersion in calculating the phonon lifetimes and κP , the thermal
conductivity was significantly underestimated, as
shown by the dashed line of Fig. 3 (c). When the
SCP dispersion was used instead, we could reacha nice agreement with the experimental data, including the temperature dependence weaker thanκL ∝ T −1 . Since the low-lying optical phonons
strongly hybridize with the heat-carrying acoustic phonons, a little temperature-dependence ofthe rattling-mode frequency gives rise to the unusual temperature profile of κL [27]. The coherent
contribution κC calculated from Eq. (11) accounts
for about 10% of total κL of BGG at 300 K. For
tetrahedrite, the temperature dependence of κL is
more exceptional as shown in Fig. 3 (f). Interestingly, the little temperature dependence can be
explained qualitatively by the Peierls term basedon the temperature-dependent SCP wave functions.
Still, the calculated κP value significantly underestimates the experimental thermal conductivity
for the entire temperature range. This discrepancy can be cured by including the coherent termκC ; the sum of two contributions, κP + κC , reproduces the experimental values even quantitatively. Such a large coherent contribution has already been reported for orthorhombic halide perovskite CsPbBr3 [10], where the particle-like thermal transport is hindered by the strong phonon-

phonon interaction. We believe the coherent term
κC should be significant not only in disorderedsolids but also in strongly anharmonic (ordered)solids where the phonon linewidths become broad,and the phonon spectral weights overlap with eachother.

4

Summary

In this short report, we reviewed the recent development of new phonon calculation methods that cantreat the intrinsic effects of lattice anharmonicity
beyond the quasiharmonic level. We showed thatthe self-consistent phonon scheme solves the limitations of the harmonic phonon theory by incorporating the quartic anharmonicity at the mean-fieldlevel. Also, the unified theory of thermal transport,
which can account for the coherent thermal transport in addition to the particle-like contribution,
was shown to better explain the anomalous thermal transport observed in complex thermoelectricmaterials.
All of the methods focused in this report are already available in the alamode software [32]. We
kindly invite interested readers to visit the homepage and try the software.
This work was partially supported by Grant-inAid for Scientific Research (number 16H06345)
from the Ministry of Education, Culture, Sports,
Science and Technology, Japan. A part of the computation in this work was performed using the facilities of the Supercomputer Center, Institute for
Solid State Physics, The University of Tokyo. This
report is based on the recent studies done in collaboration with K. Suekuni, S. Tsuneyuki, J. A.
Flores-Livas, I. Errea, R. Arita, and T. Koretsune.

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22

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[3] P. Souvatzis, O. Eriksson, M. I. Katsnelson,
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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[31] T. Tadano, Y. Gohda, and S. Tsuneyuki: Phys.
Rev. Lett. 114 (2015) 095501.
[32] T.
Tadano.
ALAMODE.
https://github.com/ttadano/alamode.

24

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of Open-Source Parallelized Tensor Network
Softwares: mptensor and TeNeS
Satoshi MORITA and Naoki KAWASHIMA
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581

Abstract
In this activity report, we overview two opensource softwares, mptensor [1] and TeNeS [2],for tensor network methods. The former is a library for massively parallel computing of tensor
networks. It provides useful functions for tensor
operations which are commonly appeared in tensor network methods. TeNeS, named for “Tensor
Network Solver”, is a solver for two-dimensional
quantum lattice systems based on an infinite tensor network state. TeNeS is originally developed
as pTNS by Tsuyosi Okubo [3] and released under
the support of Project for Advancement of Software Usability in Materials Science (PASUMS) of
the Institute for Solid State Physics, the Universityof Tokyo [4]. TeNeS can calculate the ground state
wave function for user-defined Hamiltonian andevaluate physical quantities including the magnetization and the correlation functions.

1

Introduction

In strongly correlated quantum many-body
physics, numerical simulation of low-energy
states is quite important for understanding of interesting phenomena including high-temperature
superconductivity, quantum spin liquid, topological nature, etc. To attack these problems, many
computational approaches are proposed. The
exact diagonalization method (ED) provides theexact ground state for small systems [5]. However,exponentially divergence of its computational
cost and memory usage tightly limits the sizeof systems. The quantum Monte Carlo method(QMC) also can calculate the exact results within
statistical errors, but the negative sign problem
occurs in the frustrated systems [6]. The variational Monte Carlo method (VMC) is anotherMonte Carlo method based on the variational principle [7]. Variational parameters are optimized
to minimize the energy and the resulted wave
function is expected to approximate the groundstate well. The expectation value of physicalquantities is estimated by using the Monte Carlosampling. Results of VMC are biased by choice ofthe variational wave function ansatz. The density
matrix renormalization group method (DMRG)
is a quite accurate method for one-dimensional
systems [8, 9].
Recently, tensor network methods are proposed
as a powerful tool [10–16]. DMRG can beviewed as a variational method based on a onedimensional tensor network, i.e., the matrix product state (MPS) [17]. Its higher-dimensional generalization including the projected entangled pairstate (PEPS) is quite successful [18–20]. In classical systems, the partition function can be expressedas tensor networks [21, 22]. The physical properties of the systems can be obtained by the contraction of tensor networks.
Information compression based on the singularvalue decomposition is a key idea of tensor network methods in order to avoid exponentially divergence of computational cost. Accuracy of tensor network simulations is determined by the sizeof tensors. However, computational cost and memory usage still increase very rapidly as a functionof tensor size. Thus parallel computation of tensor
network methods is unavoidable to approach inter-25

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Model
solvers

TeNeS, iTensor, TenPy

Generaltensorcalculations

mptensor, Uni10, Numpy

Linear algebra

ScaLAPCK, LAPACK

Figure 1: Hierarchical structure of tensor network
calculations. Our softwares, TeNeS and mptensor,
belongs to the top and middle levels. The softwares written in red support parallel computation
on a distributed memory system.
esting phenomena.
Tensor network calculations are classified in hierarchical structure as shown in Fig. 1. The top
level is lattice model solvers of tensor network
methods. iTensor [23] and TenPy [24] are a famous software for MPS in this level. The former is written in C++ language but the latter isa Python package. The middle level provides aframework for tensor calculations including tensor contraction and tensor decomposition A C++
library, Uni10 [25] and a famous Python package NumPy [26] are in this level. Recently, ateam of Google released a Python library ”TensorNetwork” for physics and machine learning [27].
Since almost tensor calculations are written as matrix operations, this level is a kind of wrapper toa library for linear algebra, which is the bottom
level. The well-known libraries, LAPACK [28] islocated in this level.
As we mentioned before, parallel computationof tensor network methods is necessary to investigate interesting physical phenomena within sufficient accuracy. However, the softwares listed in theprevious paragraph are not parallelized. To resolve
this situation, we are developing two softwares,
mptensor [1] and TeNeS [2] (Fig. 2). mptensor isan open-source C++ library for parallel computation of tensor networks on a distributed memory

Figure 2: Logo images of mptensor and TeNeS.
The latter represents a shape of a local tensor in
the tensor network state.
system. It provides many tensor operations commonly used in tensor network methods. mptensor
uses ScaLAPACK [29] which is a paralell versionof LAPACK, and supports MPI/OpenMP hybrid
parallel computing. On the other hand, TeNeS is alattice solve built on mptensor. It can solve quantum many-body problems on a two-dimensional
infinite lattice based on a infinite tensor network
wavefunction. TeNeS originates from pTNS developed by Tsuyoshi Okubo [3]. The official version of TeNeS (v1.0) is released on April 2020 under the support of the support of Project for Advancement of Software Usability in Materials Science (PASUMS) of the Institute for Solid State
Physics, the University of Tokyo [4].
In the next section, we briefly review tensor network methods and introduce graphical representations of tensor networks. In the third and fourth
sections, we introduce our softwares and show its
performance. The last section is devoted to summary.

2

Basics of tensor networks

In many-body problems, a huge tensor often appears naturally. One typical example is a coefficient in a wave function of a quantum N-body system|ψ =Ci1 i2 ···iN |i1 |i2  · · · |iN ,(1)where |i x  denotes a basis states on a site x andCi1 i2 ···iN can be regarded as a N-rank tensor. The
number of elements in such a tensor is O(d N ) if
each index takes a value from 1 to d. Here d corresponds the degrees of freedom on each site. Sincecomputational cost grows exponentially with the26

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a)system size N, it is difficult to treat such a hugetensor directly.
A tensor network effectively represents a manyindex tensor by decomposing it into small tensors
only with a few indices, like as,X
Ci1 i2 ···iN =T i1 k1 k2 T i02 i3 k2 k3 T i004 k3 k4 k5 · · · . (2)four-index tensor(b)A{k j }

We introduce new indices k1 , k2 , · · · , which connect between small tensors. Summation over these
indices is nothing but tensor contraction. Since k jdoes not represent any physical degrees of freedom, it is called a virtual index. On the other hand,the original indices in Ci1 i2 ···iN are named the physical indices. If the dimension of each virtual index
is D and each tensor has z indices, the number of
elements in each tensor is O(Dz ). When the number of tensors in a tensor network is polynomial inN, tensor network methods reduce exponentiallylarge computational cost to polynomial order.
In a tensor network, many small tensors connect each other by virtual indices. Its mathematicalexpression becomes messy for large networks. A
graphical representation of tensor networks is useful and intuitive. A tensor is represented by an object (circle, square, etc.) and its indices is shownby lines from a tensor. In other words, a tensor
locates on a node of a graph and its indices correspond to edges. Several examples are shown in
Fig. 3(a). Clearly, a scalar has no index, a vector
has only one leg, and a matrix has two legs. By
using terminology of the graph theory, an index ofa tensor is also called as a bond, and the dimensionof index is a bond dimension. A bond connecting
between two tensors indicates tensor contractionof two tensors. For example, a graphical represenP
tation of matrix multiplication Ci j = k Aik Bk j isshown in Fig. 3(b).
Of course, decomposition of a huge tensor into atensor network is approximation. Its accuracy depends on the virtual bond dimension D and a shapeof network. As a variational state for the groundstate of the quantum many-body problems, several
kinds of structures are proposed. One of the simplest network is the matrix product state (MPS),
whose wave function is written as a product of ma-

vectorscalariBkjmatrix=CijFigure 3: Graphical representation of tensor networks. (a) A tensor is represented by a node ofgraph and indices of a tensor corresponds to edges.
(b) A graphical representation of matrix multipliP
cation, Ci j = k Aik Bk j .
trices,Ci1 i2 ···iN =

X

Mi(1)
Mi(2)
Mi(3)
· · · Mi(N)
. (3)
1 k1
2 k1 k2
3 k2 k3
N kN−1{k j }

Note that the three-index matrix Mi(n)can ben kn−1 kn
regarded as a matrix when the physical index in
fixed. Its graphical representation is shown in
Fig. 4(a). This form can be easily derived by iteration of the singular value decomposition. The MPS
is appeared in DMRG and achieves great successin simulations of the one-dimensional gapped systems [17]. The projected entanglement pair state(PEPS) [19] is two-dimensional generalization of
MPS (Fig. 4(b)).
Important feature of PEPS is the fact that it satisfies the area law for the entanglement entropy [30].
The area law states that the entanglement entropy
in the ground state of a region A is proportionalto |∂A|, the boundary area of the region. The
entanglement entropy of a tensor network stateis bounded by the number of bonds which connects a region A and its complement. If we consider an L × L region, the entanglement entropyof PEPS clearly scales as O(L), which satisfies
the area law in two-dimensional systems. In critical (gapless) one-dimensional systems, entanglement entropy logarithmically increases with thesystem size. Since entanglement entropy of MPS
is bounded from above by log D, MPS can not represent entanglement structure of such a system.

27

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a) MPS(b) PEPS

Sl(c) MERA

Si

Sj

Sl T

=

Sk

Figure 4: Some structures of tensor network states.
The black (red) line indicates physical (virtual)bonds. (a) The matrix product state. (b) The projected entanglement pair state. (c) The multi-scaleentanglement renormalization ansatz.
The multi-scale entanglement renormalization
ansatz (MERA) shown in Fig. 4(c) resolves thisproblem by introducing additional dimension [31].
When we split the system into two parts, we needto cut O(log L) bonds in the MERA wavefunction,
which indicates that upper bound of entanglement
entropy is O(log L) instead of O(1).
Important problems in a tensor network wavefunction for the ground state are how to calculate
expectation values and how to optimize tensor elements based on the variational principle. These
problems are touched in the fourth section.
Another important application is tensor network
representation of the partition function in the statistical physics. The simplest example is the transfer matrix method for one-dimensional classicalsystems, in which the partition function is written as a product of transfer matrices. In theclassical Ising chain with the Hamiltonian H =−J i S i S i+1 , the transfer matrix is given as a 2 × 2
matrix,

 βJ
 e
e−βJ  ,M =  −βJeeβJ

Mi j = eβJS i S j(4)where β denotes the inverse temperature and S itakes ±1.
A generalization of the transfer matrix to higher
dimensional systems is possible. Let us consider
the square lattice tilted by 45 degrees and put a
local tensor on half of plaquettes as shown in Fig.5.
Obviously an index of a tensor corresponds to the

Si

Sj

Sk

Figure 5: A tensor network representation of aclassical spin model on the square lattice.
direction of spins. Tensor elements for the Isingmodel are written as
T i jkl = eβJ(S i S j +S j S k +S k S l +S l S i ) .

(5)

Another sophisticated way to obtain a tensor network representation is based on the singular value
decomposition of the bond Boltzmann factor W.
In the Ising model, W is 2 × 2 matrix with W ss =
eβJss . From the singular value decomposition,
W = UΣV † , we obtain a local tensor as√∗ ∗σi σ j σk σl U si U s j V sk
V sl ,(6)
T̃ i jkl =swhere σi denotes the singular value of W. In contrast to the previous example, a network of T̃ is thesame as the original lattice of the model.
Contraction of the tensor network is a quite important task of tensor network methods. For quantum systems, it appears in the inner product of two
tensor network states and the expectation value ofphysical quantities. In the classical systems, it directly relates to the partition function. However,exact contraction is usually impossible becauseof exponentially large computational cost. The
tensor renormalization group method (TRG) [32]provides an efficient contraction scheme, which
is based on the real-space renormalization group(Fig. 6). Let us consider a tensor network on
the square lattice. A local tensor with four indices is approximated by the product of two threeindex tensors, which are calculated by the truncated singular value decomposition. Then thecoarse-grained tensor is obtained by contraction offour tensors. This step is regarded as a real-space√
renormalization with scaling factor b = 2. After

28

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyot times iteration of TRG steps, the trace of tensor,
P
Z = i, j T i ji j , corresponds to the partition function
with N = 2t under the periodic boundary condition. The animation of TRG method is available inRef. [33]. Although the computational cost of theoriginal TRG method is O(D6 ), we showed that it
can be reduced to O(D5 ) by using a randomized algorithm for the singular value decomposition [34].
Many derivatives of TRG are proposed asa more efficient and accurate method [35–38].
Since the higher-order tensor renormalizationgroup (HOTRG) [35] can be used in a higherdimensional system, it attracts attention also fromcomputational elementary particle physics. Recently we proposed a calculation method forhigher-order moments of physical quantities basedon HOTRG [39]. We showed that the finite-size
scaling analysis provides critical exponents anddistinguishes the weakly first-order and the continuous transitions. The TRG method can also be
applicable to systems with open boundaries. The
fixed-point boundary tensor at criticality has theinformation of the conformal tower described by
the boundary conformal field theory [40, 41].

3

mptensor

mptensor is a C++ library for parallel computationof tensor networks and provides tensor operations
used commonly in tensor network methods [1]. Its
target users are researchers who want to parallelize
their codes of tensor network methods. To make iteasy to translate a serial code written with Python
to a parallelized C++ code, interface of mptensor
is as much like as NumPy [26], which is a famous

T

S [3]
S [1]
S [4]
S [2]

S [2]

S [1]

S [3]

S [4]

Figure 6: Diagrams of the TRG method.

T’

mptensor

External
libraries

Tensorscalapack::Matrix

lapack::Matrix

ScaLAPACKpBLAS, BLACSLAPACK
BLAS

Index
Shape
Axes

MPI

Figure 7: The class structure of mptensor.
Python module of a multi-dimensional array andis a de-facto standard in the field of machine learning.
For high-performance computing, mptensor
supports hybrid parallel computing using MPI
and openMP. With MPI, mptensor distributes tensor elements based on a block-cyclic matrix uses
ScaLAPACK, which is a library for linear algebraon distributed-memory machines [29]. A tensor
is matricized and distributed by the block-cyclic
way. mptensor also supports LAPACK for a system without MPI.

3.1

Class structure

mptensor is composed of three classes as shownin Fig. 7. The Tensor class is a main objectof mptensor, which represents a tensor and corresponds to ndarray in NumPy. In the Tensor
class, a tensor is automatically matricized and it
elements are stored in a Matrix object. mptensor
has two kinds of Matrix classes, a wrapper classof a linear-algebra library. One uses ScaLAPACK
and the other LAPACK, which are separated by
C++ namespace.
The Index class is a short array of non-negative
integers to represent an index of a tensor. The
Shape and Axes classes are just an alias of theIndex class. These classes have a simple constructor to mimic a list of Python. The index classcan create the same list by Index(1,2,3) as wellas Python can easily create a list of integer by[1,2,3], . For C++11, an initializer list {1,2,3}
is also available instead of the index class.
The Tensor class is implemented as a templateclass. Its template parameters specify a Matrix

29

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

class and a value type of elements (double orcomplex). For examples, a real-valued distributed tensor is Tensor<scalapack::Matrix,
double> and a complex-valued non-distributed
tensor is Tensor<lapack::Matrix, complex>.
Since all functions for the tensor class accepts any
patterns of template parameters, users can easilychange a type of tensors. In addition, mptensor isdesigned to make it easy to support another library
for linear algebra in the future. It is because thetensor class can accept any matrix class if it satisfies necessary interfaces.

3.2

lates which process has the element with the given
global index.

3.3

In mptensor, many tensor operations are already
implemented. Some typical operations are listed
as follows.
• Tensor contraction (tensordot)• Tensor decomposition– Singular value decomposition (svd)– QR decomposition (qr)– Diagonalization (eigh)Access to tensor elements

To access an element of a tensor, mptensor provides two ways. One is to access an elementwith an index of a tensor, which we call a global
index. For example, we can get and set an element of a four-index tensor T by specifying(i, j, k, l). The other way is to specify a local index of a one-dimensional array where distributed
elements are stored. In mptensor, a tensor is matricized like as T i jkl = M(i j),(kl) . The huge matrix M is decomposed into small matrices by using the two-dimensional block-cyclic distribution
in ScaLAPACK. A small distributed matrix oneach MPI process is flattened and stored as a onedimensional array. The local index specifies a position in this one-dimensional array. In mptensor,
matricization of a tensor is done in the tensor class,while translation between a index of the global matrix M and a local index is calculated in the matrix
class.
Since tensor elements are distributed on MPI
processors, access by the global index needs tocheck which process has an element T i jkl . On
the other hands, such a check is not necessary
for the local index. Thus access by the local index has simpler interface like as usual array access, T[i]. We recommend a for-loop
with the local index to access all the elementsof a tensor. Member functions of the tensor
class, global index and local position perform translation between the global and local indices. We note that local position also calcu-

Tensor operations• Linear-equation solver (solve)• Arithmetic operators (T + T 0 , a × T , etc.)• Element-wise vector multiplication• Find minimum and maximum elements
These are sufficient to implement various tensor
network methods including PEPS and TRG.
Tensor contraction is one of the main operationin tensor network methods. The tensordot function takes the almost same arguments of that in
Numpy. For example, let us consider the following tensor contraction,
X
Cabc =
Aaib j B jci .
(7)
i, j

In mptensor, it is written as
C = tensordot(A, B,
Axes(1, 3),Axes(2, 0));
The third argument indicates that the second andfourth indices of the first tensor A will be contracted. (Note that array index starts from zero inC++.) The fourth argument is for the second tensor B. The third index i in B (specified by the firstelement in the fourth argument) will be contractedwith the second index of A and the first index j in
B will connects with the fourth index of A. The
resulted tensor C has three indices abc which consists of the non-contracted indices of the first tensor, followed by the non-contracted indices of thesecond.

30

(a)

10000

(b)

Elapsed Time [sec]1000

Elapsed Time [sec]Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

100
10
1
0.1
0.01

N=16384
32768
65536
10

100

10000

1000

100
10

# MPI processes

100# MPI processes

Figure 8: Elapsed time of ScaLAPACK routines, (a) a matrix-matrix multiplication (pdgemm) and (b)the singular value decomposition (pdgesvd). N is the linear size of a square matrix. The number of
OpenMP threads per MPI process is 12. The solid lines indicate the perfect strong scaling.

Elapsed time per step [sec]

10000
1000

U, S, VT);
D=16
32
48

64
128

100
10
1
0.1

10

100
# of MPI processes

Figure 9: Elapsed time per step of the HOTRG
method on the two-dimensional Ising model. The
number of OpenMP threads per MPI process is 12.
The solid lines indicate the perfect strong scaling.
Another important operation in tensor network methods is the singular value decomposition(SVD). For SVD of a tensor, we need to specify theway of matricization. For example, let us consider
the following decomposition,X
T i jkl =Uika S a (V † )al j .
(8)a

To perform this operation in NumPy, a tensor T
is matricized as T (ik),(l j) before SVD. The resulted
singular value vectors are returned as a matrix,
U(ik),a and (V † )a,(l j) . Thus we need to reshape froma matrix to a tensor. mptensor provides a usefulfunction for SVD of a tensor and the above decomposition is written in single line assvd(T, Axes(0, 2), Axes(3, 1),

The second and third arguments specify the wayof matricization. The first and third indices of T
become the row index and the others do the column index. The order of indices specified in thesecond and third arguments also determines that of
U and VT . The result of SVD is stored in the last
three arguments. U and VT are an isometric tensor
corresponding to the singular value vectors, while
S is a one-dimensional array and has the singularvalues.
The performance of mptensor strongly depends
on that of ScaLAPACK. The tensor contraction is
performed by using the matrix-matrix multiplication routines (pdgemm and pzgemm). Thus it shows
very high execution efficiency and parallel efficiency. On the other hand, parallel performance of
SVD becomes worse in many processes as shownin Fig. 8.
We show the parallel efficiency of the HOTRG
method implemented by using mptensor (Fig. 9).
Clearly the strong scaling is satisfied for larger
bond dimension D. It is because the heaviest
part of HOTRG is contraction of a tensor network,
which is scaled as O(D7 ). We note that deviationfrom the strong scaling in small bond dimensions
is due to the singular value decomposition which
has O(D6 ) scaling.

31

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

4

(a)

TeNeS

TeNeS is a tensor-network solver for quantum many-body problems on an infinite twodimensional lattice [2]. TeNeS can calculate theground-state wavefunction for user-defined Hamiltonian and evaluate user-defined physical quantities, including the magnetization and the correlation functions. TeNeS uses TOML [42] as the format of input files. This is a very simple configuration file format, easy to parse into data structures and also human-readable. The input file ofthe main program, tenes, defines simulation parameters, unit cell information for TNS, observables, and time-evolution operators. Since it israther complicated for beginners, we provide twohelper programs, tenes simple and tenes std,
to generate an input file as similar to HΦ [5] andmVMC [7]. By using tenes simple, users easily
create an input file of the predefined models andlattices. TeNeS (v1.0) supports generation of the
input file for the spin-S Hamiltonian  
2 
αααH=Ji j S i S j + B S i · S j 
α=x,y,zi jHS iz + ΓS ix − D(S iz )2
−

(9)

i

on the square, triangular or honeycomb lattice. A
more complicated model is also possible by editing
an input file directly.
The variational wave function of TeNeS is represented by infinite tensor network called an infinite projected entangled paired state (iPEPS) or an
infinite tensor network state (iTNS). Each tensor
has five indices. One corresponds to the physical degrees of freedom. The others, called virtualbonds, connect with tensors on the nearest neighbor sites. The bond dimensions of the physicaland virtual bonds are denoted by d and D, respectively. In iTNS, we need to assume a lattice translational symmetry with a certain period. Figure10(a) shows a diagram of iTNS with 2 × 2 sublattice structure. We note that TeNeS always uses
a tensor network on the square lattice. Other twodimensional lattices including the honeycomb and(b)

Figure 10: (a) Graphical representation of the
iTNS wavefunction with 2 × 2 sublattice structure.
(b) Diagram of the inner product Ψ|Ψ, which iscalled the double layered tensor network.
triangular lattices is properly mapped to the squareone.
To obtain the expectation value of a physicalquantity in iTNS, we need to calculate tensor networks corresponding to Ψ|O|Ψ and Ψ|Ψ. The
diagram of Ψ|Ψ is called the double layered tensor network (Fig. 10(b)). To calculate contraction of this infinite network, TeNeS uses the corner transfer matrix method (CTMRG) [19,20]. We
focus on a part of the network and the other partis approximated by the corner transfer matrices
and the edge tensors [43, 44]. These environment
tensors are optimized by absorbing the local tensor until convergence. The accuracy of the environment tensors is determined by its bond dimension χ. Since the bond dimension after contractionof the physical bond in the double layered tensor
network is D2 , we usually take that χ is proportional to D2 . The computational cost of CTMRG
is O(D10 ) or O(D12 ) depending on the way of thepartial (truncated) SVD in CTMRG.
In order to approximate the ground state by
iTNS, we need to optimize elements of tensors. TeNeS supports the imaginary-time evolution
method based on|ΨiTNS   e−τH |Ψ0 ,(10)where |Ψ0  is the initial iTNS. If τ is sufficiently
large, the right hand side converges to the groundstate and then the left hand side is expected to be agood approximation of the ground state with iTNS
ansatz. TeNeS assumes that the Hamiltonian canbe written as a sum of short range two-body interactions and uses the Suzuki-Trotter decompo-

32

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyois similar to that of SVD in ScaLAPACK (Fig. 8).
We note that elapse time of the simple update perstep is 0.01% of the full update.

5

Figure 11: Elapsed time of TeNeS simulations
with the virtual bond dimension D = 10. The blue
square denotes elapsed time per step of the full update. The orange circle is tensor contraction for
calculation of the expectation value.
sition. To avoid divergence of the dimension ofvirtual bonds, TeNeS supports two kinds of truncation approaches, so-called the full update [46]and the simple update [47]. The former solves the
optimization problems of the whole network by using the CTM environment and has higher accuracy
than the latter. Its computational cost is the same as
CTMRG, that is, O(D10 ) or O(D12 ). On the other
hand, the simple update considers only a part of
network. Its computational cost is O(D5 ), which
is much cheaper than the full update. It is known
that the simple update has strong dependence on
the initial value and usually overestimates the magnetization. Thus we need to take care of results
obtained by the simple update.
The accuracy of iTNS calculation depends on
the bond dimension D. However, the computational cost is rapidly increases. Thus parallel computation is necessary to obtain accurate results.
TeNeS supports parallel computation since tensor
operations are done by using mptensor. We show
elapse time of TeNeS in Fig. 11, where we simulate the transverse field Ising model on the squarelattice. We use a real-valued iTNS with the virtual bond dimension D = 10 and set χ = D2 for
CTM. Since calculation of the expectation value
is tensor contraction, its parallel efficiency is quite
good. On the other hand, the full update includes
the singular value decomposition. Its performance

Summary

In this paper, we have reported recent activitiesof developing tensor network softwares, mptensor
and TeNeS. The former is an MPI/OpenMP hybrid parallelized tensor operation library. It provides many tensor operations commonly used in
the tensor network methods and is already used in
the published papers [48, 49]. One of future issues
for mptensor is implementation of quantum number conserving tensors. If the system has a certain symmetry, its tensor network representation
has a corresponding non-trivial structure [52]. This
technique not only improves accuracy but also reduces computational cost and memory usage because such a tensor is block-diagonal. Another future issue is automatic differentiation, which becomes a common tool in a field of machine learning. Recently, application of automatic differentiation to tensor network methods was proposed andsucceeded to obtain accurate results [53]. Since
it requires huge memory, its parallelization should
become important for large-scale calculation.
TeNeS is an open-source program package forcalculation of two-dimensional quantum states
based on iTNS. An advantage of TeNeS over othernumerical approaches is that it can treat infinite
systems. In this article, we only show the parallel performance of TeNeS because of space limitations. Accuracy of TeNeS simulations will beappeared elsewhere [50]. We hope that TeNeS
becomes a useful standard tool for a wide rangeof researchers who are interested in the stronglycorrelated many-body problems.

Acknowledgements
TeNeS is developed by Tsuyoshi Okubo, Yuichi Motoyama, Kazuyoshi Yoshimi, Takeo Kato and the authors. The original version of TeNeS is developed
as pTNS by Tsuyoshi Okubo [3]. Development and33

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

release of TeNeS are supported by “Project for advancement of software usability in materials science”
of the Institute for Solid State Physics, the University ofTokyo. We would like to thank Kenji Harada, Hiroshi
Watanabe and Synge Todo for collaborations in developing mptensor. The numerical calculations of thiswork were performed with the supercomputer System B(sekirei) in the Institute for Solid State Physics, the University of Tokyo. This work was supported by MEXT
as ”Exploratory Challenge on Post-K computer” (Frontiers of Basic Science: Challenging the Limits) and Priority Issue on Post-K Computer (Creation of New Functional Devices and High-Performance Materials to Support Next-Generation Industries), and by JSPS KAKENHI Grant Number 19H01809.

References[1] https://github.com/smorita/mptensor[2] https://www.pasums.issp.u-tokyo.ac.jp/tenes[3] https://github.com/TsuyoshiOkubo/pTNS[4] https://www.pasums.issp.u-tokyo.ac.jp/[5] M. Kawamura, et al., Comput. Phys. Commun.
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[22] H. H. Zhao, et al., Phys. Rev. B 81, 174411(2010).
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Commun. 236, 65 (2019).
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Phys. Rev. X 9, 031041 (2019)34

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Disorder-Free Glass Transitions of Spins and Orbitals
in a Frustrated Pyrochlore Magnet
1

Kota Mitsumoto1 , Chisa Hotta2 and Hajime Yoshino1,3
Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan
Osaka University, Toyonaka 560-0043, Japan.
2
Department of Basic Science, University of Tokyo, Tokyo 153-8902, Japan
3
Cybermedia Center, Osaka University, Toyonaka, Osaka 560-0043, Japan

Abstract:

glasses obtained by supercooling molecularliquids or making densely packed soft-matterslike colloids. The most important basic question there is to clarify whether the so-called
Kauzmann transition[9], which is a putative,
idealized thermodynamic glass transition, cantake place in the supercooled liquid state.
Recently important progress was made on thetheoretical side: a mean-field theory which
combines the density functional theory of
liquids [10] and the replica method used instatistical mechanics of disordered systems[11] established that the ideal glass transition
exists (at least) in the large dimensional limit(see for a review [12]). However, the fateof ideal thermodynamic transition in finite
dimensions is largely unknown [13].
The
problem is difficult to solve precisely becauseof the glassiness: the extremely sharp increaseof the relaxation time (viscosity) going deeper
into the supercooled liquid state makes it very
difficult to measure quantities in equilibrium.
Another reason is that the super-cooled liquidstate is a meta-stable state which should
be replaced by the crystalline state in true
equilibrium. A possible way out of these
difficulties is to seek simple lattice models,
which mimic the basic phenomenology ofstructural glasses, carefully designed to avoid
crystalline transitions, and allow various
simulation techniques developed for latticemodels [14].

In this activity report, we present an
overview of our recent extensive Monte Carlosimulations performed on the ISSP supercomputer (SYSTEM B) [1][2][3] to study our effective theoretical model for the disorder-freespin-glass transition observed experimentallyin the pyrochlore oxide Y2 Mo2 O7 . By taking
into account not only the spin but also the orbital degrees of freedom of the Mo ions, wefound a new type of glass transition - spinorbital glass transition.

1

Introduction

Glass is a generic state of matters which canbe found in a diverse range of systems ranging from soft to hard condensed matters. Yet,
unlike crystalline states with long-ranged ordering of periodic structures, the very mechanism(s) of the emergence of glasses remainquite elusive. The exceptional case is the family of disordered magnets with quenched disorder, i. .e. spin-glasses. In spin-glasses, the existence of thermodynamic glass transitions isestablished by experiments, theories and simulations (see for reviews [4, 5, 6, 7]). But apparently, glasses without quenched disorder ismore ubiquitous in nature and in industrial
materials. Understanding the mechanism of
the emergence of glasses without quenched disorder remains as one of the most important
unsolved problems in physics [8].
Majority of glassy systems without
quenched disorder emerge from supercooled
liquids. Typical examples are the structural

In principle, glass transitions similar to
those found in the supercooled liquids canalso take place in spin systems. Indeed one
can show exactly that the ideal glass tran-

35

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

imental system, this observation means thatthe model is too crude to capture the real system which exhibits a spin-glass transition. In
order to explain the spin-glass transition of theY2 Mo2 O7 system, previous theoretical studies assumed the presence of some amount of
quenched disorder [28, 29]. However, from themean-field theoretical point of view, disorderfree spin-glass transitions are possible [15].
Albeit in a somewhat artificial case with ahighly non-linear interaction , where the model
is built to describe an optimization problem
like the graph coloring with continuous colors, a 2nd order disorder-free spin-glass transition involving full replica symmetry breaking
emerges without passing through the superparamagnetic phase has been found (See sec.
10 of [15]).
The purpose of the present work is to
uncover the microscopic mechanism of thedisorder-free spin-glass transition observed in
the pyrochlore magnet. Our key observationin the present work [1], which is motivatedby a recent experiment [23], is that in the pyrochlore oxides, not only the spins but also theorbitals (lattice displacements) exhibit glasstransitions simultaneously - spin-orbital glasstransition. In the following, we first explain
our theoretical model and then present our results obtained by extensive Monte Carlo simulations at ISSP.

sitions can take place in spin systems without quenched disorder, by examing supercooledparamagnetic states in the large dimensional
limit [15]. However, in reality, the metastability limit of the paramagnetic state toward
long-ranged ordering of periodic structures(corresponding to the Kirkwood instability ofliquids [16]) may preempt the ideal glass transition (see for instance [17]).
A very promising playground to explore
glass physics is geometrically frustrated magnets on corner-shared lattices such as the
Kagome lattice and pyrochlore lattice (seeFig. 1 (a)). In general, glassy states appear
when periodic long-range ordering is avoided
down to very low temperatures or high densities where strong interactions become important. Therefore frustration is a key ingredient for glass physics [18]. The most spectacular example is the pyrhoclore oxcide Y2 Mo2 O7 ,which is known experimentally to exibit clearcut spinglass transitions without appreciable
quenched disorder [19, 20, 21, 22, 23, 24, 25].
Moreover, in sharp contrast to the structural glass transition mentioned above, thespin-glass transition emerges directly out ofthe paramagnetic state as a 2nd order transition much like the conventional spin-glasstransitions[4, 5, 6, 7], without the need to go
through the metastable ’supercooled’ paramagnetic state. Actually, quite remarkably, thephenomenology of the spin-glass transition andeven the critical exponents associated with thespin-glass transition [19, 20, 25] are nearly indistinguishable from that of the conventional,
canonical spinglasses with quenched disorder.
On the theoretical side, microscopic explanation of the disorder-free spin-glass transition remained a big challenge for more than 30
years. The principal magnetic interaction in
the pyrochlore oxide Y2 Mo2 O7 is the antiferromagnetic interaction between the magnetic
moments of the Mo ions sitting on verticies ofthe pyrochlore lattice. It has been establishedthat the purely antiferromagnetic Heisenberg
spin model on the pyrochlore lattice exhibits
no transitions down to T = 0 because of thevery strong geometrical frustration [26, 27].
This is remarkable given that the system isthree dimensional. Coming back to the exper-

2

Model

We consider two kinds of dynamical variables
associated with the Mo4+ (4d2 , S = 1) ionswhich sit on the vertices i = 1, 2, . . . , N of
the pyrochlore lattice. The first is the classical
Heisenberg spin Si = (Six , Siy , Siz ) normalized
as |S| = 1 which represents the magnetic moments of the Mo ion.
The second is the ’displacement’ of the Mo
ions σi = (σi,x , σi,y , σi,z ). The recent experiment [23] suggests that the pyrhocolore lattice is distorted by displacements of the Mo
ions. The displacement of a vertex (the Moions) take place along the lines connecting thetwo tetrahedra that share the vertex. Thus
the displacements of the vertices of a given
tetrahedron are either pointing toward or away36

CHAPTER 1. INTRODUCTION

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

(b)

?

a)

d)

b)

?
?

c)

strated lattices
with antiferromagnetic interactions on a triangle (top) and a tetrahedron (bottom). (b):simplexes.

%(')%* $)/$,$)$&(')"* $).$,$)$&(')#* $)0$,$)$&(')$* $)++,$)$&-"#% lattice.
Figure 1: Spins on deforming pyrhoclore(a): Pyrhoclore lattice. (b): O2 ions and(')%* $)/$,$)$&$
4+"
the numbers
1 − 4 are the sublattice indices ofmagnetic Mo ions around the i site, where(')"* $).$,$)$&(')#* $)0$,$)$&etrical Frustration!#(')$*$)++,$)$&represent
thepositionsof the Jahn-Teller distorted i
Mo4+ ions. Red and blue dashed circles
#
4+
2
!"
&#$
&'$
&"$
ions (i, j) interact
throughthe O ion as shown in the inset panel,ion. Spinson representative
a pair of Momagnetic
we review some basic aspects of geometrical frustration
in some$st of all let us note that their thermodynamic properties
unusual.
In Mo-O-Mo
ordinary systems,
wherearealpha
is theangle and r̂ij is the unit vector in the i → j direction. (c): Ice-type!#
ase monotonically by lowering the temperature and displacements
the system finally of
reachgroundstate
thetheMotetrahedron.
The different color bonds represent different exchange
is the lowest and the entropy becomes 0, satisfying the third law of thermodynamics. In this
!"
&#$
&'$
&"$
interactions. (taken from [1, 2])transition may take place from a disordered phase to an ordered phase, e.g. ferromagnets
the other hand, strongly frustrated systems may not exhibit any long-ranged order evenower than the energy scale of the interaction and opens various possibilities of unexpectedfrom the center of the tetrahedron. Furthertemperatures. In particular, some geometrically frustrated spin system shows the disorderthe yet.
experimentnsition whose microscopic mechanism has not beenmore,
understood
The goal ofsuggests
this thesisthat the disoblem for the case of a pyrochlore magnet Y2 Mo2 O
placements
follow the ’ice-rule’ [30] : the ’2-in7.
rustration in spin systems means a situation where 2-out’
spins instructure
the system (seecannotfind1a (d)).
config-As suggestedFig.
ly satisfies all the interactions. The simplest example
is
the
case
where
three
Ising
spins
on
by the experiment, we parametrized
the disgle triangle interact with each other antiferromagnetically (See Fig. 1.7 (a)). If we put an up
placements
as
σ
=
σ
ê
.
Here
we
introducediiantiferromagν
and a down spin on the site 2, the remaining spin on the site 3 cannot satisfy
ancan
Ising
variable
σi =to ±1
to represent ’in’
-3 and 2-3 simultaneously. This frustrated situation
be easily
generalized
simplexess, tetrahedra, e.t.c with spins put on the vertexes andand antiferromagnetic
interactions
along on êν which’out’ displacements
dependingwith
Jσi ,σj = J[1 + δ(r̂ij · σi + (−r̂ij ) · σj )] (δ > 0),(2)
The 1st term of Eq. (1) describes the exchange interaction between the spins on thenearest-neighbour sites < i, j > on the pyrhoclore lattice. The exchange interaction Eq. (2)between the spins on the i-th and j-th Mo ions,with the energey scale J(> 0), is mediated by
the O ion and depends on the angle α of the
Mo-O-Mo bond. (see Fig. 1 (b)(c)) Thus theexchange interaction depends on the displacements σi and σj of the Mo ions. This form
is constructed in a way to reproduce the values of the effective interactions derived microscopically from the perturbation process on a
Kanamori-type of Hamiltonian [1, 2]. Moreprecisely we parametrize it as Jσi ,σj = (1 +2δ̃)J (in, in),
√ J (in, out), (1 − 2δ̃)J (out, out),
where δ̃ = 6δ/3.
The 2nd term of Eq. (1) represents the elastic energy of the Mo4+ displacements. The
elastic energy is minimized if the ice-rule is satisfied.
There are three parameters in this system;T̃ = kB T /J is the dimensionless temperature,˜ = /3J the ratio of the energy scales between
the exchange interaction and the elastic energy

is a unit vector in the [111], [11̄1̄], [1̄11̄] andonsider extended networks made of such simplexes,
suchdirections
as the triangularlattice, kagomé[1̄1̄1]
respectively
for the sub-lattices
hlore lattice with antiferromagnetic coupling on the edges (See Fig. 1.7 (b)). The important
ν
=
1,
2,
3,
4
which
the
i-th
spin
belongs to (Sees that they are corner sharing: adjacent simplexes are connected to each other only throughFig. 1.(b)). The microscopic mechanism of thepeculiar displacements is presumably a JahnTeller effect: the displacements break the 3fold rotational symmetry of the trigonal crystal
field for the Mo ions resulting in the splittingof its eg orbital [3]. Thus we regard σi as thevariable which represents the configuration of
the orbital of the Mo ion.
Our effective model for the pyrhoclore magnet Y2 Mo2 O7 is given by the following effective
Hamiltonian,

H=



<ij>

Jσi ,σj Si · Sj − 



<ij>

σi · σj ( > 0)(1)

37

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
2.5. COMPLEX ENERGY LANDSCAPE OF OUR EFFECTIVE MODEL

65 ENERGY LANDSCAPE OF OUR EFFECTIVE MODEL
2.5. COMPLEX

2.5. COMPLEX ENERGY LANDSCAPE OF OUR EFFECTIVE MODEL

65

65

√
of decoupled
the displacement,
6δ/3ouris theam- is decoupled into (1)= 0. Then our system is
into (1)and= δ̃0.=
Then
system(a)is decoupled
(a)
=
0.
Then
our
systeminto
plitude of the displacement
call(1)(a)the spin part with purely antiferromagnetic
in-the spin(hereafterpart with wepurelyantiferromagnetic
ina)
the
spin
part
with
purelyantiferromagnetic
insimplypart
as T,with, δ). At  →[26,∞, 27]
the andlattice the orbital part withteractions [26, 27] and (2) themthe orbital
teractions [26, 27]teractionsand (2) the orbital
part (2)withdistortion
becomesstatic.
pure ’spin-ice’ type interaction
[31,
32].
Both
pure
’spin-ice’
typeinteraction[31, 32]. Bothpure ’spin-ice’ type interaction [31, 32]. Bothof them have essentially flatFinallyenergylandscape
let
us
note
what
happensif
weswitchofthem
have
essentiallyflatenergylandscapeof them have essentially flat energy landscapethecoupling
between
the
spins
and
orbitalsso that the two degrees ofoff
freedomremaindisso thatofthe
two degrees
of freedom remain disso that the two degrees
freedomremain disdisplacements)
δ=
Then ourordered down to T = 0. (latticeordereddown to T=
0. 0. downorderedto Tsystem= 0.
is decoupled into (1) the spin part with purely
antiferromagnetic interactions [26, 27] and (2)b)c)
3 Simulation
3 Simulation Methods
Simulation
Methods
the orbital(lattice) 3
partMethods
withpure ’spin-ice’(c)(b)(c) (b)(b)(c)
typeIninteraction[30, 31].simulations
Both of them
have esorder
toperforminequilbrium
In order to perform simulations
inflatequilbrium
In order tosoperform
in equilbrium
sentiallyenergythat the simulations
twoourwe
combinedthelandscapefollowing methodsin
we combined the following
methods
inourwecombinedthefollowing
methods
in ourdegrees of freedom
remain disordered down to
Carlo simulations.
Monte Carlo simulations. T = Monte
Monte Carlo simulations.
0.Single spin update:
The usual single spin
Single spin update: The usual single spin Single spin update: The usual single spin
updates by the conventional Metropolis algoupdates by the conventional Metropolis algo-updates by the conventional Metropolis algorithm is employed to update the Ising variables
rithm is employed to update the Ising
variablesrithm is employed to update
theFigure2.14: Ising
Complex variables
energy landscape of our e ective modeli = ±1 (i = 1, 2, . . . , N ).
Schematic picture of the energy landscape of our e↵ective model (right) obtained by combining a flat spin
Figure2.14: Complex energy landscape of our(a):e ective
model
3
Simulation
Methods
Figure2.14: distortion
Complexenergy(leftlandscapee ective
=
±1
(i
=
1,
2,
.
.
.
,
N
).
energylandscape
(left
top)
and a zigzag but
degeneratelandscapebottom). of(b):our
Systemsize modeli= ±1picture(iWe=
1,energy
2, adopted.landscape. . , Nof).ourae↵ective model (right) obtained
Loop update (a):method:alsoi Schematicof theby combining
a flat spin
Schematicof theenergydi↵erent
landscapeof oure↵ective
the fluctuation
ofpicture
the energy
betweenenergyminimawith model (right) obtained by combining a flat spin
L dependence of V (E) which quantifies (a):energylandscape
(left
top)
and
a
zigzagbut
degeneratedistortion
landscape(leftbottom).
(b):
Systemsize
energylandscape
(left
top)
and
a
zigzagbut
degeneratedistortion
landscape (left bottom). (b): System size
Loop update method: We
also adopted
aL dependence(E) which quantifies fluctuation
a commonlattice-ice configuration.
(c): Systemsize L dependence of V
Loop
method:We
adoptedaLconfigurations.
nonlocalupdate method
calledupdate(E)thewhichloop
quantifies
the fluctuation
the also
energybetweendi↵erent
energyminima withof Vupdateof theof
energybetweendi↵erencelattice-ice
which quantifies
the fluctuation of the energy between di↵erent energy minima withdependenceof V (E)(a):Figure2:
Energylandscape.
Schematic
Figure2:
Energylandscape.
(a):
Schematic(E)
whichquantifies
fluctuationacommonlattice-ice
configuration.
(c):
Systemsize
LdependenceofV(E) which quantifies fluctuation
a common lattice-ice configuration. (c): System size L dependence of V
nonlocal update method called
the loop
updateIn orderto perform
simulationsinequilibalgorithm,
used tosimulate
spin-ice
systems
nonlocalupdatemethodcalledpicture
the loopof the energy
betweendi↵erencelattice-ice configurations.
Figure2:
Energylandscape.
(a):
Schematicof updateenergyTheessentiallyoflandscape.
the energy
between2:
di↵erencelattice-ice
configurations.
FigureEnergylandscape. (a): Schematic
pictureofenergylandscape.
Theessenalgorithm, used to simulate
spin-ice
systems. simulate
updatetheIsingvariables
rium,[33],wetocombined
thefollowingin
itoalgorithm,
usedspin-ice
systems
flat
energylandscapeof the (withspins(left/top)
pictureof methods
energylandscape.
Theenergy
essentially
pictureofenergylandscape.
The essentiallytiallyflat
landscapesmany
enMonteCarloreflection
method:Toupour MonteCarlosimulations.
.
[33], to update the Ising variablesi.
[33],flat
to updatetheIsingvariablesiandorbitals(left/bottom)
intheabsenceof of the spins (left/top)energy landscape ofergeticallythe spinsdegenerate(left/top)flat
energylandscapeminima)
of
the
spins
(i =single
1, 2,. .spin. , N ), method:date theHeisenberg
spins
Susuali CarloMonte Carlo reflectionSingle
method:To
up- Monte
reflection
To upspin
update:The orbitals
theincoupling= 0 changes
into complex
oneand(left/bottom)
theandabsenceorbitals(left/bottom)
in the absence of(left/top)orbitalsofand(left/bottom)
in the abweused
thesinglespin
updatesbythe
1, 2,the. . . conventional, N ),datethe
date the Heisenberg spinsupdates
Si (i = by
Metropolisinthepresenceofthecopling(right).
(b),(c)
(i
=
1,
2,
.
.
.
,
N
),
thecoupling
Heisenberg=algospinsSi
0 changes
complexonechanges into complex one
senceintoof thecoupling
δthe= 0couplingchange into=a 0comMetropolisbyreflection
method [34].
we used the single spin
updatesvarianceofby
the theenergybetween di↵erent energyrithm
is employedthe
forwetheIsingvariables
σi the=used
thesinglespincopling
updatesinthepresenceof(right).
(b),(c)inthepresenceofthe
one in the presence of the coupling δ > 0copling (right). (b),(c)Over relaxation method: We also used plex
minimaobtained by quench experiments (seeMetropolis reflection method±1 (i[34].
= 1, 2, . . . , N ). Metropolis
reflection
method[34].
energydi↵erent
energyvarianceof the energy
the over relaxation variancemethod ofto theupdatethebetween(right).
(b),(c)varianceof the energy
betweenbetween di↵erent energy
textfor
details).
Over relaxation method:We
also usedOver
method:Wealso usedLoop
updatemethod:Werelaxation
also
adopteda quenchminimaobtainedbyexperiments(seeminima
Heisenberg
spins.
[35]
differentenergyminimaobtainedby quenchobtainedby quench experiments (seethe over relaxation method
toupdateexchange
thethe text
over
relaxation
methodto
updatethenonlocalupdatemethodcalledthe
loop
updateReplicamethod:
On
top
of
the
for details).
experiments (taken fromtext[2])for details).
Heisenberg spins. [35]Heisenberg
spins.systems[35]
algorithm,
used to we
simulate
spin-ice
above methods
used thereplicaexchange
Replica exchange method:
top
oftothe[32], method
to On
for thevariables
σi .exchange
Replicamethod:On top of the[36]Isingacceleratetheequilbrationofabove methods we used theMontereplicaexchange
4
Results
above
methods
weusedthereplicaexchange
the system.
Carlo reflection method: For the
method [36] to accelerateHeisenberg
the equilbrationofmethodto),accelerate= 1, 2, [36]...,N
we used the equilbration of
spins Si (i1st term of the Hamiltonian Eq. (1) by zero
the system.
thesystem.
the single
spin
updatesbytheMetropolisre- 4.1 A simple analysis of the energy
4 Results
temperature, greedy Monte Carlo updates oflandscapeflection method [33].
the spins.
procedure
ob1st
term
of
the
Hamiltonian
Eq. (1)Repeatingby zero1stthis
termof the we
Hamiltonian
Eq. (1) by zero
4.1
A
simpleanalysisoftheenergyOver-relaxation
method:
We
also
used
taineda largenumberofenergyminimaofvar4 Results
4
ResultsAs
wementioned
at
the
end
of
sec.
2,
the
entemperature,
greedyMonteCarloupdatesoftemperature, greedy Monte Carlo updates oflandscapemethod to update thethe over-relaxation
ious
energies E.
Fig.
2 (b)becomes
we display
theergy
landscapeof In
oursystemessenthe spins. Repeating thisprocedure
weobthe
spins. Repeating
2i
2 this procedure we obHeisenberg
spins.
[34]
varianceoftheenergy
V
(E)
=
h
E
h
Ei
4.1 A simple analysisoftheenergyspin
Aof theenergyAs we mentioned4.1
in theendsimple
sec. number
2,analysis
the en-oftiallyflat(with ofmany
energeticallydegenertained
aoflarge
energyminimavar-tained
a large number of energy minima of varbetweendi↵erentof thespins withlandscapeReplicaexchangemethod:On
top
theFig.ate
ergy landscapeof oursystembecomesessenlandscapeminima)if we realizations
switchthecoupling
ious
energies
E.of In2 (b)we display
theiousoff
energies
E. In beFig. 2 (b) we display theacommonspin-icelike
orbitalconfiguration
tiallyflat if weo↵coupling between tween the spins
above
methods
weswitch
usedvariancethethereplica-exchange
2 i and2
orbitals(lattice
displace2
oftheenergy
V
(E)
=
h
E
h
Ei
varianceof theh Ei 2spin
As we mentioned in the end of
2, theorbital
en-As degrees
wethe
mentionedin theofsec. 2, overthe en(averageddi↵erent
realizationsof energy
such or-Vspin (E) = h E ithesec.
spinof freedom=
0. ments)
method[35] andto accelerate
equilibrationof end
,
i.
e.
δ
=
0.
Here
let
us
show
the
rebetween di↵erentof thespins
betweenthe
di↵erentof the spins withergy landscape of our system
becomesessen-aergy
bitals).
Hereh . . .iwith
represent
averagerealizations
overourrealizations
systembecomesessenHereletus show
resultlandscapeof a simpleofquench
ex- sult
the wholesystem.
of a simple
quencha experiment
which
proa
commonspin-icelike
orbitalconfiguration
spin-ice
like orbital configuration
tially flat if we switch o↵ the couplingdi↵erent realizations
the spins witha comtially
flatinsight
if we switch
the coupling
between of common
perimentsbetween
obtainsome
on howo↵the
vides
some
insights
on(averaged
howandthe .overenergyland- realizations of such orWe
considertothe
periodic
systems
ofdi↵erent
cubic realizations(averaged
over
of
such
ordi↵erentmonorbitalconfiguration.
.
represents
the spin and orbital degrees ofenergy
freedom= 0.thespin
orbital degrees
landscapechanges
inand
the presenceof the of freedom = 0.
3 unitscapechangesin thepresenceoftheh .coupling
cells
with
togeometry consisting of L
bitals).
Here
h
.
.
.i
represent
averagethe theaverageovber
di↵erent
thebitals).realizations
Here. .iof represent
the average over
Here let us show a result of a simple
quenchexcoupling.
First
wegenerated’spin-ice’configHere
let
us
show
a
resultof a simple
quenchex-over3> spins
0. First
wegenerated’spin-ice’configtally N = 16L spins, andperform
120 sta- of δtheorbitals.
In
(c)
we
show
the
correspondingdi↵erent
realizations
withacomdi↵erent
realizations
of
the
spins
with a comurationsof’srandomly.
Note
that
any
of
periments to obtain some insight on how i theperiments to obtain some insight on how theofσrepresents’s randomly.
Note between
that anydifof
tistically independent runs
fororbital
the systemsize urations
ionetomeasurethefluctuationmonconfiguration
and
.
.
.
them
minimizethe
2nd termof thechanges
Hamiltomon orbital configuration and . . . represents
energy landscape changes in thepresenceof theenergylandscapein themthe presenceof theminimizesthe
2ndterm of the
HamiltoL =nian
4, 5,
6, 8,
evaluating
theaveragesandferentrelizations
ofthe
the
=
Eq.
(1).
Second,we
performedasimpletheaverageovber
di↵erent
realizationsofthe orbitals
averageVlatticeovber(E)di↵erent
realizations of thecoupling. First we generated’spin-ice’ configcoupling.
FirstInwethe
generated’spin-ice’config2 Second, we performed a simple
nian
Eq.
(1).
mean-squared
errorsofobservable.
fol2
energydescent
simulation
withrespect
to
the
i
h
Ei
h
E
orbitals.
In
(c)
we
show
the
corresponding
In (c) we show the corresponding
urations of i ’s randomly.lowing
Noteanalysis,that anyurationsfocus
of ion’s randomly.
Note thatanysimulationof orbitals.
descent
with respect to theweofmainly
a repre- energyonetomeasurethefluctuation
betweendifonetomeasurethe fluctuation between difthem minimize the 2nd termof theHamiltothe of
Hamilto1stofterm
the Hamiltonian Eq. (1) by zerosentative
systemat δthem= 1.5,minimize
 = 0.6. the 2nd term
4
relizations
ofwe
theperformed
orbitals Valattice(E) =ferent relizations of the orbitals Vlattice (E) =nian Eq. (1). Second, we performed a simplenianferent
Eq. (1).
Second,simple222energy descent simulation with respect to theenergyh E i descenth Ei simulation with respect to the h E 2 i
h Ei
spin

lattice

spin

spin

lattice

438

lattice4Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

78

CHAPTER 3. NUMERICAL SIMULATION

temperature, greedy Monte Carlo updates ofthe spins with orbitals σi being fixed. Repeating this procedure we obtained a large numberof energy minima of various energies E. In
Fig. 2 (b) we display the variance of the energy Vspin (E) = E 2  − E2 between different
realizations of the spins with a common orbital(lattice) configuration (averaged over different
realizations of such orbitals). Here . . . represents the average over different realizations of
the spins with a common orbital (lattice) configuration and . . . the average over different realizations of the orbitals. In Fig. 2 (c) we show
the corresponding one to measure the fluctuation between different realizations of the or2
bitals (lattice) Vlattice (E) = E 2  − E . Both(b) and (c) show that the variance grows withthe system size L suggesting lugged, complex
energy landscape.

4.2

(a)

C (t)

(c)

(d)

⌧

⌧s

Cs (t)

(b)

T

Tc

T

Tc

(f)

C̃ (t/⌧ )C̃s (t/⌧s )(e)

Critical slowing down without
long-ranged ordering
Figure 3.4: Relaxation of spins and distortions for L = 6, ✏ = 0.6(a): Spin auto-correlation function. (b): Orbital auto-correlation function. (c): Typical relaxation timeof spins. (d): Typical relaxation time of distortions. The black solid lines in the figure (b) and (d) deBy lowering the temperature we observed that
note the fits by ⌧ = A(TT)
with (A, T , z⌫) = (3.99(89), 0.0695(19), 2.79(12)) and (A, T , z⌫) =Figure3.55(4))
3: Autocorrelation
functionsand plots
relax(4.27(31),by using the least squares method.
(e), (f): Scalingof auto-correlation
the dynamics of both the spins and orbitals 0.0686(5),functions using their relaxation times. The solid lines represent the exponential fits.
ations
times
of
the
spins
and
orbitals.
L=
6,(lattice displacements) slow down significantly.
In Fig. 3 (a)-(b) we display the time autocorre-  = 0.6. (taken from [1])lation functions of the spins Cs (t) and orbitals
Cσ (t) plotted against time t. Here we used ing. Some pinch points can be seen in Sσ ,’single spin updates’ for the spins and orbitals for example at (1/2, 1/2, 1/2), at low temperto measure the dynamical observables, start- atures as well known in spin-ice systems [31].
ing from the initial configurations equilibrated
To summarize the above observations sugusing all protocols listed in sec 3. As shown in gests a simultaneous, 2nd order glass transi(c)-(d), the relaxation times grow in lowering tions of the spins and orbitals (lattice displacethe temperature following a power law. The ments) at a common temperature, into a new
independent power-law fits on the two observ- glass phase - spin-orbital glass phase, whichables suggest a common critical temperature emerges directly from the high temperature
Tc ∼ 0.07 with different exponents zν ∼ 4.2 paramagnetic (liquid) phase.
(orbital) and zν ∼ 3.5 (spin). As shown in (e)(f) the auto-correlation functions follow scaling
4.3 Non-linear susceptibilities
laws in terms of scaled times. We have checkedthat finite-size effects of the auto-correlation The signatures of the spin-orbital glass can befunction is negligible within the temperature detected by observing non-linear susceptibiliand time scales shown in the Figure. We have ties of the two degrees of freedom. As shown
found that the same type of scaling holds for in Fig. 5, the non-linear susceptibilities com = 0.65, with Tc ∼ 0.086 and almost the same puted using fluctuation formulae (see [1] forexponents as obtained above [2, 3].
the details) at lower temperatures grow negaAs shown in Fig. 4, the structure factor tively rapidly when increasing the system sizeof the spins Ss and orbitals (lattice displace- L. This observation provides an interestingments) Sσ show no hints of long-range order- suggestion for experiments: by observing not
c

39

z⌫

c

s

c

3.4. SIMULATION RESULTS

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

84

87

CHAPTER 3. NUMERICAL SIMULATION

(a)

(a) 1

(b)

0.016

( )
3

0.014
0.012

3

0.5

0.01
0

0.008
0.006

-0.5

0.004
0.002

-1
1

0
0.025

(b)

T

T
(c)

0.02

0.5

(d)

0.015
0

-1
-1

| 3|

0.005
-0.5

0

0.5

1

-1

-0.5

0

0.5

1

( )
3

0.01
-0.5

0

(c)

T

T

Figure 3.12: Magnetic and dielectric nonlinear susceptibilities at ✏ = 0.6(a), (b): Size dependence of magnetic and dielectric nonlinear susceptibilities. The dashed line represents
the freezing temperature Tc ⇡ 0.07 determined by the auto-correlation function. (c), (d): logarithmic scaleof the absolute values of the nonlinear susceptibilities.

Figure 5: Non-linear susceptibilities of thespins and orbitals (lattice displacements).  =0.6. Panels (a),(c) display the non-linear susceptibilities of the spin while (b),(d)display
the non-linear susceptibilities of the lattice displacements (orbitals). (taken from [1])(d)Figure 3.9: Structure factors for L = 6, ✏ = 0.6 above Tc (T = 0.4) in the left side and below Tc(T = 0.0625) in the right side(1)(a) and (b) show the spin structure factor Ss (0, h, l) and the orbital structure factor S (0, h, l), respectively.
(2)(c) and (d) show the spin structure factor Ss (h, h, l) and the orbital structure factor S (h, h, l), respectively.

ventional type, i. e. the one due to quencheddisorder, may take place at a lower temperature.
To get some insight into this issue within
the available computational resources, we analyzed the heat capacity C and the fraction Pof the tetrahedra which satisfies the ice ruleat various values of . At  = 0.6, 0.65, forwhich we have determined the critical temperature of the spin-orbital glass transition, we
found that the heat-capacity exhibit a peak atslightly higher temperatures, similarly to thecase of the conventional spin-glasses [4] andthe experimental result in the Y2 Mo2 O7 system [36]. We have checked that the finite-size
effects of the heat capacity are very weak [1]).
As shown in Fig. 6, the heat-capacity exhibit
an additional peak at a higher temperature atlarger values of  > 1.0. The peak at thehigher temperatures appears to follow the peakof dP/dT . This observation suggests that atlarger values of , the liquid state of the lattice
distortions exhibits a smooth crossover frompurely random one to more spin-ice like one
at higher temperatures. On the other hand,the other peak of the heat capacity located at

Figure 4: Heat maps of the structure factorsof the spins and lattice displacements. L = 6,
 = 0.6 above Tc (T = 0.4) in the left side andbelow Tc (T = 0.0625) in the right side. (takenfrom [1])only the usual magnetic non-linear susceptibility, which is used often to study conventional spin-glasses [4, 6, 7], but also dielectric non-linear susceptibility, the simultaneous
spin-orbital glass transitions suggested by thepresent work may be detected experimentally.

4.4

Static or dynamic distortions?

In our study we regard the lattice distortions (orbitals) as dynamical degrees of freedom rather than as frozen-in, static quencheddisorder. But by increasing the energy scale ofthe lattice displacements given by the parameter  in Eq. (1), one would wonder whether thelattice displacements can freeze independently
from the spins at higher temperatures. If thishappens, the spin-glass transitions of a con-

40

86

CHAPTER 3. NUMERICAL SIMULATION

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a) 1.7

1.5

C 1.4

1

(b)

¡=0.60¡=0.65¡=0.70¡=0.80¡=1.00¡=1.20

1.6

P

0.8

1.3

0.7

1.2

0.6

1.1

0.5
0.1

(d)

1.6
1.5
1.4

0.15

0.2

0.25

¡=0.60¡=0.65¡=0.70¡=0.80¡=1.00¡=1.200.1

0.3

T¡=0.60¡=0.80¡=1.00¡=1.20

(c)

0.9

0.15

(e)

0.2

0.25

0.3

T

1

T
(f)

0.9
0.8

C 1.3

P 0.7

1.2

0.6

1.1

0.5

1

0.4

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8¡=0.60¡=0.80¡=1.00¡=1.200.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8

T

T

T

Figure 3.11: ✏ dependence of heat capacity and fraction of 2-in-2-out structures for L = 5(a): Heat capacity in the narrow range of T = 0.0625 to T = 0.3. (b): Fraction of 2-in-2-out structures in
the narrow range of T = 0.0625 to T = 0.3. (c): Incremental di↵erences of fractions of 2-in-2-out structuresin the narrow range of T = 0.0625 to T = 0.3. (d): Heat capacity in the wide range of T = 0.0625 to T = 0.8.
(e): Fraction of 2-in-2-out structures in the wide range of T = 0.0625 to T = 0.8. (f): Incremental di↵erencesof fractions of 2-in-2-out structures for ✏ = 1.0, 1.2 in the wide range of T = 0.0625 to T = 0.8.

Figure 6: Heat capcity C and fraction P of tetrahedra which satisfy the ice-rule. L = 5. (a)-(c)for 0 < T < 0.3 (d)-(f) for a wider temperature range 0 < T < 0.8. (taken from [1])the lower temperatures tend to saturate to a
finite temperature T ∼ 0.16 by increasing .
Very importantly we confirmed that the orbital
degrees of freedom remain dynamically fluctuating between the intermediate temperatures
between the higher and lower peak temperatures of the heat-capacity [2, 3]. This meansthat the orbitals do not produce the putative
static quenched disorder for spins but remain
dynamical. We consider that the spin and orbital degrees of freedom interact cooperatively
at the energy scale corresponding to the lower
peak temperature and exhibit the simultaneous glass transition at that energy scale.

The criticality of the spin-orbital glass transition and its universality, consistency with theexperimental results [19, 20, 25], should be examined by approaching more closer to the critical temperatures.
Acknowledgments This work was supported by KAKENHI (No.
19H01812,
17K05533,
17K05497,18H01173,17H02916)
from MEXT, Japan. The computation in thiswork has been done using system B of theSupercomputer Center, the Institute for Solid
State Physics, the University of Tokyo.

5[1] Kota Mitsumoto, Chisa Hotta, and Hajime Yoshino. Physical Review Letters,
124(8):087201, 2020.

References

Summary and Outlook

To summarize we constructed a theoretical model to describe the spontaneous glasstransition observed in the pyrochlore oxide
Y2 Mo2 O7 and performed extensive Monte
Carlo simulations of the model. Our results
strongly suggest a new type of glass transition- spin-orbital glass transition.
There are numerous possibilities for further
works. Exploration of the parameter space,especially along the -axis, should be done
to clarify to what extent our present scenario
holds. Construction of a mean-field theory [37]would provide a useful guideline in this respect.

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294(5546):1495–1501, 2001.

[16] J. G. Kirkwood. in in Phase Transitions
in Solids, edited by R. Smoluchowski, J.
E. Mayer, and A. Weyl (Wiley, New
York, 1951).

[32] Roger G Melko, Byron C den Hertog, andMichel JP Gingras. Physical review letters, 87(6):067203, 2001.

[15] Hajime Yoshino.
2018.

[33] S Große Pawig and K Pinn. International
Journal of Modern Physics C, 9(05):727–
736, 1998.

[17] Leticia F Cugliandolo, Laura Foini, andMarco Tarzia.
Physical Review B,
101(14):144413, 2020.

[34] JL Alonso and et al. Physical Review B,
53:2537–2545, 1996.

[18] Gilles Tarjus, Steven A Kivelson, Z Nussinov, and Pascal Viot. Journal of Physics:
Condensed Matter, 17(50):R1143, 2005.

[35] K Hukushima and K Nemoto. Journal of
the Physical Society of Japan, 65(6):1604–
1608, 1996.

[19] MJP Gingras, CV Stager, BD Gaulin,
NP Raju, and JE Greedan. Journal of
applied physics, 79(8):6170–6172, 1996.

[36] NP Raju, E Gmelin, and RK Kremer.
Physical Review B, 46(9):5405, 1992.
[37] Kota Mitsumoto and Hajime Yoshino. in
preparation.

[20] MJP Gingras, CV Stager, NP Raju,
BD Gaulin, and JE Greedan. Physical review letters, 78(5):947, 1997.

42

3.2

First-Principles Calculationof Material Properties

43

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Mechanisms of Semiconductor Interface Formation and its Electronic
Properties based on Quantum Theory
Atsushi Oshiyama
Institute of Materials and Systems for Sustainability, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8601
in

In the fiscal year of 2019, on the basis of thethefabricationofelectronic

devices.

total-energy electronic-structure calculations andUnderstanding of bond configurations near themolecular

step on the atomistic level is necessary in order todynamics

simulations

within thedensity-functional theory, we have studied atom-

identify thereactivity at

the

step

edges.

scale behavior during the epitaxial growth ofFurthermore, epitaxial graphene can be prepared

power semiconductors, silicon carbide (SiC) andon SiC surfaces, and the surface steps of SiC also

gallium nitride (GaN). The main computa tional

play an important role. Hence, it is certainly

tools are our RSDFT (Real Space Density

important and inevitable from both science andFunctional Theory) code and RS-CPMD (Car-technology viewpoints to identify the atomic steps

Parrinello Molecular Dynamics) code. We haveon SiC and clarify their energetics, that has notclarified 1) the structures and energetics, and thenbeen achieved yet. Our previous calculations [6]the morphology of SiC surface steps [1,2], 2) theshow that the single-bilayer height steps are

liquid-like behavior of the topmost Ga atoms [3]and 3) the mechanism of oxygen incorporation
during the epitaxial growth of GaN [4,5]. The
group identification codes for the achievements
above are k0042 and m0001. Below, I explain theissues 1) and 2).

1. Step structures and morphology of Siface SiC Polar Surface
SiC is now emerging as a promising material
for power electronics. This is due to its physicalFig.1: Schematic view of the five distinct
mono-bilayer steps on SiC (0001) surface. Si
and C atoms are represented by the larger(blue) and smaller (brown) balls, respectively.
The Si2, Si3, C1 and C2 steps along the ⟨1120⟩ direction and the SC step along the ⟨1100⟩ direction are shown all together.

properties superior to Si, a current premiermaterial, such as the wider band gap and thehigher electric break-down voltage. The thin-film
growth of SiC in the step-flow mode is essential

44Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

energetically favorable compared with higher

for 5 distinct steps as a function of Si chemical

steps on SiC(0001) or (111) surface.

potential (Near step edges, the numbers of Si and

Figure 1 shows schematic view of 5 distinct

C atoms are different so that we need thesingle-bilayer height steps. There are two

chemical potential). We have found that Si2 stepdifferent classes of steps: One is [11-20] oriented

toward [1-100] is the most stable and Si3 stepand the other is the [1-100] oriented; further in thefollows.

latter, four different step edges exit which arecomparable with the Si3 step.

The

SC

step

toward[11-20]islabelled by the atomic species at the edge and the

The energetics obtained above predicts somenumber of the dangling bonds before theinteresting morphology of atomic steps on

structural relaxation as Si2, Si3, C1 and C2.

SiC(0001). Experimentally, the (0001) surface isstructuralslightly inclined along either [1-100] or [11-20]

optimization for all the possible atomic steps anddirection. When it is inclined along the [1-100],

determined their structures. Near step edges wethe surface consists of the [0001] terrace andhave found prominent rebonding between theseveral steps among Si2, Si3, C1 and C2, whereas

upper-terrace and the lower terrace Si atoms in

it consists of the terrace and SC steps when

Si2 and SC steps and also a peculiar resonant-likeinclined along [11-20]. In the former, the Si2 orrebonds for Si3 steps, as well as the C

Si3 steps are energetically favorable (Fig. 2).

dimerization for the C2 step.

However, in the latter, the SC step is energetically

We

have

performed

detailed

unfavorable compared with Si2 and also Si3 in

Figure 2 shows calculated formation energies

some range of the Si chemical potential. Hence
we expect that the steps toward [11-20] show zigzag shape consisting of, for instance, Si2 and Si3.
We have indeed found that such zizgzag-shaped
step-edge pairs of Si2 +Si3 is lower in theformation energy than the straight-shape SC stepon the [0001] surface inclined along [11-20]
direction.

2. Two-DimensionalGaliquidon

growing GaN surface
Fig. 2: Calculated formation energies ofthe mono-bilayer atomic steps on
SiC(0001) surface as a function of the Si
chemical potential μSi, measured fromthat in crystalline Si, μSi(bulk). Shaded
areas surrounded by each pair of solidlines represent the uncertainty in thecalculated formation energy.

GaN, a fundamental material worldwide used
for high performing opto-electronic devices, israpidly becoming another candidate to unseat Si
in

45

power

electronics.

Yet,

their

practical

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

realization asks for the realization of thin epitaxial

temperature, the top-layer Ga atoms get together

films of higher quality with respect to what isand exhibit the peak at much shorter distance,

done nowadays for optoelectronic applications. It

indicating some condensed phase of Ga.
By

is thus highly demanded to clarify the nature ofusing

Kubo-formula(velocity-velocity

correlation function), we have computed thethe growing GaN surface at atomistic level.
It is known that under typical conditions of the

diffusion coefficient of the top-layer Ga atom. We

epitaxial growth of GaN, the surface is Ga-rich.

have found that the diffusion coefficient jumps at

Hence we prepare Ga-rich surface and raise the1300 K from its value of 0.382 x 10-5 cm2/s attemperature by CPMD simulations from room

1100 K to the value of 0.492 x 10-4 cm2/s. We thus

temperature. We have found that, when the

conclude that this condensed phase is not a solid

temperature

growthphase but a two-dimensional liquid phase. This istemperature, i.e., 1300 K, the topmost Ga atom

corroborated by the absence of the peaks except

suddenly moves from their original position. The

for the first peak at 1300 K in Fig. 3. The notion

calculated Ga-Ga pair correlation function isthat the GaN surface during the epitaxial growth

shown in Fig. 3. At room temperature, the top-

is 2-diemnsional liquid is unrecognized in the past

layer Ga atoms vibrate around their original

and important to consider mechanism of thepositions. The pair correlation function shows aepitaxial growth.

peak determined by the Ga coverage. Then withRelated Publications

increasing temperature,[1] K. Seino and A. Oshiyama, Appl. Phys. Exp.

reachesthethetypicalpair correlation

function shows the peak at the same position with

13, 015506 (2020).

increasing peak width, showing the enhanced[2] K. Seino and A. Oshiyama, Phys. Rev. B

thermal vibration. However, at the growth(2020) to be published.
[3] K. M. Bui, M. Boero, K. Shiraishi and A.
Oshiyama, Jpn. J. Appl. Phys. 59, SGGK04(2020).
[4] F. Shintaku et al., Appl. Phys. Exp., 13,055507 (2020)[5] D. Yosho et al., Phys. Sta. Solidi - Rapid Res.
Lett. 2000142 (2020).
[6] K. Sawada, J.-I. Iwata, a. Oshiyama, Appl.
Phys. Lett. 104, 051605 (2014).

Fig. 3: Evolution of the Ga-Ga pair correlation function in the top-layer of GaN during
the heating process. The initial distance of 6.4
Å corresponds to the relaxed system fromwhich dynamical simulations were started.

46

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analyses on electronic structure and magnetic property inhigh-performance spintronics and magnetic materials
Tatsuki ODA1,2, Indra PARDEDE1,2, Afrioni Roma RIO2, Achmad Maulana GANI2,
Daiki YOSHIKAWA2, Tomosato KANAGAWA2, Hasan Al RASYID2, Masao OBATA1,2
1

Institute of Science and Engineering, Kanazawa University, Kanazawa, Ishikawa 920-1192
2

Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa,
Ishikawa, 920-1192

Magnetic anisotropy calculation.

with

an

available

experimental

We have developed a computational

measurement, as shown in Fig.1. Thismethod of magnetic anisotropy energy

agreement implies that our method is(MAE) using the noncollinear spin

promising on the estimation of MAE.

density functional theory (NC-SDFT).

We have established a calculation

This method enables us to estimate themethod of MCAE in the same time. The

MAE including both contributions to the

MCAE part was evaluated from both

MAE from magnetocrystalline anisotropy

methods of total energy (TE) and grand-

energy (MCAE) originating from spin-

canonical force theorem (GCFT) [1]. All

orbit coupling and the shape magnetic

MCAE values from the TE were wellanisotropy energy (SMAE) originating

reproduced by those from the GCFT

from spin dipole-dipole interaction [1]. In

method. The advantage of GCFT methodtheover the TE method makes analysis of thecalculation

of

SMAE,

the

contribution was estimated from the spin

atom-resolved

density distribution that is obtained in thecontributions of MCAE. In Fig.2, one can

NC-SDFT. One can expect an accurate

easily recognize the portions of large

SMAE. Indeed, we have found some

contribution to MCAE. Such figure cancorrections on SMAE coming from thebe compared with the orbital-resolved

quadrupole component of atomic spincomponent of band dispersion curves. As

density [2,3].

a result, the MCAE is deeply understood,

We applied the method to the freestanding

Co/Ni(111)multilayer

andk-resolved

combined with its anisotropy of orbitalthatcomponents. The atom-revolved MCAE

indicates a perpendicular anisotropy [1].

is also very useful to understand the

The results indicated a good agreement

atom/layer alignment giving rise to large

47

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 1. MAE in Co/Ni multilayer structure
as num. of multilayer.

MCAEs. In the application of Co/Ni(111),

Fig. 2 k-resolved MCAE in Co/Ni(111)multilayer structure.

we recognized that the Co/Ni interface
makes a large perpendicular magnetic

Other contributions.

anisotropy.

We have developed a noncollinear
spin version of van der Waals density

NC-SDFT under magnetic field.

functional scheme [5]. We have also

We implemented a density functional

contributed a theoretical part of thescheme which enables application of a

spintronics application in the system of

uniform external magnetic field. In theinterfacial

implementation, the rotation of the

PtCoO/ZnO [6].

magnetic

anisotropyofmagnetic moment on an atom wasdescribed using the NC-SDFT calculation.

References.

The[1] I. Pardede et al.: J. Magn. Magn. Mater. 500

newschemewassuccessfully

applied to a ferromagnetic slab with a(2020) 166357.

perpendicular magnetic anisotropy and an[2] T. Oda and M. Obata: J. Phys. Soc. Jpn. 87

antiferromagnetic material [4]. These(2018) 064803.

results were discussed along with thesimplemodel.

This

approach[3] T. Oda et al.: IEEE Trans. Magn. 55 (2018)may

1300104.

provide a useful tool in analyzing[4] A. R. Rio et al.: J. Phys. Soc. Jpn. 89 (2020)

magnetic properties of materials. In the

035002.

scheme, the Kohn–Sham equation was
solvedself-consistently

with[5] M. Christivana et al.: J. Phys. Soc. Jpn. 55

the(2019) 104601.

noncollinear spin density in the system.

[6] M. Al-Mahdawi et al.: Phys. Rev. B 100(2019) 054423.

48

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio optimization of 4f -3d intermetallic
ferromagnets for permanent magnets
Munehisa Matsumoto
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581
andInstitute of Materials Structure Science, High Energy Accelerator Research Organization
Oho 1-1, Tsukuba, Ibaraki 305-0801
April 30, 2020

Today’s main-stream commercial permanent
magnets are made of sintered Nd-Fe-B alloys [1], or rapidly quenched alloys with analogous ingredients [2] that is fabricated into hotdeformed magnets. Their main-phase compound is a 4f -3d intermetallic ferromagnet,
Nd2 Fe14 B [3]. Its magnetization of 1.6 Tesla atroom temperature and relatively good temperature dependence of anisotropy field [4] makes
Nd2 Fe14 B a champion magnet compound forpractical applications in the temperature range
from 300 K to 500 K, while its relatively low
Curie temperature at 585 K, almost half of
the Curie temperature of elemental Fe, leaves
only a small temperature margin as compared to Sm-Co magnets whose Curie temperature reaches the range of 1000 K. The hightemperature properties that are not very excellent pose a drawback for the Nd-Fe-B alloy,
leading to various proposals for alternative materials including NdFe12 N [5, 6] and SmFe12 [7],which cannot escape other problem concerning structure instability. In parallel with suchquest for the possible next-generation champion magnets, it is important to better understand today’s champion magnets and verify
if there is any marginal space left for a possible improvement of R2 Fe14 B-based permanent magnets (R=rare earth). Thus we havebeen investigating optimally degined materi-als with a pool of candidate chemical compositions, made of preferrably light rare earth elements and iron-group elements, where a goodcompromise involving all of the desired properties, such as structure stability, magnetization, magnetic anisotropy and Curie temperature, can be reached within a restricted lattice
structure of R2 T14 B (T=Fe or Co).
In order to explore the chemical composition space in a combinatorial way, we run
massively parallel computer simulations forR2 T14 B covering a virtual space spanned by
R’s and T’s utilizing AkaiKKR [8], the opensource package for ab initio electronic structure
calculations based on Korringa-Kohn-Rostoker(KKR) Green’s function method implementing
coherent potential approximation. Once a selfconsistent electronic structure is reached, anestimate of the Curie temperature can be done
as a post-processing to the converged result,based on an approximation to consider the lowmost excitations on the Fermi level dominantly
contributed from the ferromagnetic spin waves.
Atomic-pair wise exchange couplings can be
estimated based on a magnetic force theorem
following Liechtenstein et al. [9] and a realistic
Heisenberg model defined from them can besolved by the mean-field approximation. The
working lattice constants are basically takenfrom past experiments [3].

49Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Curie temperature of R2Fe14B (K)

1400
1200

Calc. (MTA) on the expt. lattice
Expt.

1000
800
600
400

fully utilize the data obtained within the prohibitively crude approximation based on spinmodels even for intermetallics.
More extensive data collections to elucidate
the overall trends have been in progress andwill be published elsewhere.

2000

La Ce Pr Nd

Sm

Gd Tb Dy Ho Er TmYb Lu

References

R[1] M. Sagawa, S. Fujimura, N. Togawa,
H. Yamamoto, and Y. Matsuura,
J. Appl. Phys. 55 (1984) 2083.

Figure 1: Calculated Curie temperature of
R2 Fe14 B (red squqre) based on muffin-tin approximation (MTA). For a comparison, theexperimental data (blue circle) taken from
Ref. [3] are also shown.

[2] J. J. Croat, J. F. Herbst, R. W. Lee, andF. E. Pinkerton, J. Appl. Phys. 55 (1984)
2078.
[3] For a review, see e.g. J. F. Herbst,
Rev. Mod. Phys. 63 (1991) 819.

Calculated Curie temperature in a representative cross section of the overall chemical composition space, (R,T), are shown in
Fig. 1. Here we show the computational data
set based on local density approximation [10]and within muffin-tin approximation. An analogous and more comprehensive data set within
atomic-sphere approximation is published elsewhere [11]. It is seen that the overall trendwith respect to the species of rare-earth elements is described satisfactorily, while thequantitative accuracy is not as excellent. The
systematic deviation is reasonable, considering one of the biggest approximations we havemade in modeling a metallic system only withspin degrees of freedom, as if our target systems were insulators. On top of that, temperature dependence of lattice constants would
not entirely be negligible under the strong influence of the magnetovolume effect in sucha strong ferromagnet [12]. Since the Curie
temperature is mostly contributed from 3delectrons, the relative trend within a materials family where the 3d-electron part is common seems to be well described. As long as
we are aware of the particular way the systematic deviation between theory and experiment comes in, it is expected that we can care-[4] S. Hirosawa, Y. Matsuura, H. Yamamoto,S. Fujimura, M. Sagawa, H. Yamauchi,
J. Appl. Phys. 59 (1986) 873.
[5] T. Miyake, K. Terakura, Y. Harashima,
H. Kino, S. Ishibashi, J. Phys. Soc. Jpn.
83 (2014) 043702.
[6] Y. Hirayama, Y. K. Takahashi, S. Hirosawa, K. Hono, Scr. Mater. 95 (2015) 70.
[7] Y. Hirayama, Y. K. Takahashi, S. Hirosawa, K. Hono, Scr. Mater. 138 (2017)62.
[8] http://kkr.issp.u-tokyo.ac.jp[9] A. I. Lichetenstein, M. I. Katsnelson, V. P. Antropov, V. A. Gubanov,J. Mag. Mag. Mater. 67 (1987) 65.
[10] S. H. Vosko, L. Wilk, and M. Nusair,
Can. J. Phys. 58 (1980) 1200.
[11] MM, H. Akai, Phys. Rev. B 101 (2020)
144402.
[12] for a review, see A. V. Andreev,
Handbook of Magnetic Materials, Ed.
K. H. J. Buschow, Vol. 8, Chapter 2(1995).

50

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Data integration between theory and experiment for
rare-earth permanent magnets
Munehisa Matsumoto
Institute of Materials Structure Science, High Energy Accelerator Research Organization
Oho 1-1, Tsukuba, Ibaraki 305-0801
June 15, 2020

Materials in practical use are characterizedwith macroscopic properties in a space-timescale comparable to the human scale, as rareearth permanent magnets are with remanent
magnetization and coercivity that works in operation environments that are typically out ofthermal equilibrium. It is desirable to have aworking methodology to understand and control those macroscopic properties of materials from the fundamental laws for atoms andmolecules.
We have been in quest for such materials
design scheme spanning over the microscopic
and macroscopic physics. We have recently
constructed an iterative approach between experimental data and theoretical data, taking
as our playground a material of recent interest, namely, SmFe12 with substitution elements such as Ti, Co, and Zr, a candidate material for a new permanent magnet. Effects of
Ti, Co, and Zr for multiple prerequisite properties for permanent magnet utilities, put in
multiple sublattices, are investigated utilizing
both of ab initio theoretical data and experimental data from neutron diffraction. Goingback and forth between the Rietveld analysis
for the latter and ab initio calculations basedon local density approximation (LDA) until afixed point is reached, dual site preference of Zr
in SmFe12 has been newly elucidated, in contrast to the prevailing assumption in the literature that Zr replaces Sm only. This wayof data-integration analysis has been tenta-

tively called “LDA+Rietveld” method [1], as
has been constructed in an analogous spirit to
LDA+DMFT (DMFT =dynamical mean field
theory) [2].
For LDA+Rietveld, we have utilized
AkaiKKR [3] for incorporating the substituteelements with a continuous variables of theconcentration. OpenMX [4] is needed as wellin order to address the structure stability withcalculated formation energy. In LDA+DMFT,
LmtART [5] has been utilized combined witha continuous-time quantum Monte Carlo
impurity solver adapted for our realistic
simulations.
Taking LDA+DMFT as a prototype, wehave made one step forward in constructing a working simulation framework to bridgeover the microscopic scale and the macroscopic
scale.

References[1] MM, T. Hawai, K. Ono, Phys. Rev. Applied 13 (2020) 064028.
[2] MM, Phys. Rev. Materials 4 (2020)
054401.
[3] http://kkr.issp.u-tokyo.ac.jp[4] http://www.openmx-square.org[5] http://savrasov.physics.ucdavis.
edu/mindlab/MaterialResearch/
Scientific/index_lmtart.htm

51

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Physics of Electrochemical Interfaces
Osamu SUGINO

Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
The

metal-solution

interfacerecognizedasaquantum

exhibits various properties undermechanically extended particle; ourthe influence of the electrical double

first-principles

layer formed around the interface.

simulations

Our group has been elucidating thecapture the crossover, which can bereaction dynamics and adsorption

explained by a lattice gas model withprocesses

microscopic

a quantum hopping term, or theperspective using interface-adapted

Boson-Hubbard model. The results

first-principles

providefromacomputational

path-integral

for

new

of

the

hydrogen

TiO2

has

on

evolution reaction.

twodifferent

themes: (A) the quantum nuclear

(B)

1

into

mechanism

followingandinsights

methods. This year, our lab focusesthe𝜃 = 2/3

Defective

the

been

effect of hydrogen adsorption at therecognized as a future material forPt(111)-solution interface [1] and (B)hydrogen fuel cell catalysts because

the role of defects in the activation ofof coexistence of the stability andoxygen reduction reactions at theactivity, but the mechanism of the

TiO2-solution interface [2].

oxygen reduction reaction (ORR) is(A) Hydrogen atoms are known to

unknown. To search for the active

exhibit large quantum effects, butsite of this material, we took a high-these effects have been investigatedthroughput

only at the full mono-layer coveragethermodynamics. Since important(𝜃 = 1) or the low coverage limit (𝜃 ≪key to the activity is in the relative

1 ). In the former, hydrogen isstability

recognized as a classical particle

intermediates,

modified by the zero-point energy,

investigated how one can control theand in the latter, hydrogen isstability by doping. Contrary to52

approach

of
O

based

on

the

reaction

and

OH,

we

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

many materials like platinum, TiO2

a novel fuel cell.

surfaces were found to bond O andReferencesOH[1] L. Yan et al. Phys.Rev.B101, 165414

differently

when

doped

differently, suggesting it possible to(2020).

sufficiently flatten the potential[2] Y. Yamamoto et al. J.Phys.Chem.C123

energy19486 (2019).

discovery

profile

for

has

ORR.

This

stimulated

experimental collaborators to design

53

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DFT sampling analysis on interfaces and electrolytes in novel
batteries
Yoshitaka TATEYAMA
Institute for Solid State Physics,
Center for Green Research on Energy and Environmental Materials (GREEN), National
Institute for Materials Science (NIMS), 1-1 Namiki, Tsukuba, Ibaraki 305-0044
sulfideWe are working on (1) developments ofelectrolyte,

andabufferlayer,

theoretical, computational and data-driven

respectively. For the LCO/LPS interfaces, wetechniques [1,2] as well as (2) understanding ofsampled over 20000 configurations and foundsurface and interface reactions, essential in theseveral stable disordered structures involving

energy and environmental technologies such as

mixing cations and anions, leading to thebattery and catalyst [3-8]. Recently, we haveformation of a reaction layer. On the other hand,made a progress for DFT-based efficient

Li-ion sites that can be preferentially depleted

calculations of solid-solid interfaces, mainly forupon charging always exist around the cathode-all-solid-state batteries [1].

SE interfaces irrespective of the interfacial

We have been exploring the atomistic

order/disorder (See Li Chemical potential inunderstanding of this interfacial resistance

Figure). Therefore, we conclude that themechanism with DFT-based calculations [4].

dynamic Li-ion depletion is likely to be a major

We first devised some systematic ways for thecause that prevents successive Li-ion transport,solid-solid interfaces and discussed possible

leading to resistance.

origins such as the space-charge layer and thereaction layer. Recently, we incorporated the
CALYPSO structure prediction technique with
our method for the interface structure search,
including mismatch treatment and lateral shift
etc [1]. In this way, we have found several
microscopic electrochemistry of the interfacial

Fig. 1 Li chemical potentials around aninterface between LiCoO2 cathode and bLi3PS4 solid electrolyte; Pristine interface(left) and Co-P exchange interface(right).

Li-ion states.
As a representative model, we investigated
the system with LiCoO2 (LCO), β-Li3PS4 (LPS),
and LiNbO3 (LNO) acting as a cathode, a54

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

21 (2019) 13788.

Through investigating the buffer layer
effects and the interfacial electronic states, we[4] Y. Tateyama, B. Gao, R. Jalem, J. Haruyama,

also deduced a probable origin for the

Curr. Opin. Electrochem. 17 (2019) 149.

interfacial Li depletion and a mean to suppress[5] B. Gao, R. Jalem, Y. Tateyama, ACS Appl.

this problematic behavior.

Mater. Interfaces, 12 (2020) 16350.
[6] M. H. N. Assadi, M. Okubo, A. Yamada, Y.

References

Tateyama, Phys. Rev. Mater. 4 (2020) 015401.

[1] B. Gao, R. Jalem, Y. Ma, Y. Tateyama,[7] A. Ishikawa, K. Sodeyama, Y. Igarashi, T.

Chem. Mater. 32 (2020) 85.

Nakayama, Y. Tateyama, M. Okada, Phys.

[2] A. Ishikawa, Y. Tateyama, J. Comp. Chem.

Chem. Chem. Phys. 21 (2019) 26339.

40 (2019) 1866.

[8] A. Ishikawa, Y. Tateyama, J. Phys. Chem. C[3] C. Yamaguchi, K. Natsui, S. Iizuka, Y.

124 (2020) 6054.

Tateyama, Y. Einaga, Phys. Chem. Chem. Phys.

55

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study on defects in wide-gap semiconductors:
SiC and α-Ga2O3
Yu-ichiro MATSUSHITA
Institute for Innovative Research,
Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152-8550
We have studied the stabilities of defects insucceeded in identifying the atomic structure ofwide-gap semiconductors on the basis of thethe defect as an ad-atom with a dangling bonddensity-functional theory (DFT). In this study,(Pb center) based on the DFT calculations [2].

we focus on SiC and α -Ga2O3 as next-

We have also calculated the formation

generation of power semiconducting materials.

energies of point defects in α-Ga2O3 [3]. We

To clarify the stable defect structures and its

have used the extended FNV method to remove

electronic properties is necessary to move thethe artifacts derived from the backgroundpower device applications forwards.

charge. We have found that Ga interstitials andFirst, we have discussed the energetics of

Ga vacancies are the major defects when the

carbon-related defects in the SiC, SiO2, and justFermi energy approaches to valence andat their interface for the systematic comparison

conduction bands, respectively.

of the stabilities of them in the three regions. As

Referencesa result, we have found that the stable forms of[1] T. Kobayashi and Y. Matsushita: J. Appl.

the carbon defects depend on the oxidation

Phys. 126 (2019) 145302. T. Kobayashi, K.

environment. In the oxygen-rich condition atHarada, Y. Kumagai, F. Oba, and Y. Matsushita:

1600K, nano carbon clusters likely to stay justJ. Appl. Phys. 125 (2019) 125701.

at the SiC/SiO2 interfaces [1]. According to the[2] T. Umeda, T. Kobayashi, M. Sometani, H.

calculations, a high temperature oxygen-poor

Yano, Y. Matsushita, and S. Harada: Appl. Phys.

condition is preferable for reducing theLett. 116 (2020) 071604.

remained carbon defects near the interface.

[3] T. Kobayashi, T. Gake, Y. Kumagai, F. Oba,

Veryrecently,

an

EDMR

and Y. Matsushita: Appl. Phys. Expr. 12 (2019)

experiment091001.

detected carbon-dangling bonds along thedirection perpendicular to the interface. We

56

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles configurational sampling ofhighly-doped ionic conductors
Shusuke KASAMATSU
Faculty of Science, Academic Assembly, Yamagata University
1-4-12 Kojirakawa, Yamagata-shi, Yamagata 990-8560
Ceramic-based

under

be found in that section). For example, Figure 1

intense research for application in battery, fuelshows the percolation of dopants in Y-doped

cell, and electrolyzer applications. TheseBaZrO3 vs. temperature calculated for several

materials are usually prepared by doping

dopant concentrations. A profound temperatureinsulating

charge-dependence is seen at 15%, which is close tocompensating defect is the hole or electron, you

the percolation threshold. Further discussion

have a semiconductor. When the compensating

including successful reproduction of the dopant

defect is a mobile ion (or ion vacancy), youconcentration for maximum conductivity canobtainbe found in Ref. [2].

anelectrolytes

materials.

ionic

When

conductor.

are

the

Often,

thesematerials are used at rather high dopant
percentages of up to ~30% where theconductivity is maximized. There is still muchcontroversy

as

to

what

determines

thismaximum, and computer simulations are
expected to help in this regard.
At such high dopant concentrations, theshort to middle-range order of the dopant
Figure 1 Percolation as functions oftemperature for dopant ratios of 7, 15, 22, and30 mol% in Y-doped BaZrO3.

arrangements should have a profound effect on
the conductivity. To simulate this, i.e., dopant
arrangements as functions of temperature anddopant content, we combined the replica

References

exchange Monte Carlo method directly with

[1] S. Kasamatsu and O. Sugino: J. Phys.:

DFT

Condens. Matter 31 (2019) 085901.

calculations

[1]

(the

softwareforachieving this was selected as this year’s[2] S. Kasamatsu et al., Chemrxiv. Preprint.

Software Advancement Project, so details can

https://doi.org/10.26434/chemrxiv.11786286.v1

57

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analyses of Atomic Structures and Atom Dynamics
at Surfaces, Interfaces and Defects
Satoshi WATANABE
Department of Materials Engineering, the University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo, 113-8656

1

Introduction

bending is caused by the accumulation of interstitial Li-ions at the metal-Li3 PO4 interfaces,
and the thickness of the Li-ion accumulation
layer is the order of a few Å. For the Li(100)interface, the band bending behavior depends
on the chemical potential of Li, µLi : Slight upward bending occurs for µLi = −2.59 eV, while
downward bending occurs for µLi = −6.11 eVowing to the accumulation of Li vacancies.
Since Au and Li are known to form alloys,
we also performed simulations taking accountof the alloy formation in the form of work function change. Figure 1 shows the calculated
electrostatic potentials and interstitial Li distribution profiles in γ-Li3 PO4 with Au(111),
LiAu3 and Li3 Au(100). In all cases, the potential profiles show upward bending and theaccumulation of interstitial Li ions near the interfaces. However, the amount of interstitial
Li-ions decreases for the alloy cases. From thisresult, we can explain the switching of VOLRAM.

The understanding on atomic structures andatom dynamics at surfaces, interfaces anddefects is crucial to facilitate innovation ofnovel nanoscale information and energy devices. First-principles calculation is a powerful tool to obtain such understanding, but stillinsufficient to tackle with complex models corresponding to real devices.
Keeping the above in minds, we have been
investigating atomic structures and atom dynamics in various systems via first-principles
calculations combined with multi-scale ormachine-learning approaches. In the followings, some of our results in the fiscal year 2018
are described.

2

Structure of interfaces between
metal and solid electrolyte

The distribution and dynamics of Li ions near
the interfaces between metal electrode andsolid electrolyte play important roles in theoperation mechanisms of novel memory device named VOLRAM [1] and all-solid-state
Li-ion batteries. We examined Li ion distribution at the interfaces between γ-Li3 PO4 andmetal electrodes by the method [2] combining
first-principles data of defect formation energies with a one-dimensional continuum model.
Our results [3] show that within the allowed range of the chemical potential of Li in
γ-Li3 PO4 , upward band bending occurs nearAu(111) and Ni(111) interfaces. This upward3

Phonon-related properties of GaN

Conisdering the facts that GaN is promisingfor power semiconductor device and thermal
management is important in power semiconductor device, we have been examining phononband structures and thermal transport properties of GaN. In the fiscal year 2018, we hadconstructed the high-dimensional neural network potential (HDNNP) [4] for crystalline
GaN, and calculated the phonon band structures and thermal conductivities using the58

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

dynamics using the phono3py package. The
calculation results from HDNNP and DFT under the same simulation conditions are in good
agreement, indicating the strong potential of
HDNNP for application in thermal conductivity simulations: The deviation from the DFT
calculation results is within 5.4% from 200 to1000 K.
Then we constructed HDNNP for GaN crystal with N vacancies, and calculated thephonon band structures and thermal conductivities of GaN with N vacancies. In our
preliminary calculations, we obtained reasonable phonon energy bands and thermal conductivities. We will check the reliability of the
HDNNP and examine the effects of N vacancy
on the phonon band and thermal conductivity
in moe detail in the fiscal year 2020.
Figure 1: Calculated electrostatic potential
and the interstitial Li fraction profiles of γLi3 PO4 as a function of the distance from theinterface z, with Au(111), LiAu3 (111), and
Li3 Au(100) (reproduced from Ref. [3]). The
reference of the electrostatic potential corresponds to the Fermi level of metal surfaces.
The chemical potential of Li is set to −2.59 eV.

References[1] I. Sugiyama, R. Shimizu, T. Suzuki, K.
Yamamoto, H. Kawasoko, S. Shiraki, and
T. Hitosugi: APL Mater. 5 (2017) 046105.
[2] S. Kasamatsu, T. Tada, and S. Watanabe:
Solid State Ionics 183 (2011) 20.
[3] K. Shimizu, W. Liu, W. Li, S. Kasamatsu,
Y. Ando, E. Minamitani, and S. Watanabe: Phys. Rev. Mater. 4 (2020) 015402.

constructed HDNNP. Our preliminary results
were described in the Activity Report 2018.

[4] J. Behler and M. Parrinello: Phys. Rev.
Lett. 98 (2007) 146401.

In the fiscal year 2019, we improved the
HDNNP and examined the phonon band
structures and thermal conductivities moreclosely [5]. To obtain data of atomic structures, energies and forces, we performed classical molecular dynamics (MD) simulations witha well-established interatomic potential andthen evaluated the energies and forces by thedensity functional theory (DFT) for structures
sampled from the trajectories of classical MD.
The final root mean square errors of force andtotal energy prediction in the validation data
were 37.8 meV Å−1 and 66.5 meV atom−1 , respectively. The lattice thermal conductivity
were calculated based on anharmonic lattice[5] E Minamitani, M Ogura, and S Watanabe: Appl. Phys. Express 12 (2019)095001.

59

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles molecular dynamics simulation of thewater/air interface using hybrid functionals
Tatsuhiko OHTO
Graduate School of Engineering Science,
Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531
Density functional theory-based molecularcondensed phases. [1]dynamics simulations are increasingly being
used

for

simulating

aqueous

We employed the CP2K code [2], which isinterfaces.

based on the mixed Gaussian and plane wave

Nonetheless, the choice of the appropriate

basis sets.

density functional, critically affecting theoutcome of the simulation, has remained
arbitrary. Here, we assess the performance ofvarious exchange-correlation (XC) functionals,
based on the metrics relevant to sum-frequency
generation spectroscopy. The structure anddynamics of water at the water-air interface aregoverned by heterogeneous intermolecularinteractions, therefore providing a criticalbenchmark for XC functionals. We find that the
revPBE and revPBE0 with the dispersion

Fig. 1: The ability of different functionals tocorrection show excellent performance. The

accurately predict water properties is directly

poor performance of the empirically optimized

compared. The

density-functionalcorresponds to better (worse) predictive power(M06-L)

manifests

theimportance of satisfying exact functional

smaller(larger) score 𝜅of the functional [1].

condition. Understanding the performance ofdifferent XC functionals can aid resolving theReferences

controversial interpretation of the interfacial[1] T. Ohto et al. J. Phys. Chem. Lett. 10, 4914

water structure and direct the design of novel,(2019).

improved XC functionals better suited to[2]

describe the heterogeneous interactions in

http://cp2k.berlios.de/

60

The

CP2K

developersgroup,

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles molecular dynamics simulation of electrondoped graphene/water interfaces
Tatsuhiko OHTO
Graduate School of Engineering Science,
Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531
Ab initio molecular dynamics (AIMD)

To modify the hydrophobic interaction, we

simulation is a powerful tool to describe

calculated

electron-doped-graphenewater

heterogeneous systems such as the water/solidinterfaces using the CP2K code [3]. Althoughinterface. Although AIMD is computationallyI got preliminary results, it seems that theexpensive, it describes electronic states beyond

integer number of electrons is too strongclassical force fields,[1] which is important forelectron doping. It will be required to thinkinterfaces.

about using plane wave codes (though they are

We have simulated sum-frequency generation

computationally demanding).

(SFG) spectra of isotopically diluted water at thewater-graphene and water-hexagonal boronnitride (hBN) sheet interfaces, using ab initio
molecular

dynamics

simulations.

The

simulations themselves were performed using
ISSP several years ago and recently the paper
was published.[2] A sharp ‘dangling’ O-D peakaround ~2640 cm-1 appearing in both simulated

Fig. 1: Structures of the graphene-water

SFG spectra evidences that both graphene andinterface.

hBN are hydrophobic. The dangling O-D peak is
10 cm-1 red-shifted at the water-hBN interface

References

relative to the peak at the water-graphene[1] T. Ohto et al. Phys. Chem. Chem. Phys. 19,

interfaces. This frequency difference manifests a

6909 (2017).

stronger O-D…N intermolecular interaction[2] T. Ohto et al. Phys. Chem. Chem. Phys. 20,

between water and hBN than a O-D…C

12979 (2018)

interaction between water and graphene.

[3]

The

CP2K

http://cp2k.berlios.de/61developersgroup,

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of first-principles electronic-structure
and transport calculation code RSPACE andsimulations for device
Tomoya ONO
Graduate School of Engineering, Kobe University
Rokkodai-cho, Nada, Kobe 657-8501

× 3 ⃗k-point mesh.

Silicon carbide (SiC) has attracted considerable attention owing to its excellent physical properties, such as its high thermal conductivity, high breakdown strength, and large
band gap. It is also advantageous that the oxidation of SiC leads to SiO2 , since it is wellknown that SiO2 exhibits good dielectric properties in Si device technology. However, unlike Si MOSFETs, SiC MOSFETs have unacceptably low carrier mobility. One of the origins of the low carrier mobility is the generation of a large number of interface defects at
the SiC/SiO2 interface during the thermal oxidation. In this study, we carried out density
functional theory calculations to examine theoxidation process of SiC(0001)/SiO2 interfaces
showin in Fig. 1.[2]The oxidation of 4H-SiC is assumed to proceed by the process which we proposed in theprevious study:[3] (a) an O2 molecule arrives
at the interface, splits, and cuts into the Si-C
bonds (2Oif ). (b) One of the O atoms among
the Si-C bonds migrates to a site between the
Si and C atoms connecting the first and second
SiC bilayers (Osub +Oif ). (c) the third O atom
comes by migration between the SiC bonds(Osub +2Oif ) (d) Due to the interface latticemismatch, CO molecule detachment occurs at
the interface (2Oif VC +CO). I found that thelargest energy barrier is 3.21 eV for process(a). Gavrikov et al. [5] employed the interface model, where two- and three-fold structures are mixed, and reported that the activation barrier is larger than 3.5 eV, which is
required for the penetration of an O2 molecule
through the interfacial layer of SiO2 . It isreported by Shen et al. [6] that the barrier
for an O2 molecule penetration is ∼ 4.0 eV.
Akiyama et al. [7] reported the activation barrier of 3.2 eV using the computational model
similar to the 4H-SiC(0001)/β-tridymite SiO2 .
Their reaction path resembles the atomic oxygen mechanism, in which O atoms diﬀuse byhopping from one bond to another, rather thanan O2 molecule penetration. Shen et al. also
reported that the barrier for the atomic oxygen mechanism is ∼ 3.1 eV. Although my reaction process (a) is similar to that proposed
by Akiyama et al., in which the O2 molecule

It is not straightforward to characterize theatomic structure of the SiC(0001)/SiO2 interface because SiO2 at the SiC/SiO2 interface ismainly amorphous. Here, I assume that crystalline structures exist locally at the SiC/SiO2
interface and employ the most possible candidate for the interface atomic structures reported in Ref. 2. RSPACE code[4] is used
for the first-principles calculations. The energy barriers in the oxidation process are computed by the nudged elastic band method. The
lateral lengths of the supercell are chosen to√
be 3a and 3a along the [11̄00] and [112̄0] directions of the 4H-SiC(0001) surface, where ais the lattice constant of SiC, and integration
over the Brillouin zone is carried out using a 2

62Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

is the reaction-limiting process.

is not a molecule after passing the interfacial
SiO2 layer, my process is diﬀerent from theirsituation, in which the interfacial O atom hops
to the SiC bond and Si2 -CO structure is generated. When I assume that the O2 molecule behaves like two O atoms at the oxidation front,
the activation barriers obtained by these theoretical calculations are comparable. Thus, O2
molecules dissociate when they pass the interfacial SiO2 layer with the barrier of ∼ 3.2 eV.
Next, let me discuss the barrier after the O
atoms cut into the SiC bonds. Gavrikov et
al. reported that the CO molecule is emitted
from the Si2 -CO structure with the activation
barrier of 2.8 eV. Since the Si2 -CO structureis less stable than the Osub +Oif structure by
0.6 eV, the total activation barrier from theOsub +Oif structure is 3.4 eV. Köhler et al.
reported the barrier for the CO molecule detachment of 3.1 eV. If the energy diﬀerence
reported by Gavrikov et al. is added, the total barrier from the Osub +Oif structure is 3.7
eV. It is also reported by Akiyama et al. thatthe activation barrier for the CO molecule detachment from the Si2 -CO structure is 1.7 eV,
which is much smaller than the results calculated by Gavrikov et al. and Köhler et al.
If I believe the larger barrier calculated by
Gavrikov et al. and Köhler et al., these results imply that the CO detachment also limits
the reaction. However, in our previous study[3], we reported that the CO desorption preferentially occurs when the interfacial C atom
is surrounded by three O atoms. The activation barriers for the migration of O atoms at
the SiC/SiO2 interface are 2.72 eV for process(b) and 2.08 eV for process (c). It is noteworthy that these barriers vary between 2.0 eV
and 2.8 eV depending on the configuration of
the O atoms at the interface. When the thirdO atom is considered, the barrier for the O2
molecule penetration is still higher than thatfor the CO detachment. Thus, it can be concluded that the CO detachment does not limit
the reaction and the O2 molecule penetration

Figure 1: Interface atomic structure of βtridymite SiO2 on SiC. Blue, brown, and redballs are Si, C, and O atoms, respectively. The
supercell contains 30 Si, 24 C, 14 O, and 8 H
atoms. H atoms are used for termination of
dangling bonds at the surfaces.

References[1] T. Ono et al., Phys. Rev. B 96 (2017)115311.
[2] T. Ono, Mater. Sci. Forum 963 (2019)208.
[3] T. Ono and S. Saito, Appl. Phys. Exp. 4(2011) 021303.
[4] K. Hirose, T. Ono, Y. Fujimoto, and S.
Tsukamoto: First Principles Calculations
in Real-Space Formalism (Imperial College, London, 2005).
[5] A. Gavrikov et al., J. Appl. Phys. 104(2008) 093508.
[6] X. Shen et al., J. Appl. Phys. 114 (2013)
033522.
[7] T. Akiyama et al., Surf. Sci. 641 (2015)
174.
[8] C. Köhler et al., Phys. Rev. B 64 (2001)
085333.

63

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-Principles Study of Excited Electron, Positronand Atom Dynamics and Optical and Thermoelectric
Properties of Nanostructures
Kazuyuki WATANABE, Yasumitsu SUZUKI,
Kazuki UCHIDA, Tomokazu YAMAGUCHI and Masashi YOSHISATO
Department of Physics, Tokyo University of Science
1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601

In this project we investigated the following four topics on the basis of time-dependent
density functional theory (TDDFT). 1) Angleresolved photoemission spectroscopy (ARPES)
in low-dimensional periodic structures, 2)
Stationary-state electron scattering using acomplex injecting potential (CIP), 3) Opticaland thermoelectric properties of low dimensional materials, and 4) Development of theexchange-correlation term in TDDFT.
1) Angle-resolved photoemission spectroscopy
in low-dimensional periodic structures [1]:We proposed a new approach based on
TDDFT for the calculation of ARPES of
low-dimensional periodic structures, such asgraphene, silicene, and polyacetylene. The calculated ARPES spectra reproduced the occupied energy band structures fairly well. We
further investigate the electron doping effect on ARPES by considering Li-intercalated
bilayer graphene and found a shift in the
Fermi energy. These show that the present
method can provide reliable ARPES spectra
for materials for which ARPES experiments
are diﬃcult to perform under some conditions. We note that the present method is simpler and uses a more direct one-shot TDDFT
calculation for ARPES than previous theories. Further applications to time-resolved andspin-resolved ARPES simulations will be presented elsewhere. The simulations have been
conducted by our homemade TDDFT code,

KENS. Parallelized calculations have been performed using System B.
2) Stationary-state electron scattering using acomplex injecting potential [2]:We simulated stationary electron scattering by solving the time-dependent Schrödinger
equation with a CIP. The calculated electron transmission probabilities through onedimensional potentials and the electron interference patterns caused by double slits show
good agreement with analytical results. The
Aharonov–Bohm eﬀect is also clearly demonstrated by the presence of a vector potential
at one side of the double-slit configuration.
Also, from the simulation of the arranged-CIP
method, we predict that this new method canbe applied to BEC interference simulations.
Since the present method can be straightforwardly extended to TDDFT, we can simulate field electron emission, photo-induced
electron emission, secondary electron emission,
thermionic emission, and so on. The simulations have been conducted by our homemadecode, SCIP, using System B.
3) Optical and thermoelectric properties of low
dimensional materials [3]:We studied the optical and thermoelectric
properties of various low dimensional materials
by means of the first-principles method.
First, we applied TDDFT to the calculation of absorption spectra for two-dimensional
atomic-layer materials: mono-layer and bi-

64Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

layer hexagonal boron nitride (h-BN) andmono-layer transition metal dichalcogenides,
MoS2 and MoSe2 . We demonstrated that
the TDDFT approach with the meta GGA
exchange-correlation potential and the bootstrap kernel can capture the characteristicsof the first bright excitonic peak of bi-layerh-BN that is dependent on the layer stacking type. We also revealed that the TDDFT
method can capture the qualitative features of
the absorption spectra for mono-layer transition metal dichalcogenides, although the exciton binding energies are underestimated compared to those obtained by the many-body
pertubation theory (MBPT) calculation. This
study elucidates the usefulness of the TDDFT
approach for the qualitative investigationof the optical properties of two-dimensional
atomic layer materials. MBPT calculations
and TDDFT calculations have been conduced
using EXCITING (http://exciting-code.org/)and ELK (http://elk.sourceforge.net/) code,
respectively. Parallelized calculations havebeen performed using System B.
Next, we calculated the thermoelectric
power factor of pnictogen (P, As, Sb, Bi)nanoribbon structures using the density
functional theory (DFT) and non-equilibrium
Green’s function (NEGF) method. We foundthat the power factor properties strongly
depend on the structure of nanoribbons, i.e.,the buckled nanoribbon generally exhibit
higher power factor than the puckered one.
It was also found that the light pnictogens (P, As, Sb) have an advantage overthe heavy one (Bi) in giving a high power
factor. This study reveals a part of therelationship between the electronic structure
and the thermoelectric property of pnictogen nanoribbons, and provides the useful
information to develop the thermoelectric
devices based on pnictogen nanoribbons. All
DFT calculations and NEGF calculations
have been conduced using Quantum Espresso(https://www.quantum-espresso.org/)
and

WanT (http://www.wannier-transport.org/)code, respectively. Parallelized calculations
have been performed using System B.
4)Development of the exchange-correlation
term in TDDFT:
We developed a machine learning based approach to improve the approximation to theexchange-correlation potential of TDDFT. We
trained the neural-network projection from thetime-varying electron densities to the corresponding correlation potentials in the time dependent Kohn-Sham equation using a few exact datasets for a model system of electronhydrogen scattering. We demonstrated that
this neural-network potential can capture thecomplex structures in the time-dependent correlation potential during the scattering process
and provide correct scattering probabilities,
which are not obtained by the standard adiabatic functionals. This study oﬀers a novel way
to improve the exchange-correlation potentialof TDDFT. The simulations have been conducted by our homemade code. Parallelized
calculations have been performed using System B.

References[1] K. Uchida, Y. Akimoto, K. Einaga, andK. Watanabe, Jpn. J. Appl. Phys. 58,
128001 (2019).
[2] T. Yamaguchi, K. Uchida, K. Varga, andK. Watanabe, J. Phys. Soc. Jpn. 89,
044002 (2020).
[3] Y. Suzuki and K. Watanabe, Phys. Chem.
Chem. Phys. 22, 2908 (2020).

65

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio phonon calculation for Ca5Ir3O12
Kazuma NAKAMURA
Quantum Physics Section, Kyushu Institute of Technology
1-1 Sensui-cho, Tobata, Kitakyushu, Fukuoka, 804-8550
4

The title compound has recently attracted
attention as a thermoelectric material because
it has a relatively high Seebeck coeﬃcient.
In this study, we report an ab initio study
about electronic and phononic properties for
Ca5 Ir3 O12 . In particular, we investigated theeﬀect of spin-orbit interaction (SOI) on the
low-energy properties [1].

Energy (eV)

3

(a)

2
1
0
-1
-2
-3
-4
0.6

Energy (eV)Density functional calculations with planewave basis sets were performed using thexTAPP code [2], where the ultrasoft pseudopotential and the generalized gradient approximation (GGA) of the exchange correlation potential were employed. The cutoﬀ energies in
the wavefunction and charge densities were 64
and 900 Ry, respectively, and the SOI was explicitly considered. To study the eﬀects of SOI,
we performed the usual GGA calculation andcompared it with the result including the SOI.
Below, we refer to the former as GGA and to
the latter as SO-GGA. The atomic and lattice
parameters were optimized with an 8×8×8 kpoint sampling, and we found that SO-GGA
reproduces the experimental crystal structure
quite well. The Fermi-surface calculations
were performed with the dense 21×21×63 kpoint sampling to obtain the detailed surface structure [3]. Phonon calculations with afrozen phonon approximation were performed
using the PHONOPY for 1×1×3 and 2×2×1
supercells [5, 6]. For the k-point sampling,
11×11×11 was used for 1×1×3 supercell calculation, and somewhat coarse 9×9×5 was used
for the 2×2×1 supercell calculation.

0.4

(b)

0.2
0

-0.2
-0.4

L

M

(c)

A
L

M

A

H

(d)

Γ

K

Γ

A
L

H

K

Γ

M

H

K

Γ

Figure 1: (Color online) (a) Ab initio electronic band structure considering the SOI in
Ca5 Ir3 O12 . The energy zero is the Fermi level.
(b) A zoom of the low-energy band structure,
where the SO-GGA result (thick red curves)is compared with the usual GGA result (thinblue curve). (c) Calculated Fermi surface for
SO-GGA and (d) GGA.

Figure 1(a) shows our calculated band structure. To see the SOI eﬀect, the SO-GGA band66

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

M points. However, since the calculation conditions for the 2×2×1 calculation are rough, it
is necessary to perform the calculation undermore severe conditions.

(thick red curves) is compared with the GGA
band (thin blue curves) in Fig. 1(b). An appreciable diﬀerence can be observed in the lowenergy bands; the GGA result exhibits metallic bands, particularly along the L-M or H-Klines. When the SOI is switched on, the metallic bands are split and a pocket-like band structure appears. The gap size due to the SOI is
about 0.3 eV, which is comparable to the valence bandwidth 0.5 eV.

700

(a)

600

Energy (cm-1)

500

Figures 1(c) and 1(d) show the Fermi surfaces based on the SO-GGA and GGA, respectively. We see that the GGA Fermi surface
is contributed from the two bands (indicatedin dark-blue and bright-red colors), while the
SO-GGA Fermi surface is basically formed by
the one band; the SOI makes the bright-red
colored GGA Fermi surface disappear. In the
SO-GGA Fermi surface, since the SOI resolves
the band degeneracy, the Fermi surfaces are
seemingly two (dark-blue and bright-blue colored surfaces); however, these two are originated from the same band. Also, in the SOGGA Fermi surface, we see a sheet structure
along the c∗ -axis (the Γ-A line), which indicates a nesting trend along this direction. We
note that the SOI is relevant to the narrowing of the sheet separation between the blue
colored Fermi surfaces.

400
300
200
100
0
-100
600

(b)

500

Energy (cm-1)

400
300
200
100
0
-100
-200

L

M

Γ

A

H

K

Γ

Figure 2: (Color online) Ab initio phonon dispersion with the SOI in Ca5 Ir3 O12 . Panels(a) and (b) show results based on 1×1×3 and2×2×1 superlattice, respectively.

References

Figures 2(a) and 2(b) are our calculated
phonon dispersions with SOI for 1×1×3 and2×2×1 supercells, respectively. It was foundthat the experimental results at the room temperature are better reproduced by the 1×1×3
supercell calculation. The panel (b) is a preliminary phonon calculation on a 2×2×1 supercell. This supercell includes the displacement degree of freedom in an in-plane 2×2 superlattice, and we can investigate the phonon
instability within this superlattice. On theother hand, the 1×1×3 supercell can clarify
the triple-period phonon instability along thec-axis. Within these two supercells, we observe
phonon softening in the 2×2×1 supercell calculation; there is a sign of softening at the K and[1] K. Matsuhira, K. Nakamura, Y. Yasukuni, Y. Yoshimoto, D. Hirai, Z. Hiroi:
J. Phys. Soc. Jpn. 87 (2018) 013703/1-5.
[2] http://xtapp.cp.is.s.u-tokyo.ac.jp[3] http://fermisurfer.osdn.jp[4] https://atztogo.github.io/phonopy[5] T. Hasegawa, W. Yoshida, K. Nakamura,N. Ogita, and K. Matsuhira:: J. Phys.
Soc. Jpn 89 (2020) 054602/1-11.
[6] H. Hanate, T. Hasegawa, S. Tsutsui, K.
Nakamura, Y. Yoshimoto, N. Kishigami,
S. Haneta, and K. Matsuhira1: J. Phys.
Soc. Jpn 89 (2020) 053601/1-5.

67

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio derivation of eﬀective low-energy model of
Ca5Ir3O12
Kazuma NAKAMURA
Quantum Physics Section, Kyushu Institute of Technology
1-1 Sensui-cho, Tobata, Kitakyushu, Fukuoka, 804-8550

dxy and dyz orbitals. Here, the notation of
the orbital follows a local coordinate system
ﬁxed to the IrO6 octahedron. Based on thisobservation, we perform parameter derivationof the dxy /dyz model. Figure 1 is a comparison of the Wannier-interpolation band (greendashed curves) and the original band (red-solid
curves). We see that the original band has
been completely reproduced. Note that the initial guess setting is very important for obtaining such reproducibility. We set the dxy anddyz orbitals as initial guesses, where the initial guess orbitals are represented in the local
coordinate system ﬁxed to IrO6 octahedrons,
and additionally rotated the spin quantization
axis. This treatment is very important to satisfy the symmetry of the calculated Wannierorbitals, that is, all 12 Wannier orbitals havethe same spread.

In this report, we report a ﬁrst-principles
derivation of an eﬀective low-energy model for
Ca5 Ir3 O12 . In order to perform the eﬀectivemodel derivation of materials with strong spinorbit interaction (SOI) such as iridium system,
we extended the ﬁrst principle eﬀective-model
derivation software RESPACK [1] to the spinor
type.
The density-functional band-structure calculations for Ca5 Ir3 O12 are performed using
xTAPP [2] with the experimental lattice parameters [3]: a = 9.3490 Å and c = 3.1713
Å. We use the norm-conserving pseudopotential and the generalized gradient approximation (GGA) of the exchange correlation
potential. We use 8×8×8 k-points for sampling in the ﬁrst Brillouin zone. The energy cutoﬀ is set to be 144 Ry for the wave
functions, and 576 Ry for the charge density.
The interaction parameters are calculated using the constrained random-phase approximation method, in which we employ the scheme
for the band disentanglement. The energy cutoﬀ for the dielectric function is set to be 20 Ry.
The total number of bands used in the calculation of the polarization is 300, which includes
the unoccupied states up to ∼ 26 eV with respect to the Fermi level. To study the eﬀects
of SOI, we performed the usual GGA calculation and compared it with the result including
the SOI. Below, we refer to the former as GGA
and to the latter as SO-GGA.

3

Energy (eV)

2
1
0
-1
-2
-3

L

M

Γ

A

H

K

Γ

Figure 1: (a) Ab initio density functional band
structure considering the spin-orbit interaction
in Ca5 Ir3 O12 .

From the fat band analysis, it was found thatthe band structure near the Fermi energy is

68Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

We next show in Fig. 2 the resulting maximally localized Wannier functions for dxy /dyz
model. The panels (a) and (b) indicate the dxy
and dyz Wannier functions, respectively. Notethat in this plot, three independent Wannierfunctions are shown in one panel.

Table 1: Main parameters of dxy /dyz model of
Ca5 Ir3 O12 , where we show 3 nearest-neighbor(NN) transfers, onsite transfers, and largest inNN
NN
terchain electron transfer. txy↑,yz↑
and tyz↑,xy↑
onsiteare nearest neighbor trasnfers. Also, txy↑,yz↓
is the spin-orbital couplings in the same site.
The interaction parameters with the bare (unscreened) and constrained RPA (cRPA) arelisted. VNN is the orbital-averaged value of thenearest-neighbor interactions. Also, VIC is theorbital-averaged value of the interchaicn interaction. The unit of the parameters is eV.
SO-GGA

GGA

NN
txy↑,yz↑

0.167

0.167

NN
tyz↑,xy↑

0.210

0.208

largesttinterchain

0.032

0.039

onsitetxy↑,yz↓

0.213

-

U
U′
V NN
V interchain
J

bare

cRPA

bare

cRPA

9.87
9.19
4.43
2.86
0.27

2.43
1.95
0.99
0.52
0.21

10.03
9.28
4.39
2.86
0.29

2.23
1.68
0.77
0.44
0.23

As another achievement, we calculated theRaman frequency [4] and the phonon dispersion curves [5].

References[1] https://sites.google.com/view/kazuma7k6r[2] http://xtapp.cp.is.s.u-tokyo.ac.jp

Figure 2: Maximally localized Wannier functions of Ca5 Ir3 O12 : (a) dxy and (b) dyz Wannier functions.

[3] M. Wakeshima, N. Taira, Y. Hinatsu, and
Y. Ishii, Solid State Commun. 125, 311(2003).

Our derived model parameters for Ca5 Ir3 O12
are summarized in the Table 1. The spin-orbit
coupling is estimated as 0.213 eV. The nearest
neighbor parameter tN N is 0.167 eV, the onsite interaction U based on constraind RPA is
2.43 eV, and the nearest-neighbor interaction
V is estimated as 0.99 eV. Then, the correlation degree of freedom (U − V )/t is 8.62.

[4] T. Hasegawa, W. Yoshida, K. Nakamura,N. Ogita, and K. Matsuhira:: J. Phys. Soc.
Jpn 89 (2020) 054602/1-11.
[5] H. Hanate, T. Hasegawa, S. Tsutsui, K.
Nakamura, Y. Yoshimoto, N. Kishigami, S.
Haneta, and K. Matsuhira1: J. Phys. Soc.
Jpn 89 (2020) 053601/1-5.

69

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculations of thermoelectric
properties in magnetic materials
Fumiyuki ISHII, Susumu MINAMI, Rifky SYARIATI, Akihiro HORI,
Hikaru SAWAHATA, Naoya YAMAGUCHI, Monika NUR
Nanomaterials Research Institute, Kanazawa University
Kanazawa, 920-1192, Japan

1. Development of Methods and Codes
The thermoelectric conversion based on theanomalous Nernst eﬀect (ANE) has attracted
much attention because the ANE realizes thehigh-density integration more easily comparedto that based on the Seebeck eﬀect[1]. The
ANE is the phenomenon that the electric
power is created along the direction perpendicular to both the temperature gradient andthe magnetization in magnetic materials. Thiseﬀect is induced by the anomalous Hall conductivity (AHC), and if the AHC changes drastically as a function of the Fermi level, we expect the large ANE[2]. In our previous firstprinciples study, we predicted that an electron
doped EuO skyrmion crystal shows the large
ANE induced by the finite Chern number at
the Fermi level[3]. For discovery and designof new materials which have the large ANE
via computational high throughput screening,
we need an eﬃcient computational method
to investigate the Fermi level dependence of
the AHC. We have implemented the code ofcomputing the AHC applicable to metallic
systems in OpenMX package[4] by improving
Fukui-Hatsugai-Suzuki method[5]. Using thiscode, we computed AHCs σxy (ε) and transverse thermoelectric conductivities αxy (ε) in
two-dimensional ferromagnetic materials.
2. Applications to 2D Materials
The discovery of magnetism in the twodimensional materials[6] open a way for realizing thermoelectric devices based on anoma-

lous Nernst eﬀect. The surface phonon scattering advantage in the two-dimensional materials can decrease the thermal conductivity
which can increase the thermoelectric figureof merit ZT [7].The magnitude of anomalous
Nernst eﬀect itself depend on Seebeck eﬀect
or anomalous Hall eﬀect[2, 3]. In our previous
study, we reported that the half-metallic materials possess large anomalous Nernst eﬀect[8].
Here, we performed first-principles calculations to explore the anomalous Nernst eﬀect ofhalf-metallic transition-metal dihalides monolayer using OpenMX package[4]. We analyzed its magnitude based on the semiclassical transport theory and found that there islarge anomalous Nernst eﬀect at 100 K. The
large Berry curvature which contributed bybands near Fermi level is the main reason ofits large magnitude. These results suggest thattransition-metal dihalides monolayer can potentially be used in thermoelectric devices.
3. Thermal Conductivity and ZT
To evaluate eﬃciency of thermoelectric materials, it is important to examine the contributionof thermal conductivity to the thermoelectric
figure of merit ZT that represents the performance of the material. Since the thermal conductivity can be described for each electron
and lattice, in this research, we theoreticallycomputed both electronic and lattice thermal
conductivity, and then evaluated ZT . Theoretical analysis of lattice thermal conductivity is conducted by Boltzmann transport the-70Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ory with relaxation time approximation. In
order to do this, it is necessary to determine
the inharmonic atomic force constant exactly,
and an accurate analysis is carried out by
first-principles calculations based on density
functional theory. As computational codes,
OpenMX package[4] is used as a density functional calculation, and ALAMODE[9, 10] isused as a lattice thermal conductivity calculation. The half-Heusler compounds are ternarycompounds, have composition formula of XYZ,
and are expected as thermoelectric materials
that exhibit high power factor in a medium
temperature range of about 600 to 1000 K. We
analyzed thermoelectricity and thermal conductivity of ferromagnetic half-metallic halfHeusler MnCoSb[8]. We evaluated the ZT for
the Seebeck and anomalous Nernst eﬀect. We
discussed carrier and temperature dependenceof ZT .
4. Surface Structures and Atomic Radii
To design new functional materials, surface
alloying is an eﬀective way to obtain desired materials. Surface alloys are synthesized by inserting atoms into the surface. This
topic has attracted a lot of research attention lately because of some of its applications, such as spintronics[11], where there isa giant spin splitting in Bi/Ag(111) surface
alloys[12, 13]. Many types of surface alloys
have been studied: for example, Ge/Ag(111),
Pb/Ag(111), Bi/Ag(111), and Sn/Ag(111).
One structure that has been observed in ex√√
periments with surfaces is 3 × 3 R 30◦ .
Structural studies for surfaces alloys can provide important information for forming metalsemiconductors interface and metal interfaces.
The metal-semiconductor interface is very important to industry, for example, the Si/Ag
interface is a promising candidate for solar
cells. We systematically explored the structural stability of M /Ag(111) surface alloys by
first-principles calculation using the OpenMX
package[4], where M is group III (B, Al, Ga,
In and Tl), IV (C, Si, Ge, Sn and Pb) and V

atom (N, P, As, Sb and Bi). We focused on thecorrugation parameter d which is determinedby the height of the M atom from the Ag atomin the plane of the top-most atom. We introduced concept of atomic radii to understandthe tendencies of corrugation in M /Ag(111).
The formation energy for each M atom is also
calculated to determine the stability of the surface alloys. We discussed the dependence of M
atoms on corrugation parameters.

References[1] Y. Sakuraba, Scr. Mater. 111, 29 (2016).
[2] Y. P. Mizuta and F. Ishii, Sci. Rep. 6,28076 (2016).
[3] Y. P. Mizuta, H. Sawahata, and F. Ishii,
Phys. Rev. B 98, 205125 (2018).
[4] T. Ozaki et al., http://www.openmxsquare.org/[5] T. Fukui, Y. Hatsugai, and H. Suzuki, J.
Phys. Soc. Jpn. 74, 1674 (2005).
[6] B. Huang et al., Nature 546, 270 (2017).
[7] R. Anufriev, J. Maire, and M. Nomura,Phys. Rev. B 93, 045411 (2016).
[8] S. Minami, F. Ishii, Y. P. Mizuta, and
M. Saito, Appl. Phys. Lett. 113, 032403(2018)[9] T.Tadano, https://alamode.readthedocs.io[10] T. Tadano, Y. Gohda, and S. Tsuneyuki,
J. Phys.: Condens. Matter 26, 225402(2014)[11] C. R. Ast et al., Phys. Rev. Lett. 98,
186807 (2007).
[12] I. M. Mcleod et al., Surf. Sci. 604, 1395
(2010).
[13] N. Yamaguchi, H. Kotaka, and F. Ishii, J.
Cryst. Growth 468, 688 (2017).

71

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Reduction of Rare Metals in Formic Acid Decomposition
Catalysts and Oxygen Storage Materials
Yuji KUNISADA
Center for Advanced Research of Energy and Materials, Faculty of Engineering,
Hokkaido University, Sapporo, Hokkaido 060-8628
We investigated the catalyst adsorption

catalytic activity using a theoretical volcano

and diffusion properties on non-metal element

plot reported in the previous study.[1] From

doped graphene with the aid of the first-

the adsorption energy of intermediates, we

principles calculation based on the density

estimated the reaction activities. We found

functional theory (DFT). We also investigatedthat the embedded Cu atoms in graphene

the corresponding catalytic activity. Besides,

show higher activity than Cu clusters on

wegraphene.

investigatedproperties

of

the

oxygensubstituted

absorption

brownmillerite

Weoxides.

also

investigatedtheoxygenabsorption properties of partially substituted

At first, we investigated adsorption and

Ca2AlMnO5.

We

revealedthat

Mn-sitediffusion properties of Cu clusters on non-substitution is favorable for the oxygen

metal element doped graphene. We also

absorption-desorption process than Al-site

considered Cu oxide clusters and Cu atoms

substitution.

embedded in the graphene basal plane. We

We also studied the isotope effect on theperformed the total energy and electronic

alkene hydrogenation process on Rh-based

structure calculations using The Vienna AbIntermetallic catalyst [2] and the structure andinitiomagnetism of Ca2RuO4 nanofilm.[3]simulation

package(VASP).

We

installed a parallelized VASP with Intel® MPI

References

Library and Intel® Math Kernel Library. We[1] J. S. Yoo, F. A.-Pedersen, J. K. Nørskov, F.

found that the adsorption energies andStudt: ACS Catal. 4 (2014) 1226.

diffusion activation barriers of Cu clusters[2] S. Furukawa, P. Yi, Y. Kunisada, K.

increase by non-metal element doping into

Shimizu, Sci. Technol. Adv. Mater.

graphene lattice. We note that Cu oxide

20 (2019) 805.

clusters also show the same trend, and the[3] H. Nobukane, K. Yanagihara, Y. Kunisada,

embedded Cu atoms in graphene have quite

Y. Ogasawara, K. Nomura, Y. Asano, S.

high stability. We also investigated theTanda, Sci. Rep. 10 (2020) 3462.

72

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Material exploration by advanced first-principles simulation
Shinji TSUNEYUKI
Department of Physics, School of Science,
The University of Tokyo, 7-3-1 Hongo, Bunkyo-Ku, Tokyo 113-0033
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
The density functional theory (DFT)-based

X-ray diffraction data from high-pressure

first-principles electronic structure calculation

experiments), we aimed to establish simulation

method has played an important role as amethods that strongly support experimental

powerful research tool in material properties andresearch on materials under extreme conditions,as a predictor of new materials and structures.

new materials with only poor quality crystals,

Weand materials containing hydrogen that are

have

been

developing

fundamental

difficult to observe experimentally.

simulation methods, such as the accurate
calculation of the lattice thermal conductivity

In this method, instead of finding the global

using DFT calculations and the prediction of theminimum of the multi-dimensional potential

superconducting transition temperature using

energy surface 𝐸(𝐑) as a function of the atomic

superconducting

theorypositions R, we define the effective potential(SCDFT), in collaboration with experimentalists.

𝐹(𝐑) by the sum of 𝐸(𝐑) and a so-called

densityfunctional

In this fiscal year, we focused on determining

penaltyfunctionthe crystal structure of unknown materials, andincreases

when

predicting the physical properties of these newintensity 𝐼calc (R)deviates from the experimental

materials in collaboration with the experimental

one 𝐼obs :𝐷[𝐼obs , 𝐼calc (R)],thesimulatedwhich

diffractiongroups of the Grant-in-Aid for Scientific

𝐹(𝐑) = 𝐸(𝐑) + 𝛼𝑁𝐷[𝐼obs , 𝐼calc (R)].

Research on Innovative Areas "Hydrogenomics:

Here, N is the number of atoms in the simulation

Creation of Innovative Materials, Devices, andcell and a is a control parameter. Note that, in

Reactivecase of the powder diffraction. 𝐼obs and 𝐼calc (R)Processes

usingHigher-Order

Hydrogen Functions" (FY 2018-2022) and theare functions of diffraction angle.

Tokodai Institute for Element Strategy. In
particular,bydeveloping

structure

simulation

Previously, as a first trial, we adopted

data-assimilated

methods

based“crystallinity” for the penalty function, in whichon

we used diffraction angles but not the diffraction

incomplete experimental data (e.g., incomplete

intensity [1]. The method is useful when the73

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

relative intensity of diffraction peaks is notprobability. Therefore, we also investigated thereliable. It is, however, not necessarily robust

efficient sampling of the average diffraction

when the crystal symmetry is extremely low, or

pattern of the system (Fig. 1). We are currently

the noise in the experimental data is very large.

working on a test calculation combining thismethod with the neural network potential.

Therefore, in FY 2019, we introduced thecorrelation between 𝐼calc (R) and 𝐼obs for the
penalty function. With this penalty function, we
can treat all the diffraction data, including eventhe noise, on the same footing and utilize as
much information as possible. We found the new
penalty function improves the predictability of
crystal structures.
We also developed a method to search forstructures by treating the potential energy 𝐸(𝐑)
and

the

penaltyfunction𝐷[𝐼obs , 𝐼calc (R)] independently of each other,

Fig. 1 An average structure of the high-using their gradients to avoid local stabletemperature phase of LiCB9H10 determined bysolutions [2].

the data assimilation method.

Using these methods, it is possible to searchfor complex structures containing more than 100

References

atoms in the simulation cell. However, the[1] N. Tsujimoto, D. Adachi, R. Akashi, S. Todo

search becomes difficult when a specificand S. Tsuneyuki, Phys. Rev. Materials 2,

element in a material is disordered, i.e., a053801 (2018).

specific element partially occupies multiple sites[2] D. Adachi, N. Tsujimoto, R. Akashi, S. Todo,or arrangements in a unit cell, or two

and S. Tsuneyuki, Comput. Phys. Commun. 241,

components occupy the same site with a certain

92 (2019).

74

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study for widening the potential of spinpolarized positron experiments
Mineo SAITO
Institute of Science and Technology, Kanazawa University
Kakuma, Kanazawa, 920-1192 JapanSpin

polarized

positronoxides and nitrides are due to thetechniquedetectedfact that the atomic radii of the firstsome spin polarized vacancies in

raw atoms are small and thus thesemiconductors.

spinannihilation

polarized

We

cation

study

spin-

vacanciesindensities

aresubstantiallylocalized at the four nearest anions

wurtzite structure semiconductors

in. the cation vacancies.

(BeO, ZnO, ZnS, CdS, BN,AlN, GaN

Finally, we study the symmetry

and GaP) by using first-principles

lowering effect from C3v to Cs whichcalculations based on the density

reduces the magnetic moments; wefunctional theory. We find that C3v

study

geometries are the most stable andpairing and departing distortions.

are spin-polarized. Two majority

The magnetic moment becomes 0 in

spin electrons occupying the defect E

the case of II-VI semiconductors andlevel lead to the magnetic moment of

the magnetic moments become 1 μB

2

II-VI

in the case of III-V semiconductors.

semiconductors. On the contrary, in

We find that these low spin states

the case of III-V semiconductors,

have higher energies than the C3v

threeelectrons

high spin states due to the fact thatoccupying the defect E and A1 levels

the symmetry lowering effect do not

inducesignificantly stabilize the system.

μ

in

B

the

case

majorityspinof

the magnetic moment of 3

μB.
Theenergies

spin
are

large

polarization
inthesemiconductors consisting of firstrow anions, i.e., oxides and nitrides.
The stabilities in the cases of the

75

the

possibilities

of

both

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Unification of massively parallel quantum material simulationand data-driven science
Takeo Hoshi
Department of Applied Mathematics and Physics, Tottori University,
4-101 Koyama-Minami, Tottori 680-8550, Japan.
(

The present project was carried out for the

https://www.pasums.issp.u-tokyo.ac.jp).

joint research between quantum material

Since the analysis method has a general

simulation and data driven science. Related

mathematical foundation, it is also applicable tomathematical studies and software development

other experiments, such as X-ray or electron

were also carried out. The main collaborators

diffraction

are K. Tanaka (Tottori U, D. student), H.

electronic structure calculations were carried

Imachi (Tottori U, now in Preferred Networks),

out for a 10-nm-scale pentacene thin film as aK. Yoshimi (ISSP), I. Mochizuki, T. Hyodo

foundation of flexible transistor [3]. Semi-(KEK-IMSS), T. Fujita (IMS), T. Fukaya

localized wavefunctions that expand over

(Hokkaido U), Y. Yamamoto (UEC), H. Matsui

several tens of molecules were obtained, which(Yamagata U) and T. Ogita (TWCU).

isexperiments.

consistenttoelectron

(ii)

spin

Large-scale

resonance

The main achievements are explained

experiment. The study was carried out by ourhereafter. (i) The data analysis software wasoriginal code ELSES ( http://www.elses.jp/ ),developedfor

an order-N electronic state calculation code

positrondiffraction

total-reflection

high-energynovelwith a ab initio based tight-binding method. In

experimental technique for surface structure

addition, several fundamental methodologies

determination

using

were developed for large-scale calculation of

TRHEPD are being conducted intensively atorganic flexible device materials [4,5]. (iii)theSeveral fundamental numerical algorithms were

Slow

(TRHEPD),[1,2].

Positrona

Experiments
Facility,

InstituteofMaterials Structure Science, High Energy

investigated [6-8].

Accelerator Research Organization, revealing

published for reviews of our recent researchsurfaceactivities in large-scale electronic structure

structureofinterest.

Figure1demonstrates the structure determination of the(iv) Two books were

calculations with supercomputers [9,10].

Ge(001)-c(4x2) surface [2]. At April of 2020,
thesoftwarepromoted todevelopment

activitywasReferences

Project for Advancement of[1] Development of data-analysis software forSoftware Usability in Materials Science in ISSP

total-reflection high-energy positron diffraction76

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(TRHEPD), K. Tanaka, T. Hoshi, I. Mochizuki,

Appl. Math. 376, 112830/1-13 (2020)

T. Hanada, A. Ichimiya, T. Hyodo, Acta. Phys.

[8] K𝜔 -- Open-source library for the shifted

Pol. A 137, 188-192 (2020).

Krylov subspace method, T. Hoshi, M.

[2] Two-stage data-analysis method for total-

Kawamura, K. Yoshimi, Y. Motoyama, T.

reflection

Misawa, Y. Yamaji, S. Todo, N. Kawashima, T.

high-energy

positrondiffraction(TRHEPD), K. Tanaka, I. Mochizuki, T.

Sogabe,Hanada, A. Ichimiya, T. Hyodo, and T. Hoshi:

http://arxiv.org/abs/2001.08707

Submitted;[9] Recent progress in large-scale electronic

Preprint:

Submitted;

Preprint:

https://arxiv.org/abs/2002.12165

state calculations and data-driven sciences, T.

[3] Numerical aspect of large-scale electronic

Hoshi and S. Ito, Chap. 14 of Handbook ofstate calculation for flexible device material, T.

SiliconHoshi, H. Imachi, A. Kuwata, K. Kakuda, T.

Technologies 3rd Ed., Elsevier (2020).

Fujita, H. Matsui, Japan J. Indust. Appl. Math[10] Numerical methods for large scale36, 685-698 (2019).

electronic state calculation on supercomputer, T.

[4] Charge-transfer excited states in the

Hoshi, Y. Yamamoto, T. Sogabe, K. Shimamura,

donor/acceptor interface from large-scale GW

F. Shimojo, A. Nakano, R. Kalia, P. Vashishta,

calculations, T. Fujita, Y. Noguchi, T. Hoshi, J.

Chap. 15 of 21st Century Nanoscience - A

Chem. Phys. 151, 114109/1-8 (2019)

Handbook: Nanophysics Sourcebook (Volume[5]

Computational

conductivity

study

for

electricalpropertiesoforganic

Based

MEMS

Materials

andOne), CRC Press (2019).

semiconducting polymers and metal complexhost systems, M. Ishida, M. Arita, S. Nishino, T.
Hoshi, submitted.
[6] EigenKernel - A middleware for parallel
generalized eigenvalue solvers to attain highscalability and usability, K. Tanaka, H. Imachi,
T. Fukumoto, A. Kuwata, Y. Harada, T. Fukaya,
Y. Yamamoto, T. Hoshi, Japan J. Indust. Appl.
Math 36, 719-742 (2019)

Fig.1 (a) Schematic figure of totalreflection high-energy positron
diffraction (TRHEPD) experiment.
(b) The data analysis of experimental
TRHEPD data for Ge(001)-c(4x2) surface[2].

[7] An a posteriori verification method forgeneralized Hermitian eigenvalue problems inlarge-scale electronic state calculations, T.
Hoshi, T. Ogita, K. Ozaki, T. Terao, J. Comp.

77

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Reduction of Rare Metals in Fuel Cell Catalysts andHydrogen Permeable Membrane
Norihito Sakaguchi
Center for Advanced Research of Energy and Materials, Faculty of Engineering,
Hokkaido University, Sapporo, Hokkaido 060-8628
activity of Pt clusters on non-metal element

We investigated the catalyst adsorption
and diffusion properties on non-metal element

doped

doped graphene and hydrogen dissolution anddiagram.[1] We revealed that the Pt clusters

diffusion properties in the interfaces ofshow less support effect than Pt single atoms.

ceramic materials, with the aid of the first-

Wegraphene

also

based

on

investigated

the

the

energyhydrogenprinciples calculation based on the density

dissolution and diffusion properties in thefunctional theory (DFT).

interfaces of TiN containing O impurities.

At first, we investigated adsorption andWe found that H atoms do not prefer the O

diffusion properties of Pt clusters on non-sites.

metal element doped graphene. This year, we

We also studied the tunneling effect on thealso considered Pt atoms embedded in thealkene hydrogenation process on Rh-basedgraphene basal plane. We performed the total

Intermetallic

energy and electronic structure calculations

dynamics simulation of atomic nuclei [2] andusing The Vienna Ab initio simulation

thickness dependence of the structure andpackage (VASP). We installed a parallelized

magnetism of Ca2RuO4 nanofilm.[3]VASP with Intel® MPI Library and Intel®

References

Math Kernel Library. We found that the[1] J. K. Nørskov, J. Rossmeisl, A. Logadottir,

adsorption energies and diffusion activation

L. Lindqvist, J. R. Kitchin, T. Bligaard,

barriers of Pt clusters on graphene increase by

H. Jónsson, J. Phys. Chem. B, 108

substitutional non-metal element doping. This

(2004) 17886.

catalyst

using

quantum

is because of the strong covalent bonds[2] S. Furukawa, P. Yi, Y. Kunisada, K.

between the Pt atom and substitutional

Shimizu, Sci. Technol. Adv. Mater.

dopants. Therefore, we concluded that these20 (2019) 805.

dopants

ingraphenecanprevent

the[3] H. Nobukane, K. Yanagihara, Y. Kunisada,detachment and surface diffusion of Pt

Y. Ogasawara, K. Nomura, Y. Asano, S.

clusters. We also investigated the catalytic

Tanda, Sci. Rep. 10 (2020) 3462.

78

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab-initio analysis of phonon and electron-phonon interaction
Emi Minamitani
Institute for Molecular Science,
Okazaki, Aichi 444-8585
Heat generation in semiconducting materials

DFT calculation results are used as dataset

has become a critical problem in modern

to train HDNNP. We found that thenanoscale electronics. As the size of electrictraining procedure based on force makes

devices decreases, the power density andthe root mean square error between thedevice temperature increase, which is one offorces predicted by HDNNP and DFT less

the

major

degradation

factorsofcontributing

devicetothethan 40 meV/Å. As typical examples, we

performanceandpresent the results of Si and GaN bulk

reliability.

crystals. The deviation from the thermal

The main carrier of heat in semiconductors is

conductivity

the phonon, which is a quantum of lattice

within 1% at 200 to 500 K for Si and within

vibration.

5.4% at 200 to 1000 K for GaN.

Current

theoreticalframeworks

calculated

using

DFT

is

require accurate prediction of the interatomic
force in the solid. Density functional theory(DFT) calculation is one of the most wellestablished techniques for accurate force
prediction, including the effect of changes inthe electronic state with atomic displacement.
However, the high computational cost limits theapplication of DFT calculation in thermal
conductivity simulations.

Fig. 1 Comparison of thermal conductivity
obtained from DFT calculation and HDNNP for

We apply the high-dimensional neuralbulk Si (a) and GaN (b).

network potential (HDNNP). We generated
the random but reasonable structures werefirst generated from the trajectories ofclassical molecular dynamics simulations,

References

and then the energy and forces in each[1] E. Minamitani, M. Ogura, and S. Watanabe,

structure were evaluated by DFT. These

Appl. Phys. Express, (2019) 12, 095001

79Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electrochemical Reaction Analysis Using Density Functional
Calculation + Implicit Solvation Model
Jun HARUYAMA
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
We have studied charge transfer reaction at

Figure 1 (b) shows the grand potential Ω ofelectrode/electrolyte solution interfaces in Li-

pristine, LinC6mHl/hLi2CO3, and VLi + Li+, Lin-ion batteries (LIB) using density functional

1C6mHl/hLi2CO3

theorycalculation combined withfunction of the chemical potential of an

implicit solvation model. This simulation iselectron µe. In the ESM-RISM calculations, µe

called ESM-RISM,1 i.e., the effective screening

is measured from the potential at inner solution

medium (ESM)2 + the reference interaction site

region ΦS. It is possible to compare µe at

model (RISM)3, and implemented in Quantum

different

Espresso package.4

solution directly.5 The difference between two(DFT)+ Li+(1 M LiPF6 EC), as aelectrodes

contacting

the

same

This year, we focused on Li-ion transfer

equilibrium potentials on different electrodes

reaction (R) at the interface of graphite

provides the electromotive force, Eemf, between

electrode/solid electrolyte interphase (SEI)/

the two electrodes as:

solution (1 M LiPF6 EC) as follows:

Eemf = − (µeq − µLi/Li+)/e

LinC6mHl + hLi2CO3 → Lin-1C6mHl + hLi2CO3 +(1),

Li+(1 M LiPF6 EC) (R).

where µeq represent the equilibrium potential of

ESM-RISM calculations were performed on thereaction (R) and e is the elementary charge.

configuration of a vacuum/slab/soltion system

Once an equilibrium potential µLi/Li+ of Li

as shown in Fig. 1 (a), where the DFT slabtransfer reaction at Li metal electrode isdomaingraphite

determined in the ESM-RISM calculation, the(LinC6mHl)/SEI (inorganic lithium carbonic acid,

electromotive force (or electrode potential

hLi2CO3), and the RISM solvent and ions, (EC,relative to the Li/Li+ reference) can beLi+,electrolyte

immediately derived. Because it was obtained

concentration of typically 1.0 M gives a smallµLi/Li+ = −3.06 eV vs ΦS in a previous study,6Debye screening length of several angstroms,

the result of µeq = −3.17 eV vs ΦS gave Eemf =the RISM region (> 40 Å) used in this0.11 V vs Li/Li+, which is in good agreement

calculation was sufficiently long.

with experiment (0.1 – 0.2 V vs Li/Li+).

andrepresentsPF6−).

Li-inserted

Since

the

80

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a)Electrode/SEI (DFT)

Additionally, it was confirmed that the

Solution (RISM)〜〜

equilibrium potential of reaction (R) cannot

1 M LiPF6 EC

depend on such as the thickness and componentof SEI. In the next physical year, the activation

Li+

Grand potential Ω (eV)

(b)

PF6−

energy of reaction (R) will be revealed underEC

operated LIB working conditions.
0.8

VLi + Li+µ Li/Li+

0.0

References

-0.8
-1.6

[1] S. Nishihara and M. Otani: Phys. Rev. B 96

Pristineµeq(2017) 115429.

-2.4
-3.2

[2] M. Otani and O. Sugino: Phys. Rev. B 73
-3.5

-3.2

-2.9

-2.6

-2.3

(2006) 115407.

-2.0

Chemical potential µe vs. ΦS (eV)[3] A. Kovalenko and F. Hirata: J. Chem. Phys.

Fig. 1: (a) ESM-RISM configurations of the

110 (1999) 10095 (1999).

vacuum/slab/solvent system: the simulation[4] P. Giannozzi et al.: J. Phys.: Condens.

cells of LinC6mHl/hLi2CO3|1M

Matter 21 (2009) 395502; 29, (2017) 465901.

LiPF6

EC

interfaces. (b) Profiles of Ω as a function of µe.

[5] J. Haruyama, T. Ikeshoji, and M. Otani,

The blue and orange lines show Ω ofPhys. Rev. Mater. 2 (2018) 095801.

LinC6mHl/hLi2CO3 and Lin-1C6mHl/hLi2CO3 +[6] J. Haruyama, T. Ikeshoji, and M. Otani: J.

Li+(1 M LiPF6 EC), respectively.

Phys. Chem. C 122 (2018) 9804.

81

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Van der Waals density functional study of molecules adsorbed on metal
surfaces
Ikutaro Hamada
Department of Precision Science and Technology, Graduate School of Engineering,Osaka University, 2-1 Yamada-Oka, Suita, Osaka 565-0871
Accurate description of the molecule-water clusters from monomer to hexamer, andsurface interaction is prerequisite for precise

found that the pentagonal water cluster is more

understanding of chemical processes at surfaces

stable than the hexagonal one on Cu(110). We

and interfaces in diverse systems including

further constructed larger water clusters such as

electrochemical energy conversion devices

octamers composed of pentamers, nonamerssuch as fuel cell, photoelectrochemical cell, andcomposed of pentagon and hexagon, those withrechargeable battery, as well as heterogeneous

two pentagons plus water monomer, and dimer

catalyst for emission control, name only a few.

composed of pentamers. We found that the

For this purpose, the van der Waals density

clusters

functional (vdW-DF) [1] and its variants haveconsistently more stable and that the calculated

been used to study a variety of systems andwater clusters can explain the high-resolution

proven accurate in describing molecule/surface

noncontact atomic force microscopy images [6].

interfaces, as well as bulk systems.

Furthermore, we found that the 2D ice rulecomposedofpentagons

areapplies to explaining and predicting the

In this project, we have studied quasi one
dimensional chain composed exclusively of

structure of water clusters on Cu(110).

pentagonal water on Cu(110). In particular, weReferences

have studied the small water clusters on[1] M. Dion et al.: Phys. Rev Lett. 92 (2014)

Cu(110) to investigate the origin of the246401.

pentagonal water chain.

[2] J. Wu and F. Gygi: J. Chem. Phys 136(2012) 224107.

All the calculations were performed using
STATE,

ourin-house[3] Y. Hamamoto, I. Hamada, K. Inagaki, and Y.

plane-wave

pseudopotential code. We used an efficient

Morikawa: Phys. Rev. B 93 (2016) 245440.

implementation [2,3] of the self-consistent[4] I. Hamada: Phys. Rev. B 89 (2014)

vdW-DF. The rev-vdW-DF2 functional was

121103(R).

used [5].

[5] A. Shiotari and Y. Sugimoto: Nat. Commun.
8 (2017) 14313.

Previously we constructed and optimized

82

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Energy Transport in Hybrid Organic-Inorganic Thermoelectric Materials
Shenghong JU
Department of Mechanical Engineering, The University of Tokyo
7-3-1 Hongo, Bunkyo, 113-8656
Thermoelectric materials can directly
convert waste heat energy to usefulelectricity. During the last decade, theorganic polymers have shown uniquefeatures such as low density, low thermal
conductivity, easy synthesis and versatile
process ability. Using organic polymers inthermoelectric materials appears to havegreat potential for producing relatively
low cost and high performance
thermoelectric devices. However, little
work on modeling and simulation isreported at present.

which the low lattice thermal conductivity
and the high electrical conductivity at low
chemical potential region contributes themost. The results suggest an effective way
to improve the thermoelectric performanceof Si-based materials.

The first main part of last year work is
about the thermoelectric property
investigation of metastable phases ofsilicon. In this work, the phonon andelectron transport properties of metastable
Si-III and Si-XII are investigated bydensity functional theory, as shown in Fig
1 and 2. The metastable Si-III and Si-XII
show one magnitude lower thermal
conductivity than the stable Si-I phase.
The effect of different three-phonon
scattering processes on the thermal
conductivity of different phases were
evaluated by removing specific scattering
processes from the Brillouin zone. Further
electron transport property calculationsuggests that the metastable Si-III and SiXII phases have higher thermoelectric
figure-of-merit than the Si-I phase in

Figure 1: Comparison of phonon transport
property in Si-I, Si-III and Si-XII.

Figure 2: Comparison of electron transport
property in Si-I, Si-III and Si-XII.

83

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

The second main part of last year work
is about the design of magnetic tunnel
junctions (MTJs) using disordered
MgAl2O4. Through Bayesian optimizationand the least absolute shrinkage andselection operator technique combinedwith first-principles calculations, weinvestigated the tunnel magnetoresistance(TMR)
effectof
Fe/disorderedMgAl2O4(MAO)/Fe(001) magnetic tunnel
junctionsto determine structures ofdisordered-MAO that give large TMR
ratios. The optimal structure with thelargest TMR ratio was obtained by
Bayesian optimization with 1728
structural
candidates,
where
the
convergence was reached within 300
structure calculations. Characterization of
the obtained structures suggested that thein-plane distance between two Al atoms
plays an important role in determining the
TMR ratio. Since the Al-Al distance ofdisordered MAO significantly affects theimaginary part of complex band structures,the majority-spin conductance of the Δ1state in Fe/disordered-MAO/Fe MTJs
increases with increasing in-plane Al-Al
distance, leading to larger TMR ratios.
Furthermore, we found that the TMR ratio
tended to be large when the ratio of thenumber of Al, Mg, and vacancies in the[001] plane was 2:1:1, indicating that thecontrol of Al atomic positions is essential
to enhancing the TMR ratio in MTJs withdisordered MAO. The present work
reveals the effectiveness and advantage ofmaterial informatics combined with firstprinciples transport calculations indesigning high-performance spintronic
devices based on MTJs.

Figure 3: Schematics of designingmagnetic tunnel junction for high tunnel
magneto-resistance ratio by combining
Bayesian optimization and first-principles
calculation.
In summary: (1) We have shown thatmetastable Si-III and Si-XII phases havehigher thermoelectric figure-of-merit thanthe Si-I phase. (2) We have successfully
designed the optimal disordered Fe/
MgAl2O4/Fe (001) structure with thehighest tunnel magnetoresistance ratio
optimal by combining the first-principles
transport calculations and Bayesian
optimization.
References[1] S. Ju, H. Chen, M. Kohno, J. Shiomi:
High thermoelectric performance inmetastable phases of silicon: a density
functional theory study, under preparation.
[2] S. Ju, Y. Miura, K. Yamamoto, K.
Masuda, K. Uchida, J. Shiomi: PhysicalReview Research, accepted, 2020.

84

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum Chemical Analysis for High-Performance Polymer Electret
Yucheng ZHANG, Zetian MAO, and Yuji SUZUKI
Department of Mechanical Engineering
The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656
Electret is dielectric material with quasi-

reaction can act as a strong charge trapping

permanent charges. Vibration Electretsite [2]. Therefore, we investigate charge

Energy harvesting (VEEH) is a clean way

stability of candidates with free amine

to convert environmental energy intofunctional group which can react with -electricity by electrostatic induction more

COOH end group of CTX-A. Electron

efficiently

oraffinity and ionization potential obtained

piezoelectric counterparts [1]. VEEH canfrom quantum chemical calculation are

be applied to low power electronics such as

used to evaluate the electron trap energy

wireless sensors, implantable medical

and hole trap energy of possible candidates

equipment and wearable device. Since theafter dehydration condensation respectively.

thanelectromagnetic

power output of the VEEH is proportional

Electronaffinityiscalculatedbyto the square of surface potential of thecomparing molecular energy at neutral andelectret, it is necessary to discover electret

negatively-charged state while ionizationmaterial with high surface charge density.

potential is computed by comparing

Furthermore, if we could find electret

molecular energy at neutral and positively-

suitable for both negative and positive

charged state. The calculated ionization

charging, the power output of VEEH will

potential of CYTOP based electret is asboom by 4 times theoretically.

follows: 13.12 eV (CTX-S), 12.03 eVCYTOP (AGC Co. Ltd.) is a fluorinated(CTX- A), 9.81 eV (CTX-M) and 7.81 eV

amorphous polymer, with its chemical(CTX-A/TAEA). Figure 2 visualizes the

structures shown in Figure 1. There arethree kinds of commercialized CYTOP, S,
A and M. CTX-A has carboxyl end groups
and CTX-M has alkoxysilane/amide end
groups. According to quantum chemical
analysis of CYTOP series with different

Fig. 1. Chemical structure of CYTOP series.

end groups, the amino bond formed after85

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

This work was partially supported by
JST CREST Grant Number JPMJCR15Q3
and JPMJCR19Q1, Japan. The calculationis performed with SGI ICE XA ISSP
system B and every calculation is held with
1 node (24 CPUs). The energy of theFig. 2. Visualization of hole trapped
orbitals for positive state of CTX-A/TAEA.

molecule is computed by DFT to CAMB3LYP/6-31+G(d,p) levelby using

quantum chemical simulation software
GAUSSIAN[4].

Molecular

dynamic

simulation package GROMACS [5] andsolid-state analysis package VOTCA-CTP
are also used [6] for more accurate
Fig. 3. Normalized TSD spectra of CYTOP
electrets charged to +2 kV.

estimation. In case of CYTOP hexamers,

hole trapped orbitals of positively charged

CPU

the calculation cost is approximately 150
hours

for

quantumchemicalcalculation, 100 CPU hours for MD

CTX-A/TAEA monomer. It is shown thatsimulation and 5 CPU hours for multipole

the hole is located near the amide bond,analysis and solid-state analysis.

which is formed by the reaction between
the carboxy end group and TAEA.

References

Thermally stimulated discharge (TSD)[1] Suzuki Y. IEEJ Trans. Electr. Electr.

measurement is also done for comparison

Eng., Vol. 6, 101-111 (2011).

between calculation and experiment. Figure[2] Kim S., et al. Sci. Technol. Adv.

3 shows the TSD spectra of CYTOPMater., Vol. 19, 486-494 (2018).

polymers for positive charging. It is found[3] Kim S., et al., IEEE Conf. Electr. Insul.

that CTX-A/TAEA has the highest charge

Dielectr. Phenom., Richland, 8-1, (2019).

thermal stability with smallest computed[4] M. Frisch et al., “Gaussian 09, Rev. A.

ionization potential value. In addition, the1,” Gaussian, Inc. Wellingford, CT, 2009.

TSD spectra for positive charging exhibit[5] S. Pronk et al., Bioinformatics, 29,

multiple peaks, indicating the difference in(2013) 845-854.

the charge trapping mechanisms between[6] V. Rulhe et al., J. Chem. Thery Comput.,negative and positive charges [3], which

7, (2011), 3335-3345.

will be analyzed in the future.

86

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical modeling of carrier
localization/delocalization and related phasetransitions
Hannes RAEBIGER
Department of Physics, Yokohama National University79-5 Tokiwadai, Hodogaya-ku, Yokohama 250-8501

1

Introduction

We investigate trends in carrier localizationin defective semiconductor/insulator systems
focusing on phase transitions. We have previously illustrated the mechanistic origin of
the Mott transition and related excitonic insulator phases [1], as well as strain induced
piezomagnetic transitions in magnetic semiconductors [2]. This year, we have clarified carrier-induced magnetic transitions intransition-metal doped Ga2 O3 systems [3, 4],as well as charge trapping in resistive memory(ReRAM) devices [5]. Also, an introductory
review of first principles methods for defects
in semiconductors/insulators was published asa book chapter [6].

2

Ga2 O3 systems

We carry out density-functional calcualtions
using the VASP code with in-house developed corrections for band-gap [7] and selfinteraction [2]. Band-gap correction of Ga2 O3
is achieved applying non-local external potenN LEP =-6.4 eV,tial parameters as follows. VO,sN
LEP
VO,p =-2.0 eV for oxygen [7], and for Ga,
N LEP =10.0 eV, V N LEP =2.5 eV, andwe use VGa,sGa,p
UGa,d =9.0 eV to achieve best fit of several
physical parameters (see Table 1). For Cr 3d,
we set U =2.6 and J=1.0 eV. [7] We further
cross-validate these parameters against selfinteraction corrected VP-SIC in the KKR-CPA

framework (see [3] for details).
Table 1: Physical properties of β-Ga2 O3 . Eg
is band gap energy (eV) and m∗e is effective
electron mass.[3]

a(Å)
b/a
c/a
V (Å3 )∆V (%)β(deg)
Eg∗
me /mepure GGA
12.40
0.250
0.475
219.43
+5.1
103.8
2.0
0.19

GGA+NLEP
11.90
0.251
0.471
197.26
-5.5
104.1
4.7
0.37

Exp.
12.2140.249
0.475
208.85103.824.9
0.28

Carrier-mediated ferromagnetism in Crdoped β-Ga2 O3 .[3] First of all, we find that Cr
prefers the octahedral lattice site in β-Ga2 O3
by ∼1 eV against the tetrahedral site. We thenshow that Cr in the octahedral site has a negative charge transition close to conduction band
minimum, so the system may become charged.
Magnetic interaction among Cr impurities isinvestigated as a function of Cr–Cr distance up
to ∼8.5Å. For nonconductive systems, we finda weak antiferromagnetic coupling for nearest
neighbor Cr–Cr pairs, and zero interaction for
all other pairs investigated. We then include
carrier-electrons, which cause negative charging of Cr impurities. We further find that suchcarrier-doping switches on a strong ferromag-

87netic interaction, which persists up to ∼6ÅCr–
Cr separation.
Optical properties  and κ phases of Ga2 O3
doped with cobalt.[4] In collaboration with experimental work, we investigate the modulation of optical absorption edge in  and κ
phases of Ga2 O3 by Co doping. Co impurity
levels, as well as those of some typical native
impurities, are calculated from first principles.
We then calculate the optical absorbance forseveral Co doped systems at several defect concentrations. This is used to re-interpret experimental observations, which previously asserted
band-gap modulation based on changes in optical gap upon Co doping. However, our calculation shows that the optical gap changes instead are due to Co impurity levels. We further
present a new band diagram to clarify changes
in work function due to Co doping in thesesystems.

3

Low resistivity High resistivity
state
state

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Q>0
CB
eφ(z)

CB
eφ(z)
EF
VB

eVb

Q<0
CB
eφ(z) E
F

VB

+Vb
eφb

EF
VB

e
e
e

–Vb

eVb

e

e
e
e

e
e

eφ(z) CBEF
VB

Figure 1: Band bending solutions of ReRAM
device, and switching by external bias.
241115(R).
[2] H. Raebiger, S. Bae, C. Echeverrı́aArrondo, and A. Ayuela: Phys. Rev.
Mater. 2 (2018) 024402.

Charge trapping in ReRAM
systems[3] K. Ichihashi, H. Shinya, and H. Raebiger:
Appl. Phys. Express 13 (2020), 021002.

We describe resistive memory ReRAM devices by a metal/insulator/metal sandwich
structure, and investigate charge trappingby numerically solving Poisson’s equation.
We develop a self-consistent Poisson solver,where charge stored in device is solved selfconsistently together with potential over device under different bias voltages. We discover
new band-bending solutions characterized bydifferent amount of charged stored in the system, and reversible switching between thesedifferently charged states, illustrated in Figure 1. This electrostatic switching mechanism
provides a novel interpretation for ReRAM operation, and resolves the mystery of extremely
fast sub-nanosecond switching.

[4] K. Yamanaka, H. Raebiger, K. Mukai,
and K. Shudo: J. Appl. Phys. 127 (2020)065701.
[5] H. Raebiger, A. C. M. Padilha,
A. R. Rocha, and G. M. Dalpian:
J. Phys. D (accepted, 2020, DOI:
10.1088/1361-6463/ab7a58).
[6] E. Ertekin and H. Raebiger: Ch. 7 in
Characterisation and Control of Defects
in Semiconductors, ed. F. Tuomisto (IET,
United Kingdom 2019) pp. 289–343.
[7] H. Raebiger, S. Lany, and A. Zunger:
Phys. Rev. Lett. 101 (2008) 027203.

References[1] S. Bae and H. Raebiger: Phys. Rev.
B (Rapid Communications) 94 (2016)88

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio study on the metallization andsuperconductivity in metallic superhydrides
Ryosuke Akashi
Department of Physics, University of Tokyo
Hongo, Bunkyo-ku, Tokyo 113-0033

In this project, we studied the mechanism of
the metallic and superconducting properties ofthe superhydrides–the compounds containing
anomalously large formula ratio of hydrogen–recently synthesized under megabar pressures.
The discovery of the 200-kelvin superconductivity in the compressed H2 S (Ref. [1]) has
triggered extensive study on the pressure induced superconductivity of hydrogen compounds. Later studies revealed that the novel
phase containing excess hydrogen atoms, H3 S,
emerges under extreme pressures, which is responsible for the experimentally observed highTc superconductivity. This has motivatedthe exploration of pressure induced hydrogenexcess compounds.
First, we numerically examined the superconducting properties of some crystalline lanthanum and yttrium superhydrides, LaHx andYHx , for possible explanation of the experimentally observed superconducting transition
temperature (Tc ) (260 K and 240 K, respectively) in these systems. We calculated Tc
for theoretically predicted crystal structuresof LaH10 and LaH16 from first principles.
Specifically, we solved the gap equation of thedensity functional theory for superconductors(SCDFT) (Ref. [2, 3, 4])with the Migdal approximation. Also, theelectron-electron Coulomb repulsion that suppresses the pairing is also incorporated. ∆ isthe order parameter and nk labels the KohnSham band index and√crystal wavenumber,2 + ∆2
respectively. Enk =ξnk
nk and β is
the inverse temperature. The non-diagonalpart of the kernel of Eq. (1) K is composedof the phononic and electronic contributions:
K = Kph + Kel . On the other hand, the diagonal part Z includes only the phononic one:
Z = Z ph . To evaluate the phononic parts
we need to calculate the Eliashberg function
α2 F (ω), which is roughly the phonon densityof states weighted by the coupling strength
to the electrons. The electronic part is calculated as the two-particle matrix element of
the screened Coulomb interaction, where theone-particle states and dielectric function arecalculated by the first-principles Kohn-Shamequation. All the components were calculatedwith the plane-wave basis code package quantum espresso (Ref. [5]). The phononic properties of the yttrium compound was supplemented with the anharmonic correction using
the stochastic self consistent harmonic approximation [6].
We show in Table I the values of Tc calculatedwith the SCDFT gap equation [Eq.(1)],βEtanh 2n′ k′2
1∑∆nk = −Znk ∆nk −Knkn′ k′∆n′ k′ . as well as characteristic parameters of α F (ω)
2 nk
En′ k′∫
α2 F (ω)(1)
λ = 2 dω
,
(2)
ω ]
[ ∫
Here, the phonon-mediated Cooper pairing ef2
α2 F (ω)
logω .
(3)ωln = expdω
fect is included within the Eliashberg theoryλω

89Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

(c)

(b)

(a) 20Sulfur-p

15
Energy [eV]10(1)tSpσ-Hs

5
0

Γ

-5

X

-10

Hydrogen-s

M(1)
tSs-Hs(4)tHs-(H)-Hs

-15
-20

Sulfur-s

-25
Γ

X

M

Γ

R

M

X

0.2
0.4
R0
DOS [1/(eV sp unit)](4)
tSs-SsFigure 1: (a) Crystal structure of the high-Tc phase of cubic H3 S and its band structure and DOS.
The thin and bold lines represent the first-principle and Wannier band structures, respectively.
(b) The simple cubic Brillouin zone and positions of the loop-like continuous saddle points inthe band structures. (c) The minimal Wannier model that reproduces the saddle loop aroundthe M point. See Ref. [12] for more details.

Table 1: Coupling constant λ (Eq. (2)), typicalfrequency ωln (Eq. (3)), and the superconducting transition temperature Tc calculated with
the SCDFT gap equation Eq. (1).
LaHx [9]YHx
LaH10 LaH16 YH6Pressure (GPa)
200
200
165
λ
3.75
1.82
1.71
ωln
905
1366 1332
Tc (K)
271
156
156

Experimentally observed Tc for the lanthanum
systems strongly depends on the trials [7, 8].
The synthesis with excess hydrogen yielded Tc
varying from 250 K to 210 K. Our calculation
indicates that the high-Tc phase corresponds to
LaH10 (left column), whereas the low-Tc phase
could be a mixture of LaH10 and LaH16 (middle column). We have published this result
in Ref. [9]. For the yttrium hydride, on theother hand, our calculated Tc (right column)
was substantially lower than the experimental value (∼ 240 K). At this point we have notreached to a plausible understanding of the origin of the discrepancy [10].

state in the sulfur superhydride H3 S. According to preceding studies, it hosts a sharp peakat the Fermi level in the electronic density ofstates (DOS) N (E) (Fig. 1 (a)), which has arole of boosting the Tc via the relation λ ∝N (EF ) with EF being the Fermi level. Its origin has, however, yet been clarified. To elucidate the mechanism of its formation, we first
performed a close analysis of the band structure and found that the DOS peak structure
mainly originates from the loop-like continuous
saddle points around the M point in the primitive cubic Brillouin zone (Fig. 1 (b)). Next, weconstructed the Wannier model using quantum espresso and Wannier90 (Ref. [11] program packages. Our model consists of sulfurs, p and hydrogen-s like orbitals and almost
perfectly reproduces the first-principles band
structure especially around the Fermi level(Fig. 1 (a)). We then calculated the eﬀective
band structures with this Wannier model withomitting the interorbital hopping parameters.
Finally, we found that a simple model reproduces the key feature in the band structure;
the saddle-point loops around the M point. In
this model (Fig. 1 (c)), the simple cubic ScF3
sites and the nearest-neighbor and selected far-

We also addressed the metallic electronic

90

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ther neighbor hopping parameters have been
extracted from the original Wannier model.
The nearest-neighbor hoppings for the s-likeand p-like orbitals on the simple cubic ScF3
lattice geometry yields a saddle point at the
M point, and in addition, the selected farther
neighbor hopping “pushes down” the state at
the M point to form the continuous loop of thesaddle point. This understanding on the origin of the DOS peak in the celebrated high-Tc
superconductor H3 S has been published [12].
Computational detail.
The generalized
gradient approximation for the exchangecorrelation potential was employed [13] for the
calculations of LaHx , YHx and H3 S. MPI parallelized calculations were performed with respect to k points (-npool option) as implemented in pw.x code. The screened electronelectron Coulomb matrix elements [4] were
calculated with an in-house code with the
openmp parallelization. The calculations weremainly done in System B.

References[1] A. P. Drozdov, M. I. Eremets, and I. A.
Troyan, V. Ksenofontov, and S. I. Shylin,
Nature (London) 525, 73 (2015).
[2] M. Lüders, M. A. L. Marques, N. N. Lathiotakis, A. Floris, G. Profeta, L. Fast, A.
Continenza, S. Massidda, and E. K. U.
Gross, Phys. Rev. B 72, 024545 (2005).

[6] I. Errea, M. Calandra, and F. Mauri,Phys. Rev. B 89, 064302 (2014).
[7] M. Somayazulu, M. Ahart, A. K. Mishra,
Z. M. Geballe, M. Baldini, Y. Meng, V. V.
Struzhkin, and R. J. Hemley, Phys. Rev.
Lett. 122, 027001 (2019).
[8] A. P. Drozdov, P. P. Kong, V. S. Minkov,
S. P. Besedin, M. A. Kuzovnikov, S.
Mozaﬀari, L. Balicas, F. F. Balakirev, D.
E. Graf, V. B. Prakapenka, E. Greenberg, D. A. Knyazev, M. Tkacz, and M.
I. Eremets, Nature (London) 569, 528(2019).
[9] I. A. Kruglov, D. V. Semenok, H. Song,R. Szczȩániak, I. A. Wrona, R. Akashi,
M. M. D. Esfahani, D. Duan, T. Cui, A.
G. Kvashnin, and A. R. Oganov: Phys.
Rev. B 101, 024508 (2020).
[10] D. V. Semenok, R. Akashi et al., in preparation.
[11] A. A. Mostofi, J. R. Yates, G. Pizzi, Y.S. Lee, I. Souza, D. Vanderbilt, and N.
Marzari, Comput. Phys. Commun. 185,
2309 (2014).
[12] R. Akashi: Phys. Rev. B 101, 075126(2020).
[13] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys. Rev. Lett. 77, 3865 (1996).

[3] M. A. L. Marques, M. Lüders, N. N. Lathiotakis, G. Profeta, A. Floris, L. Fast, A.
Continenza, E. K. U. Gross, and S. Massidda, Phys. Rev. B 72, 024546 (2005).
[4] R. Akashi, M. Kawamura, S. Tsuneyuki,
Y. Nomura, and R. Arita, Phys. Rev. B
91, 224513 (2015).
[5] P. Giannozzi et al, J. Phys.: Condens. Matter 21,
395502 (2009);
http://www.quantum-espresso.org/.

91

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on physics of gap-state control
at metal/semiconductor interfaces
Takashi NAKAYAMA

Department of Physics, Chiba University
1-33 Yayoi, Inage, Chiba 263-8522
Due to the break of atomic bonds and the lackof translational symmetry, gap states appear insemiconductor layers around metal/semiconductor
interfaces, which have the energy position in theband gap and are localized around the interface.
These states induce the electron transfer between
metal and semiconductor layers and determine avariety of physical phenomena at the interface,such as Schottky barrier (SB), defect density, andmetal-atom ionization. However, it is still unclear
how to control the gap states. In this works, westudied the SB and tunneling current at various
interfaces and clarify the origins of gap-state
generation/annihilation and deformation using thefirst- principles calculations.
We first consider metal/Ge interfaces, whereFermi energies of most of metals are locatedaround the valence-band top of Ge irrespective of
the kinds of metals. This is called the Fermi-level(FL) pinning and interrupts desirable low-resistive
metal/n-Ge contacts. Although the breakdown of
FL pinning was recently observed at TiN/Ge(001)interfaces, its origin has not been clarified. To
simulate the interfaces, we adopt (1×1)--(3×3)
TiN/Ge(01) repeated-slab models with various
interface structures and calculate their SBs using
local potential profiles.
Figure 1 shows calculated SBs for hole carriers
ate various interfaces. The SBs at Ti-rich interfaces
like abrupt (a-2) are around 0.0eV corresponding to
the FL pinning, while the SBs at N-rich interfaces
such as (b-2) and (c) have large values above 0.3eV,
which is in good agreement with experiments. The
origin of such SB variation is understood byobserving the projected densities of states (PDOS)
of interface atoms, which are shown in Fig.2.

Fig.1. Left: calculated Schottky barriers for holecarriers at various TiN/Ge interfaces. Right:
schematic pictures of interface structures. (a-2):
abrupt Ti-rich interface, (b-2) and (c): N-richinterfaces with TiN2 and Ge3N4 interface layers.

For (a-2) interface, the continuous PDOS, thus thegap states, appear around 0.0eV for interface Ge
atoms due to the orbital hybridization between Ti
and Ge, which induces electron transfer from TiN
to Ge and realizes the FL pinning. On the other
hand, we can see the suppression of gap states in
the PDOS of interface Ge for (b-2) interface, whichis caused by the production of interface N-Ge
bonds. In this way, the interface covalent bonds
eliminate the gap states in interface Ge layers.
Next, we consider how the interface bonds affect
the SBs. We artificially produce metal/X/Ge(001)interfaces with various segregation atoms, X, thatterminate interface Ge, and calculate the SBs, theresults being shown in Fig.3 for Al/X/Ge cases. We
found the chemical trend that the segregation of IIand III-family atoms lowers the SBs, while that ofV- and VI-family atoms raises the SBs. By
analyzing electronic structures in details, it was
shown that such trend reflects the valency of X

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig.4. (a): calculated tunneling probability ofelectrons at Si-p/n junction as a function ofelectric field, for the cases with (red line) andwithout (blue) dopants. (b) and (c): energy
distribution of tunneling electrons and resonancestate at doped p/n junction.

Fig.2. Calculated projected densities of statesof interface atoms around TiN/Ge interfaces
with (a-2) and (b-2) structures shown in Fig.1.
Ge(1) and Ge(2) correspond to the first andsecond layer germanium atoms, respectively.

Si-p/n junction. Figure 4(a) shows calculated
current as a function of applied electric field. Whenthe dopant is embedded in p/n junction (red line),
the current is markedly enhanced, which is causedby the tunneling through the dopant state as seen in
the energy spectra in Fig. 2(b). Figure 2(c) shows awavefunction of such dopant state. This state is aresonance state between isolated dopant state andgap state produced by the penetration of
conduction-band state of right-handed bulk Si
layers into the band gap. By changing not only thespacial and energy positions of dopant state but
also the electric field, we can control suchresonance. In this way, the gap-state characteristics
are controlled by the electric field.
All these calculations were performed using thexTAPP, VASP, and pspwf codes. In order to realize
the calculations for the present interface systems,
because the system is made of a large number ofatoms (300-1000 atoms), the advanced computing
facility having multi-task and higher-speed CPU(more than 64 cores × 2.5GHz), larger-size
memory (around 128GB), and larger-size strange(more than 1 TB) is indispensable. These
conditions are realized only by the ISSP
supercomputing systems.

Fig.3. Calculated Schottky barriers for holecarriers at Al/X/Ge interfaces with various
segregation atoms, X. Ec and Ev denote theconduction-band-bottom and valence-band-top
positions of bulk Ge, respectively.

atoms; when X-Ge bonds are produced at theinterface, the electron transfer occurs from X to Ge
for X atoms with less than 4 valence electrons,
while the additional transfer occurs from X to Al
for X atoms having more than 4 electrons. In thisway, not only the termination of interface Ge bonds
but also the kinds of termination atom is important
to deform the gap state and depin the FL.
Finally, we study how the gap states change inelectric field. We consider the tunneling current at

93Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical analysis of ion conduction mechanism of highly
concentrated electrolytes for secondary batteriesAtsuo YAMADA
Department of Chemical System Engineering,
The University of Tokyo, Bunkyo-ku, Hongo, Tokyo 113-8656
Highlyconcentrated

electrolytes

have

imposed

under

NVT

ensemble.

The

recently attracted much attention owing to theirequilibration of 10 ps at 1 fs time interval was

unique electrochemical properties derived fromfollowed by the sampling of 200 ps.

an unusual coordination structure, where theWith increasing the salt concentration, theligand (solvent/anion) exchange reactions areligand exchange reactions become active

responsible for the ion transport, while themainly via FSA anions (Fig. 1). The increased

vehicular-type mechanism is dominant in theion radius (decreased Lewis acidity) of cations

diluted electrolyte [1]. Herein, we theoreticallyalso activates the ligand exchange reactions byinvestigated the salt concentration dependence

weakening the interaction with the ligands.

of ionic conduction mechanism in AFSA/DME

Therefore, both the higher concentration andelectrolyte (A = Li, Na, K) using quantum

increased cation size should promote the ligand

molecular dynamics (MD) simulations.

exchange-type ion transport.

All the calculations were performed using
divide-and-conquer density functional tight-

Referencesbinding (DC-DFTB) method [2]. A modified[1] M. Okoshi, C.-P. Chou and H. Nakai, J.

3OB parameter set based on first-principles

Phys. Chem. B 122, 2600 (2018).

calculations was adopted, and a constant[2] Y. Nishimura, H. Nakai, J. Comput. Chem.,

temperature condition of 298.15 K was

40, 1538 (2019).

Fig. 1 Relationships between frequencies of ligand exchange, A, and salt concentration.

94

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles Theoretical Study of Chemical
Reactions in Heterogeneous Catalysts
S. E. M. PUTRA, T. N. PHAM, S. A. Wella, F. MUTTAQIEN, Y. J. WONG, H. KIZAKI,K. INAGAKI, Y. HAMAMOTO, I. HAMADA, and Y. MORIKAWA
Department of Precision Engineering, Graduate School of Engineering,Osaka University, 2-1 Yamadaoka Suita, Osaka 565-0871

In 2019-2020, we carried out theoreticalanalysis of chemical processes at surfaces andinterfaces, formic acid adsorption and decomposition on Cu(111) [1], enhancement of CO2hydrogenation by O-C-O bending vibration
mode [2], trimer formation of NO Cu(111) [3],and CO oxidation and oxygen reduction reaction at Pt single atom catalyst supported
by graphene edges [4]. We also investigateddopant in semiconductors, namely, transition
metal doped ZnSnAs2 [5], and As and B codoping in Si [6]. In this report, we report theenhancement of CO2 hydrogenation by vibration excitation [2].
Recently, formic acid (HCOOH) has been
considered as a potential material for hydrogenstorage. Storage of HCOOH is easier and safer
compared with other hydrogen storage material because HCOOH is a non flammable liquid
at STP. HCOOH can be decomposed on metal
surfaces through dehydrogenation process into
CO2 and H2 , or dehydration process into CO
and H2 O. Cu catalysts have been reported to
selectively decompose HCOOH through dehydrogenation process. The decomposition of
HCOOH does not occur on Cu(111) when exposed to the gas phase HCOOH at room temperature. On the Cu(111) surface, HCOOH
was reported to form polymeric structures
when exposed to the gas phase HCOOH at low
temperatures, then the decomposition occurs
by heating those polymeric HCOOH.
In the present study, we have investigated

the adsorption and decomposition mechanismsof monomeric HCOOH on Cu(111) by using
density functionals that account for the vdW
forces and compared with room temperatureexperimental results.
Our calculations were performed using the
STATE (Simulation Tool for Atom TEchnology) code[7]. Here, we compared results obtained using the PBE functional with thoseusing the van der Waals density functionals(vdW-DFs), i.e., optB86b-vdW and rev-vdWDF2 [8] functionals. We also included the dispersion correction proposed by Grimme with
PBE (PBE-D2). The implementation of theself-consistent vdW-DF in the STATE code is
described in Ref. [9].
The reaction path for the decomposition(Edec ) of the OH-perpendicular configurationon the Cu(111) surface is shown in Fig. 1. The
calculated activation energies of decomposition(Edec ’s) with ZPE correction are 0.37 eV, 0.31
eV, 0.32 eV, and 0.30 eV for PBE, PBE-D2,
rev-vdW-DF2, and optB86b-vdW functionals,
respectively, indicating that the Edec are almost independent among the considered functionals in this work. PBE-D2 and vdW-DFs
produce lower Edec than Edes by (0.16−0.27
eV).
Figure 2 shows the calculated desorption
and decomposition rates per surface adsorbate.
In this analysis, we used the calculated results by rev-vdW-DF2 energy functional. At
low temperatures, the decomposition process

95

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

becomes faster than the desorption process,while at higher temperatures, the desorption
process becomes dominant due to large preexponential factor for the desorption process
and the transition temperature between thetwo processes is ∼ 187 K. These results arein very good agreement with the experimental
situation that there is no HCOOH decomposition on Cu(111) by exposing the surface to thegas phase HCOOH at room temperature.

References[1] S. E. M. Putra, F. Muttaqien, Y.
Hamamoto, K. Inagaki, I. Hamada, and
Y. Morikawa: J. Chem. Phys. 150 (2019)154707.

Figure 1: (a) Decomposition process of the
OH-perpendicular configuration. IS, TS, andFS represent initial state, transition state, andfinal state, respectively. (b) Energy profile for
the OH-perpendicular configuration
decomposition on Cu(111).

[2] J. Quan, F. Muttaqien, T. Kondo, T.
Kozarashi, T. Mogi, T. Imabayashi, Y.
Hamamoto, K. Inagaki, I. Hamada, Y.
Morikawa, and J. Nakamura: Nature
Chem. 11 (2019) 722.
[3] T. N. Pham, Y. Hamamoto, K. Inagaki,
D. N. Son, I. Hamada, and Y. Morikawa:
J. Phys. Chem. C 124 (2020) 2543.

Temperature / K
500

250

167

125

100

12

1.0×10Rate per surface adsorbate / s-1

Desorption: lattice gas model
Decomposition[4] S. A. Wella, Y. Hamamoto, F. Iskandar,
Suprijadi, Y. Morikawa, and I. Hamada:J. Chem. Phys. 152 (2020) 104707.

8

1.0×104

1.0×10[5] H. Kizaki and Y. Morikawa: Jpn. J. Appl.
Phys. 58 (2019) 110601.

0

1.0×10-4

1.0×10[6] K. Tsutsui and Y. Morikawa: Jpn. J.
Appl. Phys. 59 (2020) 010503.

-8

1.0×10

0

0.002

0.004

0.006

0.008

0.01

-1

Temperature / K[7] Y. Morikawa: Phys. Rev. B 51 (1995)
14802.

Figure 2: Calculated reaction rates per surface
adsorbate for the desorption and decomposition of OH-perpendicular configuration. Red
dashed line with circle and blue solid line withsquare dots line represent the decompositionand desorption rates obtained by using the 2D
lattice gas, respectively.

[8] I. Hamada:
121103.

Phys. Rev. B 89 (2014)[9] Y. Hamamoto, I. Hamada, K. Inagaki,
Y. Morikawa: Phys. Rev. B 93 (2016)245440.

96

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Design of Gate Dielectrics of Future GaN Power
DevicesKenji SHIRAISHI
Institute for Materials and Systems for Sustainability,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601
We

performed

thedensity-functionalenergy barriers. The calculated occurrence rate

calculations that clarify atomic and electronic

for the transformation is high enough to assure

structures of the oxygen vacancy VO inthat the thermal annealing at typical temperatureamorphous (Al2O3)1-x(SiO2)x mixed oxides, aand time causes the conversion of thepromising candidate for the gate insulator inelectrically active VO to the inactive VO,

future GaN power devices [1]. We constructed

providing a further advantage of (Al2O3)1-

microscopic models for the amorphous structurex(SiO2)x as the gate insulator over other oxides

by the melt-quench scheme and then examine allsuch as SiO2 and Al2O3.
Density of states

the possible oxygen vacancies and determine thetotal-energy minimized VO structures. We founda clear tendency that the VO formed at theoxygen site surrounded by less Al atoms has

(a)

-20

(b)

-20
-20

lower formation energy. More importantly, we

VO state
-15

-15
-15

-10

-5

0

5

-10

-5

0

5

-10

-5

Energy level (eV)

0

5

10

10

(c)

find that VO surrounded by Si atoms alone
induces no deep levels in the energy gap of GaN,
whereas VO surrounded by more Al atoms
induces a deep level. This theoretical finding
Fig.1: Density of states of the (Al2O3)0.70(SiO2)0.30
mixed oxide containing a single oxygen vacancy VO
obtained by HSE, (a) surrounded by Al atoms and (b)surrounded by Si atoms. The origin of the energy is set
at the valence band maximum. (c) Atomic structure of a
VO surrounded by Si atoms. A Si-Si bond is formed after
removal of the oxygen atom. Silver, blue, and red
spheres represent the Al, Si, and O atoms, respectively.

strongly infers that the majority of VO in
amorphous (Al2O3)1-x(SiO2)x is electricallyinactive and not very harmful in device
operations. We further explore the possibilitiesof the structural transformation from theReferences

electrically active VO to the electrically inactive[1] D. Kikuta, K. Itoh, T. Narita, and T. Mori,
Al2O3/SiO2 nanolaminate for a gate oxide ina GaN-based MOS device, J. Vac. Sci.
Technol. A 35, 01B122 (2017).

VO. We identified reaction pathways for suchtransformation and obtain the corresponding97

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of Thermoelectric Properties of Clathrate
Compounds with Ab Initio Calculations
Masato OHNISHI
7-3-1, Hongo, Bunkyo-ku, The University of Tokyo, Tokyo 113-8656
Clathratecompounds

aredoping level can enhance ZT significantly (seepromisingcandidates for thermoelectric materials in terms

Figure).

of the “electron-crystal phonon-glass” concept.

properties, we obtained possible structures atClathrate compounds are composed of guest

finiteatoms encapsulated in cagelike structures. It is

expansion and Monte Carlo method [1] andexpected that electrons can smoothly transport

thermoelectric properties were averaged forin the frame work while phonons are scattereddifferent possible structures. Phonon properties

by guest atoms. Particularly, in type-I clathrateof the clathrates were calculated with using acompounds, guest atoms vibrate in a strong

self-consistent phonon (SCP) theory based onanharmonic

first-principles calculations [2]. Our state-of-potential

because

they

are

To

investigate

temperature

analysiswithmethodthermoelectric
using

composed of a Weaire-Phelan structure, which

the-artshows

divides a space with the maximum volume withagreement with experimental data.

aclusteragood

the same cross-sectional area. While off-center
clathrates such as type-I Ba8Ga16Sn30, in which
guest

atoms

vibrateinanharmonic

potential,

haveconductivity,

silicon-basedadouble-welllowthermalclathrates

arepreferable for actual use in terms of thematerial cost.

Fig. Temperature-dependent dimensionlessthermoelectric figure of merit (ZT) of type-I Sibased clathrate with different carrier
concentrations.

In this study, we show that aluminum
substitutions

canenhancethermoelectricperformance of silicon-based clathrates, type-I

References

Ba8Ga16Si30.

[1] R. Kubo: J. Phys. Soc. Jpn. 12 (1957) 570.

Comparing

calculated

thermoelectric figure of merits (ZT) with thoseM. Ångqvist, P. Erhart et al., Chem. Mater. 29,

obtained in experiment, we concluded that (a)7554 (2017) and 28, 6877 (2016).

aluminum additive enhances ZT with lowering[2] Tadano et al. Phys. Rev. Lett 120, 105901

doping level and (b) further suppression of(2018).

98

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculations of multiferroic interfaces
Yoshihiro GOHDA
Department of Materials Science and Engineering, Tokyo Institute of Technology
J1-3, Nagatsuta-cho 4259, Midori-ku, Yokohama 226-8502, Japan

manent magnets [6–8].

To obtain large magnetoelectric coupling in
multiferroic materials, multiferroic interfaces
are promising, because single-phase multiferroic materials exhibit typically antiferromagnetism preventing from having net magnetization [1, 2]. In addition to multiferroic interfaces, many types of magnetic interfaces are offundamental importance to enhance the performance of magnetic materials. Nevertheless,our understanding from electron theory is far
from being satisfactory. Since first-principles
calculations of magnetic interfaces are computationally challenging, such study is also of importance in the sense of large scale computations.

0.4∆O-Ti (Å)

0.3
0.2
0.1
0.0

−0.1
−0.2
−0.3
−0.4

Fe(Y)Si(Z) (Pup)
Si(Y)Si(Z) (Pup)
CoCo
(Pup)

Fe(Y)Si(Z) (Pdown)
Si(Y)Si(Z) (Pdown)
CoCo(Pdown)TiO (1) TiO (2) TiO (3) TiO (4) TiO (5)Figure 1: Relative displacements ∆O−Ti = zO −zTi in the tetragonal BaTiO3 (001) film for each interface. For the Fe(Y)Si(Z) case, average valuesfor ∆O−Ti are shown. The first layer TiO2 (1) is
the interface layer, whereas the fifth layer TiO2 (5)has the bulk atomic positions of BaTiO3 .

In this project, we performed first-principles
calculations of magnetic interfaces related withmultiferroic materials [3–5] and permanent
magnets [6–8]. We demonstrated enhancement of magnetoelectric coupling by insertionof Co atomic layer into Fe3 Si/BaTiO3 (001) interfaces from first principles [3]. As is shownin Fig. 1, the interface Co monolayer helps
the interface ferroelectric polarization exhibit
enough, whereas the interface electric polarization is killed by Si without the Co monolayer at the interface. Other transition-metalmonolayers are also investigated [4]. In addition, crystal-growth mechanism was also clarified for Co2 FeSi and Co2 MnSi films on singlecrystalline oxides by identifying the initial disorder at the deposition and the formation energy of random alloys relative to ordered alloy [5] by using both of OpenMX [9] and AkaiKKR [10]. Substantial progresses were obtained also for microstructure interfaces in per-[1] T. Taniyama, J. Phys.: Condens. Matter 27,
504001 (2015).
[2] K. Fujita and Y. Gohda, Phys. Rev. Appl. 11,024006 (2019).
[3] Y. Hamazaki and Y. Gohda, J. Appl. Phys.
126, 233902 (2019).
[4] R. Costa–Amaral and Y. Gohda, in preparation.
[5] K. Kudo, Y. Hamazaki, S. Yamada, S. Abo, Y.
Gohda, and K. Hamaya, ACS Appl. Electron.
Mater. 1, 2371 (2019).
[6] A. Terasawa, M. Matsumoto, T. Ozaki, and Y.
Gohda, J. Phys. Soc. Jpn. 88, 114706 (2019).
[7] Y. Ainai, Y. Tatetsu, A. Terasawa, and Y. Gohda, Appl. Phys. Express 13, 017006 (2020).
[8] Y. Ainai, T. Shiozawa, Y. Tatetsu, and Y. Gohda, Appl. Phys. Express 13, 045502 (2020).
[9] T. Ozaki, Phys. Rev. B. 67, 155108 (2003).
[10] H. Akai, J. Phys. Condens. Matter 1, 8045
(1989).

99

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Determination of the ionization energy and theelectron affinity of organic molecular crystals fromfirst-principles
Susumu Yanagisawa
Faculty of Science, Department of Physics and Earth Sciences, University of the Ryukyus
Nishihara, Okinawa, 903-0213

Ionization energy (IE) and electron affinity (EA) are fundamental quantities of organic
semiconductors, and understanding the factorsthat determine the energy levels is of primary
importance to the research and development of
the organic electronics materials such as thoseof organic light-emitting diodes, organic fieldeffect transistors, and organic photovoltaics,
dominating energy barrier for injection of acharge carrier (hole and electron).
IE and EA are measured with direct photoemission and inverse photoemission techniques,
respectively. Notice here that the energy ofthe hole or electron injected into the sample is measured, i.e., IE (EA) is the magnitude of the energy difference between the neutral N-electron and the positively-(negatively)charged N−1 (N+1)-electron systems. Thus,
the measured IE and EA implies many-bodyinteraction between the injected charge andthe surrounding polarization clouds inside theorganic solids which screen the injected charge.
A complex of the injected charge and thesurrounding dynamically induced polarization
clouds are referred to as quasiparticles, which
are theoretically well-described with the selfenergy determined by the many-body perturbation theory within the GW approximation.
Given an experimental measurement of a few
organic monolayers on a substrate such as silica and graphite, it is of importance to investigate the electronic structure of an organic filmof a few monolayer thickness with a reliable

theoretical method. For such purposes, a periodic slab model approach is useful. To avoid
the computationally demanding periodic slab
calculation with GW , the electrostatic potential in a periodic slab was described within
DFT-GGA, which was aligned to that in abulk system. In the bulk system, the electronic
polarization upon the injected charge was described within the GW approximation.
In this study, with a combination of theGW approximation suitable in general to solidor bulk systems and a periodic slab approachat the DFT-GGA level, I investigated polymorphs of pentacene (PEN) and perfluoropentacene (PFP). I theoretically demonstrated
that the IE and EA at the surface are dominated by the electronic polarization (Ep ) upon
the injected charge induced by the surrounding
polarization clouds, and the electrostatic energy (S) crucially affected by the orientationof the molecule at the surface of the organic
semiconductor[1].
The geometrical configurations of the organic semiconductor bulk was determined with
the STATE program code, with the lattice constants fixed to the experimental values. For
the crystal structure and the lattice constants,
two typical polymorphs were considered: single crystal and thin film phases of PEN, fabricated on SiO2 and graphene substrates, respectively, and, herringbone and π-stacking motifs
for PFP, that were reported to grow on the
SiO2 and graphene, respectively.

100

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

For the optimized crystal geometries, I estimated the Ep upon the excess hole and electron, based on the quasiparticle self-energy
within the GW approximation. I used themodified version of the GW space-time code,
which enables highly parallelized calculations.
The resulting ionization energy (Is ) and electron affinity (As ) are displayed by horizontal
dotted dashed lines in Fig. 1. Here, the electronic polarization Ep was obtained as half thedifference between the crystalline fundamental
gap and that in a gas phase, assuming that
Ep+ = Ep− . The Is and As change drasticallywhen the molecular orientation at the surface
is taken into account, and thus, the non-zero
S + and S − contribute. The calculated Is andAs are in agreement with experiments.
Overall, while Ep , which is approximated by
the charge-induced dipole interaction, is quantitatively described within the GW approximation, the present methodology of estimating the electrostatic contribution S seems todescribe well the electrostatic nature of themolecular orientation dependence of Is andAs at the surface, i.e., the charge-quadrupole
interaction[2]. The method lacks descriptionof the decreasing polarization at the surface
which amounts to the change of the quantitiesby ≈ 0.2 eV[3]. Nevertheless, considering thehuge computational cost involved in treatmentof the slab within GW , the method is suitable for quantitative treatment of an organic
semiconductor nano-scale thin film, which is
required for nano-scale or sub-nanoscale control of the materials properties.

References[1] S. Yanagisawa: Jpn. J. Appl. Phys. 59(2020) 031002.
[2] B. J. Topham and Z. G. Soos: Phys. Rev.
B 84 (2011) 165405.
[3] J. Li et al.: J. Phys. Chem. Lett. 7 (2016)
2814.

(a)

Pentacene (5 ML)
A = 1.39 0.44g

Ep=1.36

As= 2.31
Is= 4.77

Ep=1.36
Ig= 6.59

0.04

P−

Ep=1.41

P−

As [w/o mol.ori.]

As= 2.84 As [w/o mol.ori.]

Is [w/o mol.ori.]

Is= 5.23 Is [w/o mol.ori.]

Ep=1.41
0.05

P+

0.46

P+

Single crystal (010)
Lying orientation

Thin film (001)Standing orientation(b)

Perfluoropentacene (5 ML)

Ag= 2.66 0.55

0.28
−

P
Ep=1.28

As= 4.49

Ep=1.33

P−

As [w/o mol.ori.] As= 3.71 As [w/o mol.ori.]

Is [w/o mol.ori.] Is= 5.87 Is [w/o mol.ori.]
Is= 6.78
Ep=1.33
P+
Ep=1.28
P+
Ig= 7.50
0.30
0.56
Herringbone (100)π-stack (010)Standing orientation
Lying orientation

Figure 1: Determination of ionization energy(Is ) and electron affinity (As ) for the pentacene
and perfluoropentacene polymorphs. The experimental gas phase ionization energy (Ig )and electron affinity (As ) are indicated by thehorizontal dashed lines, and the thick horizontal solid lines indicate Is and As at the crystalline surfaces. The vertical dashed lines display the polarization energies P + or P − , which
are comprised of the electronic polarization Ep
displayed by the double-headed arrows and theelectrostatic energies S + or S − indicated by
the thick one-headed arrows. For comparison,
the ionization energy and the electron affinity
without taking into account the molecular orientation at the surface, i.e. S + =S − =0, areshown by horizontal dotted dashed lines.

101

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DFT Prediction of Bulk Rashba Eﬀect
in Multiferroic Oxide
Kunihiko Yamauchi
ISIR-SANKEN, Osaka University, Ibaraki, Osaka 567-0047

Based on ab-initio approach using massive parallel computer simulations, we studied
Rashba eﬀect, which causes spin splitting ofbands through the spin-orbit interaction. This
year, we focused on multiferroics — the materials which show both ferroelectric and antiferromagnetic orders — in order to investigate
the particular Rashba eﬀect emerging with themagnetic symmetry that contains spin-flipping
symmetry operations.
Density-functional theory (DFT) calculations were performed using the VASP codewith GGA+U method. BiCoO3 crystalizes in
the polar P 4mm crystal structure in which
the Co3+ (d6 ) ion located at the center of
the O6 octahedron is significantly displaced
toward the apical O ion, leading to a pyramidal coordination rather than an octahedral
coordination. The magnetic symmetry with
the C-type antiferromagnetic order (defined bymagnetic space group P 4′ mm′ ) keeps the spindegeneracy of bands at the high-symmetric k
points. As shown in Fig.1, we found that thecharacteristic vortex-like in-plane components of the spin texture of the Rashba eﬀect
developing around the Z point while the outof-plane spin component is negligible [1].
The magnetic symmetry can be reduced
when the Co spins are canted with respect to
the C-AFM configuration in the real space. We
assumed the application of external magnetic
field along the [100] direction, by canting two
Co spins simultaneously. As a result, we observed a distortion of the energy isocontour
along the ky axis and a downward shift of thecenter of spin vortex.

R2

ky

R1

A

kx

Figure 1: Spin texture (shown by magenta arrows) and energy contour plot of the
conduction-bottom band in the kz = 1/2 plane(centered at the Z point) in BiCoO3 .
While the theoretical predictions in thepresent study call for future experimental confirmation, we speculate that this phenomenon
can be rather common among the antiferromagnetic polar systems; in future works, one
can explore the possibility of Rashba eﬀects invarious multiferroic systems, such as BiFeO3
and PbVO3 .

References[1] Kunihiko Yamauchi, Paolo Barone, andSilvia Picozzi, Phys. Rev. B 100 (2019)
245115.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-Principles Molecular-Dynamics Study of Structural andElectronic Properties of Covalent Liquids and Glasses under
Pressure
Fuyuki SHIMOJO, Shogo FUKUSHIMA, and Akihide KOURA
Department of Physics, Kumamoto University, Kumamoto 860-8555
The investigation of the dynamic properties

cost of numerical integration in the TI methodof covalent liquids and glasses under pressureby using an ANN potential compared withis important from perspectives of geophysics as

FPMD-based TI calculations, while keeping

well as fundamental liquid-state science. For

first-principles accuracy. By comparing withthis purpose, it would be important to consider

the results by FPMD, we confirmed that thethe stability of materials states under various

ANN-based TI method gives the free energy

conditions from the viewpoint of free energy.

within the accuracy of less than 0.1 meV/atom

To accurately evaluate which state is mostwith more than 100 atoms.

stable, the thermodynamic integration (TI)
method has been used by calculating the freeenergy [1]. While the TI method based on firstprinciples

molecular

dynamics(FPMD)

simulations can obtain the free energy with
sufficient precision [2], the system size isseverely limited by its high computational cost.
In order to handle adequate system sizes
while retaining first-principles accuracy, weFig. 1: Melting temperature T as a function of
the number of atoms N.

adopt an interatomic potential constructed byartificial neural-network (ANN) models trained
by FPMD simulations. This study aims toReferences

establish a method for the precise evaluation of[1] D. Frenkel and A. J. C. Ladd, J. Chem. Phys.

the free energy using the TI based on the ANN-81, 3188 (1984).

MD simulations. To that end, we have[2] O. Sugino and R. Car, Phys. Rev. Lett. 74,

calculated the size dependence of the melting

1823 (1995).

temperature of rubidium as shown in Fig. 1 [3].

[3] Fukushima et al., Phys. Rev. B 100, 214108(2019)

We successfully reduced the computational

103

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of diffusion process of ionic species
in organic solvent
Kazuto AKAGIWPI-AIMR, Tohoku University, Katahira, Aoba-ku, Sendai, Miyagi 980-8577
Further improvement of Li-ion batteries

EC” and “43 EC + 3 Li+” systems were used as(LIB) is strongly expected still now. The

training set. “360 EC + n Li+” systems (fromperformance of LIB depends on various factors,

0.1M to 3.0M) were used for production run.

and optimizing transport properties of Li-ion is

The initial generation was prepared from theone of the most important items. The

original parameters of AMOEBA FF with 20%

microscopic transport mechanism in organic

random noise. The parameter sets formed fourelectrolytes, however, remains unclear. To

groups with the evolution, and only one groupelucidate it, we have developed a genetic

survived at 60th generation. Some of themalgorithm based optimized force field (FF)successfully

which achieves large-scale and long-time

coefficient and density calculated by VASP. Not

classical MD simulation.

only the solvation structure of Li-ions but also

reproducedthediffusion

Polarizable FFs such as AMOEBA andpotential of mean force (PMF) for detachment

APPLE&P are potentially applicable to large

and attachment of EC were also reasonably

scale simulation for LIB systems, but theirdescribed. The diffusion of Li-ion becomesreliability is not sufficient as they are. In order

slower at high concentration and it statisticallyto optimize AMOEBA FF and mimic theturned out that the lack of free EC molecules

thermodynamic properties obtained by rev-

decreases attachment/detachment events. The

vdW-DF2 density functional for target systems,

detailed results are prepared for publication.

we made a framework of multi-objective
genetic algorithm, in which not only relative
potential energy but atomic forces on each atomfrom VASP are reproduced by TINKER.
Pure ethylene carbonate (EC) and EC with
Li-ion systems were assessed. The dimension

Fig. 1: (a) Improvement of solvated structure.

of parameter space to be optimized is 132, and(b) PMF along detachment of EC (DFT and FF).

more than 150 MD snapshots sampled from “9104Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on the stability of magnetic alloys
Yasutomi TATETSU
Meio University, Biimata, Nago, Okinawa 905-8585
Transforming crystal structures of materials

Fe site. There are two different Wyckoffby adding pressure, heat, or other elements is

positions of Pd labelled by 2e and 2g in Z3-

one of the fundamental approaches to discover

FePd3. From detailed analyses, we concluded

novel physical properties. Recently, a new Z3-

that the new Z3-type Fe(Pd,In)3 structure, in

type

was

which a Pd atom at a 2e site is replaced with an

discovered by Teranishi’s group in Kyoto

In atom, is more stable than In-doped L12-

University [1]. The new structure was obtained

FePd3 structures. These results are consistentby introducing a third element of In into L12-

with the experimental results from XRD,

FePd3, which is the thermodynamically stable

EXAFS, and STEM-EDS analyses.

Fe(Pd,In)3

crystalstructure,phase of binary Fe–Pd systems. Although theaddition of In might be the key behind this new
0.4

Eform (eV/u.c. with 8 atoms)

finding, the physical aspects of In in stabilizing
the new structure is unclear and cannot be
understood deeply only through experiments.

Z3ïFe2Pd5In
L12ïFePd6In

L12ïFePd3
Z3ïFePd3

0ï0.4

In this study, we performed theoreticalï0.8

analyses for the stability of an In-doped novel

ï1.2

Fe–Pd phase to check the systems’ formation

ï1.6

energies using OpenMX. The model structures

ï2

for the calculations were based on the chemical

Pd(e)

Fe

Fe

Pd(g)

Pd

In sitecomposition ratio of Z3-FePd3 obtained from

Figure ： The comparison of the formation

experiments. The In sites were chosen byenergies of In-doped Z3- and L12-type FePd3.

replacing Fe or Pd sites with a specialquasirandom-structure method implemented in

References

the Alloy Theoretic Automate Toolkit [3]. We[1] K. Matsumoto et al., in preparation.

investigated stable sites for In in the Z3-FePd3[2] http://www.openmx-square.org

structure by comparing formation energies[3] A. van de Walle et al., Calphad Journal 42,

which is illustrated in the figure. We found that

13 (2013).

an In stably occupies the Pd site rather than the105Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electrode Properties of Novel Lithium-Ion Secondary
Battery Materials: First-Principles Calculations
Hiroyoshi MOMIDA, Motoyuki HAMAGUCHI, Hiroshi KATSUMOTO, Tatsuya TAKAHASHI
Institute of Scientific and Industrial Research, Osaka University
8-1 Mihogaoka, Ibaraki, Osaka 567-0047

We have studied electrode properties of Liand Na-ion secondary battery materials by
first-principles calculations. The computations
are done by using HiLAPW and Quantum
Espresso codes.
X-ray absorption spectra in NaFeSO4 F
for exploring Na-ion battery reactions
We study electronic and spectroscopic properties of NaFeSO4 F, which has been a candidate cathode material for Na-ion batteries[1, 2]. NaFeSO4 F have been often synthesized experimentally from NaF and FeSO4 , andthe calculated result shows that NaFeSO4 F isslightly stable in energy than the two-phasemixture of NaF and FeSO4 . The average voltage of NaFeSO4 F cathode is calculated to be
3.08 V with respect to the Na anode, andthat comes dominantly from valence changes
as Fe2+ /Fe3+ in NaFeSO4 F/FeSO4 F. X-ray
absorption spectra (XAS) near K-edges at Fe,
Na, and F are calculated for NaFeSO4 F andFeSO4 F as the cathodes in fully-discharged
and fully-charged states, respectively, and also
for NaF and FeSO4 as possible residual materials in real cathodes (Fig. 1). The results
show that XAS near K-edges, especially at F
as well as Fe, provides us useful information toclarify battery reactions and structures in thecathodes.
O-redox and O2 -release reactions in Liexcess cation-disordered rock-salt oxides
Li2+2x Mn1−x Ti1−x O4Thecation-disordered rock-salt oxides
Li2+2x Mn1−x Ti1−x O4 with the Li-excess

amount x are one of promising Li-ion battery
cathodes. We study the cathode properties of
the Li2+2x Mn1−x Ti1−x O4 models (Fig. 2) withx ranging from 0 to 0.3 by the first-principles
calculations, considering cation and anion
redox reactions with O2 -releases [3]. Eﬀects
of x on voltage-capacity curves and electronic
structures are studied, and the results showthat Mn-redox reactions predominate in earlycharging processes. As charging reactions
further proceed, O-redox reactions contributeto the cathode reactions more significantly forhigher x. From the formation energy analyses,
it is found that O atoms tend to be released
from the cathodes especially in late charging
processes with a trend of easier O2 -releasefor higher x, possibly accounting for lower
experimental capacities than the theoreticalvalues.
Na-ion battery performance and reaction mechanism of SnS anodeWe study the Na-ion battery performanceof SnS as an anode material by the firstprinciples calculations [4, 5]. From formationenergy analyses, the discharge reaction processes of the Na/SnS half-cell system are clarified. We calculate the phase diagram of Na–
Sn–S ternary systems by constructing convexhull curves of Na–Sn–S, and show a possible
reaction path considering intermediate products in discharge reactions. Voltage-capacity
curves are calculated based on the Na–SnS reaction path that is obtained from the ternary
phase diagram. It is found that the conver-106

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

XAS intensity (arb. units)

XAS intensity (arb. units)

7105
1.5

7115

7125

7135

7145

(a) x = 0
Ti
O

7155

Fe K-edge
1.0

Li

FeSO4
(experiment)
FeSO4F (C2/c)

Mn

Na0FeSO4F

0.5

a
b

FeSO4

6995

678
1.5

688

7005
7015
Energy (eV)
698
708

7025

7035

718

728

F K-edge
NaF

1.0

b

FeSO4F(C2/c)
Na0FeSO4F

0.5

0.0
650

660

670
680
Energy (eV)

690

700

Figure 1: Calculated x-ray absorption spectra(XAS) near Fe and F K-edges of NaFeSO4 F
materials [1]. Experimental XAS is also plotted with the upper energy scale.

bc(d) x = 0.3aaNaF (experiment)

NaFeSO4Fac(c) x = 0.2

NaFeSO4F

0.06985(b) x = 0.1

c

b

c

Figure 2: Calculated model structures of
Li2+2x Mn1−x Ti1−x O4 [x = (a) 0, (b) 0.1, (c)0.2, and (d) 0.3] with the cation-disorderedrock-salt structures [3].
the insertion and the conversion reactions at
early and late discharging processes, respectively. Based on the estimated reaction formula, voltage-capacity curve is calculated, andthe result well accounts for the experimentallyobserved two-plateau behavior.

sion reactions and subsequently the alloying
reactions proceed in the SnS electrode, contributing to its high capacity compared withthe metallic Sn electrode, in which only thealloying reactions progresses stepwise. To confirm the calculated reaction process, x-ray absorption spectra (XAS) are calculated for Na2 S
and SnS in discharged and charged states, respectively.

References

Conversion-type reaction mechanism of
FeF3 cathodes for Li-ion batteries[3] M. Hamaguchi, H. Momida and T.
Oguchi: Electrochim. Acta 330 (2020)
135286/1-8.

The perovskite-type FeF3 is one of promising cathodes for Li-ion batteries because of its
high capacity, but reaction mechanism has notbeen clarified yet. In this work, we study discharge reaction processes by calculating formation energies of Li–Fe–F materials. We theoretically find that the discharge reaction proceeds as FeF3 + 3Li → Li0.5 FeF3 + 2.5Li →FeF2 + LiF + 2Li → Fe + 3LiF, showing[1] H. Momida, A. Kitajou, S. Okada andT. Oguchi: J. Phys. Soc. Jpn. 88 (2019)124709/1-6.
[2] A. Kitajou, H. Momida, T. Yamashita, T.
Oguchi and S. Okada: ACS Appl. Energy
Mater. 2 (2019) 5968-5974.

[4] H. Kotaka, H. Momida, A. Kitajou, S.
Okada and T. Oguchi: Chem. Rec. 19(2019) 811-816.
[5] H. Kotaka, H. Momida, A. Kitajou, S.
Okada and T. Oguchi: J. Comput. Chem.
Jpn. 18 (2019) 78-83.

107

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study ofquantum transport in nanostructuresNOBUHIKO KOBAYASHI
Department of Applied Physics, University of Tsukuba
1-1-1 Tennodai Tsukuba Ibaraki 305-8573

Introduction50

An understanding of the electron transport
properties of materials has resulted in theemergence of an important and versatile problem, not only for the fundamental research ofscience but also for the applications of electronics. Quantum nature is essential in nanoscale
systems, and atomistic analysis based on detailed electronic states calculations are indispensable to discuss the transport property.
In order to investigate transport properties,
we have developed the nonequilibrium Green’s
function (NEGF) method, and the O(N) timedependent wave-packet diﬀusion (TD-WPD)
method on the basis of the density functional
theory (DFT). Using these methods, we haveinvestigated charge, head and spin transport
properties of materials. [1, 2]

2

O(N) method for transport
calculations

Organic semiconductors have attracted muchattention for their applications to flexible,
printable, lightweight, and low-cost electronic
devices. They are crystals that are assembliesof π-conjugated molecules weakly bonded byvan der Waals interactions, and single crystallization has been achieved, enhancing themobility. It is expected that the mechanismof carrier transport in organic semiconductors
can be elucidated and that materials exhibiting high mobility can be developed by novel
molecular synthesis.[3]We developed the O(N) TD-WPD method
for the quantum transport calculation of hugesystems of up to 100 million atoms a decadeago.We calculated the conductance and the108

Mobility m (cm2 V-1 s-1)

1105Prediction (Calculation for PBE-TS structure)
Experiment (FET mobility)
Calculation for experimental structure
Calculation for MMFF94 structure

1

200

220
240 260 280 300
Temperature T (K)

Figure 1: Temperature dependence of mobility
along the column direction in a C10-DNBDTsingle crystal. For comparison, the experimental values of FET mobilities are also shown as
triangles.

mobility of the system with micron-orderlengths at room temperature at the atomistic levels. Using this method we can study
the transport properties from diﬀusive to ballistic regimes including the eﬀect of realistic
electron-phonon scattering, and determine themean free path and relaxation time from anatomistic viewpoint. We performed DFT calculations of electronic structures and interactions between molecules of single-crystal organic semiconductors including the eﬀect ofthe van der Waals interaction, and applied the
TD-WPD method to the analysis of transport
properties of the organic semiconductors.
Using TD-WPD method, we have proposeda prediction methodology to obtain chargetransport properties of organic single crystals from their structural formula.
Pre-Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

diction of material properties of newly designed molecules is a long-term goal in organic electronics. As a demonstration, we
employ the promising molecule C10-DNBDT.
We succeeded in quantitative evaluation of
charge mobility of the single crystal using
our quantum wave-packet dynamical simulation method. Here, the single-crystal data iscomputationally obtained by searching possible packing structures from structural formulaof the molecule. The proposed methodology
can be a theoretical design technique for efficiently developing new high-performance organic semiconductors, since it can estimate thecharge transport properties at early stage inthe process of material development.[4]hancement in the figure of merit by doping,which is in agreement with experimental work,and show further enhancement by the optimized doping. Furthermore, electronic structures of thin films are examined. It is shownthat calculated electrical conductances reachto twice larger than that in the bulk, and thecalculated Seebeck coeﬃcients in thin films aresuppressed by the metallicity, remain maximally to about a half of the results in thebulk.[6]References
3

NEGF-DFT method

We have developed a Simulation code for
Atomistic Kohn-sham Equation (SAKE) for
the ab-initio electron transport calculation
based on the DFT and NEGF formalism.[5] We
have applied the method to analyses of thermoelectricity of magnetic semiconductors.
Thermoelectric materials have attracted
considerable attention from viewpoints not
only of materials science but also of applications for energy harvesting by waste heat, andintensive works have been devoted to enhance
conversion eﬃciency from thermal energy into
electricity. The eﬃciency is expressed as afunction of the figure of merit ZT = σS 2 T /κ,where σ, S, κ and T are the electrical conductivity, the Seebeck coeﬃcient, the thermal conductivity and the temperature, respectively,
and the thermoelectric power factor is written
as σS 2 . Enhancement of thermoelectric eﬃciency is not an easy task since the Seebeck
coeﬃcient, the electrical conductivity, and thethermal conductivity are not independent ofeach other. There is the trade-oﬀ between σ
and S, and materials with high electric conductivity tend to have high thermal conductivity.
We analyze the thermoelectric properties ofa magnetic semiconductor using SAKE program. The electronic transport properties,
Seebeck coeﬃcient, and the figures of meritare estimated for doped systems and thinfilms. We theoretically demonstrate the en-

109[1] N. Kobayashi, H. Ishii, K. Hirose,
Jpn. J. Appl. Phys. 57, 08NA01 (2018).
[2] N. Kobayashi, H. Ishii, K. Hirose, in 3D Local Structure and Functionality Design of Materials eds H. Daimon, Y. C. Sasaki (World
Scientific, 2018) p133.
[3] A. Yamamura, H.Fujii, H. Ogasawara, D.
Nordlund, O. Takahashi, Y. Kishi, H. Ishii, N.
Kobayashi, N. Niitsu, B. Blulle, T. Okamoto,Y. Wakabayashi, S. Watanabe, and J. Takeya,
Commun. Phys. 3 20 (2020)[4] H. Ishii, S. Obata, N. Niitsu, S. Watanabe, H.
Goto, K. Hirose, N. Kobayashi, T. Okamoto,and J. Takeya,
Sci. Rep. 10, 2524 (2020)[5] H.Takaki, N.Kobayashi, K.Hirose,
J. Phys. Cond. Matter. (2020) in press.
[6] H.Takaki,
K.Kobayashi,
M.Shimono,
N.Kobayashi, K.Hirose, N.Tsujii, T.Mori,
Jpn. J. Appl. Phys. 58 SIIB01 (2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Prediction of properties of organic ferroelectrics andpiezoelectrics by ﬁrst-principles calculation
Shoji ISHIBASHI
Research Center for Computational Design of Advanced Functional Materials (CD-FMat),
National Institute of Advanced Industrial Science and Technology (AIST)
Tsukuba, Ibaraki 305-8565

Organic charge transfer complexes show avariety of crystal structures and electronic
properties. Among them, there is a class ofcompounds called“mixed-stack compounds”,
in which electron-donor and electron-acceptor
molecules stack alternatively along a certain
direction. Some of them show ferroelectricity.
Tetrathiafulvalene-p-chloranil (TTF-CA) is atypical example. Kobayashi et al. successfullymeasured spontaneous polarization in TTFCA and obtained a value of 6.3 µC cm−2 [1].
Furthermore, they found that the polarization
value is more than 20 times larger than thatof the point charge model, and their directions
are opposite. To clarify the origin of this exotic
ferroelectricity in TTF-CA, we made theoretical analyses in terms of Born eﬀective chares aswell as maximally-localized Wannier orbitals[2, 3]. We have shown that only 2 bands below
the band gap are responsible for the emergenceof polarization and also that the electron ﬂow
from cell to cell on these electronic states is theorigin of the exotic polarization in TTF-CA.
Recently, Mezzadri et al.
reported
the structure of the low-temperaturephaseof
3,3,5,5-tetramethylbenzidinetetracyanoquinodimethane(TMB-TCNQ)
and pointed out that this phase is potentiallyferroelectric [4]. Similarly to the TTF-CA
case, TMB and TCNQ molecules stack alternately and form one-dimensional columns.
We have applied the above-mentioned
computational methods to investigate theferroelectricity in TMB-TCNQ and foundsimilarities and dissimilarities with TTF-CA[5].
In addition, theoretical calculations to
obtainspontaneous-polarization
vectorsfor organic ferroelectrics D22bpy-Dia andD55dmbp-Dia have been performed.
Theobtained results explain the experimentallyobserved values well [6].

References[1] K. Kobayashi, S. Horiuchi, R. Kumai, F.
Kagawa, Y. Murakami, and Y. Tokura:Phys. Rev. Lett. 108 (2012) 237601.
[2] S. Ishibashi and K. Terakura: J. Phys.
Soc. Jpn. 83 (2014) 073702.
[3] K. Terakura and S. Ishibashi: Phys. Rev.
B 91 (2015) 195120.
[4] F. Mezzadri, N. Castagnetti, M. Masino,
and A. Girlando: Cryst. Growth Des. 18(2018) 5592.
[5] S. Ishibashi, S. Horiuchi, and K. Terakura: unpublished.
[6] S. Horiuchi, S. Ishibashi, K. Kobayashi,
and R. Kumai: RSC Adv. 9 (2019) 39662.

110

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of metal/oxide interfaces with large
mismatches
Hongping LI1 ,Mitsuhiro SAITO2 , Chunlin CHEN1 , Kazutoshi INOUE1 , Kazuto AKAGI1 ,and Yuichi IKUHARA1,2,∗
1Advanced Institute for Materials Research, Tohoku University, Sendai, Miyagi, 980-8577
2
Institute of Engineering Innovation, The University of Tokyo, Yayoi, Tokyo, 113-8656

Metal/oxide heterointerfaces are widely usedin engineering, and their microstructures govern the macroscopic properties. We investigated the interaction and bonding reconstruction at Pd/ZnO {0001} interfaces with large
mismatches by density functional theory calculations combined with atomic-resolution scanning transmission electron microscopy. It has
been believed that the interfacial interactions
are very weak at incoherent interfaces withlarge mismatches, and metal–oxide interfaces
can be more favorable than metal–metal interfaces.
To gain insight into the local atomic structures of each interface, ﬁrst-principles calculations were performed using the Vienna ab initio Simulation Package (VASP). The electronic
wave functions were expanded by plane waves
up to a kinetic energy cutoﬀ of 400eV. The
generalized gradient approximation in the formof the Perdew–Burke–Ernzerhof exchangecorrelation functional was implemented in our
calculations. A supercell containing seven Pd
lattices matching six ZnO lattices along theinterfaces was constructed to compensate themismatch which agree with the experimental
result. The surface atoms of the ZnO slabs
were passivated by H atoms to eliminate theeﬀects of dangling bonds, and a 15Å vacuum
area was embedded into the outer Pd surfaces
to avoid unwanted interactions. For k-point
sampling, a 1 × 1 × 1 Monkhorst–Pack grid
was applied in the irreducible Brillouin zone
for the supercell calculations. Convergencewith a 2 × 2 × 1 Monkhorst–Pack mesh was
also tested for both interfaces, and the diﬀerences in the total energy and atomic conﬁgu-

rations could be neglected. The convergencethreshold for self-consistent iteration was set
at 1.0 × 10−4 eV/atom, and the atomic positions were fully relaxed until the maximal force
on each atom was less than 0.05eV/Å. To analyze the interfacial stability of the epitaxial
systems, the adhesive energy was calculated by
Ead = [EPd−slab + EZnO−slab –Etotal ]/A, where
Etotal , EPd−slab , and EZnO−slab are the interfacial total energy and the energies of individual Pd and ZnO slabs, respectively, and A
is the interfacial area. Then, we get Ead =2.66J/m2 and 3.52J/m2 for the Zn-terminatedPd (111)/ZnO (0001) and (0001̄) interface, respectively, implying that the nonstoichiometric Zn-terminated Pd (111)/ZnO (0001̄) interface is energetically favorable. The interfacial atoms were located almost at bulk lattice
points for the stoichiometric Zn-terminatedPd(111)/ZnO(0001) interface while the interfacial Pd and Zn atoms underwent relatively large relaxations at the nonstoichiometric Zn-terminated Pd(111)/ZnO(0001̄) interface, making the interface relaxed to release the large interfacial mismatch. The PdZn bonds exhibited site-dependent characteristics and gradually transitioned from covalent
to ionic at the Pd(111)/ZnO(0001) interface,whereas most of Pd-Zn bonds exhibited strong
covalent behavior at the Pd/ZnO(0001̄) interface [1].

References[1] H. Li, M. Saito, C. Chen, K. Inoue, K. Akagi, Y. Ikuhara: Acta Mater. 179 (2019)237-246.

111

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Firefly Oxyluciferin Anions in Aqueous Solutions
Yoshifumi NOGUCHI
Department of Applied Chemistry and Biochemical Engineering, Graduate School ofEngineering, Shizuoka University, Johoku 3-5-1, Hamamatsu, Shizuoka 432-8561, Japan

Oxyluciferin anion, known as a light emitter

indicatedachargeleakagefrom

thein the firefly bioluminescence process, is a key

oxyluciferin anion to the surrounding watermolecule in understanding the mechanism ofmolecules. In addition, we discussed thethe firefly bioluminescence process. Althoughvalidity of a modeled aqueous solution, such as

significant effort has been taken in various

QM/MM or PCM methods, in which the charge

studies targeting the oxyluciferin anion, most oftransfer between solute and solvent is restricted.

its properties still remain unclear. This is

In order to describe the charge leakage from the

because, from the perspective of simulations,

oxyluciferin anion and reproduce our full QM

the environmental conditions surrounding theresults, at least 10 water molecules should be

oxyluciferin anion are too complicated. In

included into QM region.

addition, the oxyluciferin anion is too sensitive
for the environments.
In this study, we applied the first-principles
Born-Oppenheimer

molecular

dynamics

simulations (BOMD) to three possible isomersoftheoxyluciferin anion

(see

Fig.

1)
Phenolate-ketosurrounded by 64 water molecules, andsimulated the photoabsorption spectra for 1000

Fig.

randomly selected molecular geometries from

Phenolate-enol Phenol-enolate

1. Three possible isomers of theoxyluciferin anion.

the trajectory [1].
The simulated spectra are in a good

References

agreement with the experiments. The remaining[1] Y. Noguchi, M. Hiyama, M. Shiga, H.

error is less than 0.1 eV in comparison with the

Akiyama, and O. Sugino: J. Chem. Theory

peak top positions. Our full QM simulations

Compt.,

112

15(2019)

5474.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles investigation on electronic structure
modulation via coherent phonon excitation
Yasushi SHINOHARA1,2
1

Photon Science Center,

The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656
2

Department of Nuclear Engineering and Management,

The University of Tokyo, Hongo, Bunkyo-ku, Tokyo 113-8656
Recent progress of coherent light source

representation, all-symmetric, modes. These

technology allows us to observe quantum

results

invokethat

dynamics in time-domain (TD) driven by intense

modulation due to the optical phonon, excited as

and short laser pulses [1,2], rather thancoherent phonon via the IR pump pulse. Eachfrequency-domain (FD) observation such as thepart of the energy-dispersion has a different

standard spectroscopies. The TD information

coupling with the phonon modes. By extracting

usually contains more than complementarya frequency structure |𝑆(𝐸, 𝑘; 𝜔 = 𝜔phonon )| ,information of FD data because of phasemuch finer information of electron-phonon

information, namely time-origin is clearlyinteraction than Raman spectra is expected to be

introduced by the pulse. Very recently, more

extracted. To prove this scenario, we perform an

extreme and flexible pulse shaping is available

ab-initio

such that two-color mixing pulse composing

modulation due to the optical phonon modes

infrared (IR) and ultraviolet (UV) photon

within the density-functional theory (DFT)energies. We have investigated coherent phonon

framework within the abinit code.

simulationelectronic

that

band

structure

structure

excitation encoded in temporal modulation inFirstly, we optimize the atomic position ofangle-resolved photoemission spectra (ARPES)

the Ta2NiSe5 crystal with two functionals,

by using IR pump and UV probe pulses.

Perdew-Wang local density approximation (PW-

We observe TD-ARPES of Ta2NiSe5, a

LDA),

and

Perdew-Burke-Ernzerhof

candidate of the excitonic insulators, pumped bygeneralized gradient approximation (PBE-

1.55 eV pulse. In the time-dependent E-k

GGA). Secondly, we obtain normal modes of thespectral distribution 𝑆(𝐸, 𝑘; 𝑡) , oscillatory

lattice vibration at Γ-point via density-functional

behaviors appear. The frequencies of theperturbation theory (DFPT) with each functional.

oscillation well coincide with the optical phonon

By performing symmetry operations of thefrequencies

crystal, we assign irreducible representation tobelonging

to Ag

irreducible

113

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

the modes. We only pick up Ag irreducible

prominent change around Fermi-level of therepresentation because this mode is only excitedspectra [3]. This mode has been argued as theas the coherent phonon based on displacive

driving mode of insulator-metal (IM) transition

excitation of coherent phonon mechanism. The

via photoexcitation. Our investigation posts an

DFPT computation demands the heaviest

additional clue to understand the mechanism ofcomputational resource. Our crystal is a

the IM transition.

semimetal with PW-LDA and PBE-GGA
functional. To capture small Fermi surface, weneed fine Brillouin zone sampling that has 864
k-points. The existence of Ta requires rather highReferences

energy cutoff, 50 eV, for the plane wave. The[1] F. Krausz and M. Ivanov, Rev. Mod. Phys.

calculation takes 11 hours with 64 nodes, 1536

81 (2009) 163.

cores in the system B. Finally, we evaluate band[2] Stanislav Yu. Kruchinin, Ferenc Krausz, anddispersion with distorted atomic positions along

Vladislav S. Yakovlev, Rev. Mod. Phys.

with the normal modes obtained by DFPT. To

90 (2018) 021002.

compare with the experimental spectra, we[3] Takeshi Suzuki, Yasushi Shinohara, Yangfan

construct

Lu, Mari Watanabe, Jiadi Xu, Kenichi L.

similarspectral

informationasdifferences of k-resolved density-of-state (k-Ishikawa,

DoS) between the optimized atomic position andNaoyuki Katayama, Hiroshi Sawa, Masami

the distorted ones. The comparison between

Fujisawa, Teruto Kanai, Jiro Itatani, Takashi

experimental and theoretical data shows an

Mizokawa, Shik Shin, Kozo Okazaki, submitted,

agreement that a symmetry breaking mode,

arXiv: 2002.10037.

having 2 THz frequency, shows the most

114

Hide

Takagi,

MinoruNohara,Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

first-principles calculation of exchange coupling
constants and investigation of interface magnetism
for various phases and their interfaces of permanent
magnets
Asako TERASAWA
Department of Materials Science and Engineering, Tokyo Institute of Technology
J1-3, Nagatsuta-cho 4259, Midori-ku, Yokohama 226-8502, Japan

Improvement of Nd-Fe-B magnets without
heavy rare earth elements is one of the topics of increasing importance in the applied
physics and materials science. The key forhigh-coercivity Nd-Fe-B magnets lies in the
Nd-rich grain boundary (GB) phases [1]. However, the details of structural and magnetic
properties of those GB phases are not clarified yet. Some experiments revealed the relationship between the crystallinity of GB phases
and the relative angles between the interfaces
and the c-plane of neighboring grains [2], whichindicates the complexity of the physics in grainboundary phases in Nd-Fe-B magnets. Particularly, we targeted the exchange couplings inside and between the various phases for a computational study of magnetism in Nd-based
permanent magnets.
For this purpose, we developed “jx”, a postprocess program for OpenMX [3] to calculate
exchange coupling constants between atoms
based on the Liechtenstein formula [4]. The
details of the implementation is explained in
the published paper of [5]. During the development of jx, we found a remarkable problem about the combination of the Liechtensteinmethod and the linear combination of atomic
orbitals (LCAO) approximation. When adopting diagonal elements of non-orthogonal (NO)
Hamiltonian as eﬀective single-site potentials,
the calculated exchange coupling constants do

115

not converge as increasing the number of basis. Figure 1(a) shows the exchange coupling
constants Jij as functions of atomic distancerij for diﬀerent choice of basis sets. Here, thenotation sxpydzfw means that the basis set isconstructed from x types of s orbitals, y typesof p orbitals, z types of d orbitals, and w typesof f orbitals. It is possible to see in Fig. 1 that
the Jij profiles are similar for s2p2d1, s2p2d2,
and s3p2d2 with fluctuations of about a few
meV, whereas the Jij profiles deviate strongly
to negative values for the larger basis sets.
To solve this problem, we introduced a newscheme to orthogonalize the atomic orbitals,
namely the single-site orthogonalization (SO)scheme. In the SO scheme, we derive a basis set {|i⟩i } to orthogonalize only i-th elementfrom the original non-orthogonal orbitals {|i⟩}.
The single-site orthogonlized basis set is defined by the following equations:|i⟩i ≡ |i⟩ −∑|j⟩[S−1S ]i,i i,i ji

(1)

j∈i

|j⟩i ≡ |j⟩, j ̸= i(2)with the definitions of the neighbor set i forsite i as
i ≡ {j | j ̸= i, ⟨i|j⟩ ̸= 0}.

(3)

We found that the Jij profiles calculated with
the SO scheme exhibit a convergent behavior
as increasing the number of bases, while theyActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo25

decreases slightly depending on the basis size.
The slight decreases in SO results are well collected by introducing spin population scaling,
namely single-site orthogonalization with spin
population scaling (SOS) scheme:∆ni∆nj (SO)
(SOS)
Jij
≡
J
.
(4)
(SO)
(SO) ij∆nj∆nj

J ij [meV]

20
15
10
5
0
-5
-10

2

3

4

5

6

rij [Å]

7

8

9

10

(SO)

where Jij(a) J ij of bcc Fe by SO scheme(SO)

J ij [meV]

20
15
10
5
0
-5
2

3

4

5

6

rij [Å]

7

8

9

10

(b) Jij of bcc Fe by SOS scheme
s2p1d1s2p2d1s2p2d2Nd

s3p2d2s3p2d2f1
s3p3d2FeB

s3p3d2f1
s3p3d3s3p3d3f1

Jij [meV]
20

25

(SO)

derived by the SO scheme, ∆ni
and ∆ni
are the spin population at site i calculated using the NO basis and SO basis, respectively.
Figure 1 (b) shows the exchange coupling constants as functions of atomic distances calculated with the SOS scheme. We can see a remarkable convergence as increasing the number of bases in Fig. 1(b).
We also applied the newly developed scheme
to larger scale systems. Figures 1(c) and 1(d)show the calculated exchange coupling constants of the model of ab interface, where theamorphous Nd-Fe phase of a few nm are attached to the main phase in ab axis direction.
It can be seen in Figs. 1(c) and (d) that the exchange coupling constants behave diﬀerently inthe main phase and in the amorphous Nd-Fe
phase.
We are now preparing the submission of theabove results to refereed papers, and modified
patch of jx including the SOS scheme for future
release of OpenMX.

25

-10

is the exchange coupling constant30(c) large positive Jij in the ab interface model

References
Nd

Fe

B

Jij [meV]
105(d) negative Jij in the ab interface model[1] K. Hono et al., Scripta Mater. 67, 530 –
535 (2012).

0

Figure 1: Calculated exchange coupling constants Jij of various systems. (a) Jij of bcc Fe
as functions of atomic distance rij for diﬀerent
choices of basis sets when adopting diagonal elements of NO Hamiltonian as eﬀective singlesite potentials and (b) when adopting diagonal
elements of SO Hamiltonian as eﬀective singlesite potentials and applying the spin population scaling to the SO results. (c) and (d) Jij
in the ab interface model of Nd-Fe-B permanent magnet.

116[2] T. T. Sasaki et al., Acta Mater. 115, 269(2016).
[3] T. Ozaki, Phys. Rev. B 67, 155108 (2003).
[4] A. I. Liechtenstein et al., J. Magn. Magn.
Mater. 67, 65–74 (1987).
[5] A. Terasawa, M. Matsumoto, T. Ozaki,
and Y. Gohda, J. Phys. Soc. Jpn. 88
114706 (2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Machine-learning-driven molecular simulations for grainboundary atomic dynamics
Tatsuya YOKOI
Department of Materials Physics,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, Aichi, 464-8603
Grain boundaries (GBs), crystalline interfaces

about general or random GBs, which generally

between misoriented grains, often govern

require a large number of atoms for theirmaterial properties in polycrystals, in spite thecomputational cells, in the atomic level.

fact that changes in atomic arrangement andIn order to predict atomic structure andchemicalfew

energetics of GBs while maintaining highnanometers from GBs. Experiments withaccuracy and low computational cost, webicyrstals and theoretical calculations haveconstructed artificial-neural-network (ANN)reported that not only atomic arrangements but

interatomic

also local properties arising from atomic

calculation data, Furthermore, we integrated the

dynamics significantly vary with each GB.

ANN potentials into molecular simulationSuchthermodynamic

algorithms, with the goal of predicting local

stability, diffusivity and thermal conductivity. A

diffusional and lattice vibrational properties atbetter understanding of the connection between

GBs. Here, oxide systems and semiconductor

GB structures and their atomic dynamics is thus

compounds were chosen.

essential

The architecture of ANN potentials was based

composition

properties

for

occur

includesdesigning

withinpolycrystals

withpotentials

trained

with

DFT-

desired properties and functionalities.

on the previous studies by Behler [1]; the feed-

In order to reveal their connection, density-

forwardfunctional-theory (DFT) calculations have beenenvironments were encoded using two- andoften employed. However, DFF calculations are

three-body symmetry functions [1]. Theircomputational demanding as the number ofcutoff radii were set to 5 and 7 Å for oxides andatoms in a computational cell increases, since

compound semiconductors, respectively.

their computational time typically grows with

Training

O(N3) or O(NlnN). Due to this drawback, mostaccounting for various atomic environments to

DFT studies have investigated only GBs withincrease the generalizability of ANN potentials.

simple atomic arrangements, such as symmetric

Here the training datasets contained not only

tilt GBs with low Σ values. Still less is known

single-crystal structures but also lattice defects:

117

networkdatasets

was

employed.

were

AtomicgeneratedbyActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

point defects, surfaces and grain boundaries.
DFT total energies and atomic forces were used
to train ANN potentials. DFT calculations were
performed using the VASP code [2].
Figure 1 and 2 show the error of total energies
and atomic forces with respect to the reference
DFT data in the training dataset for Al2O3 and
PbTe, respectively. A data point distributed near
the black dashed line indicates that the ANN
potential accurately learns the training data

Fig. 1 Error of total energies and atomic
forces with respect to the reference DFT
data for (a) Al2O3 and (b) PbTe.

without large error. These figures show that all
the data points are distributed near the diagonalline, without large deviation, for both totalenergies and atomic forces. Thus the ANN
potentials accurately learn the reference DFT
results even for GBs.
The trained ANN potentials were thenintegrated

into

a

structural

optimization

Fig. 2 GB structure obtained from molecularsimulations with the trained ANN potential
for Al2O3.

algorithm and molecular dynamics (MD)simulations to predict energetically favorable
atomic arrangements at GBs not included in the
training dataset. Figure 3 shows an example ofReferences

Al2O3 GBs. The obtained structure was in[1] J. Behler, Int. J. Quantum Chem. 115 (2015)

agreement with an experimental observation1032.

and a theoretical calculation in the literature [3],[2] G. Kresse and J. Hafner, Phys. Rev. B 47

demonstrating excellent predictive ability of(1993) 558.

our ANN potential even for GBs.

[3] H. Nishimura, K. Matsunaga, T. Saito, T.

Finally we examined computational time of

Yamamoto, and Y. Ikuhara, J. Am. Ceram. Soc.

ANN-MD simulations. The computational time86 (2003) 574.

was found to linearly increase with the number[4] H. Guhl, H.-S. Lee, P. Tangney, W.M.C.

of atoms. Ultimately, MD simulations with 104

Foulkes, A.H. Heuer, T. Nakagawa, Y. Ikuhara,steps was finished in an hour even for GB

M.W. Finnis, Acta Mater. 99 (2015) 16.

structures with several thousands of atoms.

118Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study on controlling of electronic
structures and electron-transport properties of
low-dimensional materials
Yoshiyuki EGAMI
Division of Applied Physics, Faculty of Engineering, Hokkaido University
Kita 13, Nishi 8, Kita-ku, Sapporo, Hokkaido 060-8628

Recently, there has been a lot of energetic research and development of devices using low-dimensional materials. In the ﬁrstprinciples investigations, to estimate electrontransport properties of the nanoscale materials suspended between semi-inﬁnite electrodes,
self-energy matrices of the electrodes are required. The computational cost for obtaining the self-energy matrix is proportional tothe cube of the lateral length of the electrodewhich is a direction perpendicular to the transport direction. Therefore, the computational
cost increases dramatically as the system size
increases.
In this subject, the method to calculate
the self-energy matrices without any approximations and accuracy deteriorating is proposed. [1] In most cases, the electrode has a supercell structure in which a primitive unit cellis repeated in the lateral direction. Exploiting
the repetition, the proposed method calculates
the self-energy matrices of a large electrode byextending the self-energy matrices of the primitive unit cell using the singular-value decomposition. This makes it possible to greatly reduce the computational costs because calculating the inverse of a large matrix (for the supercell structure), which is the most computationally expensive, can be replaced by that of thesmall matrix (for the primitive unit cell). Furthermore, by comparing the self-energy matrix directly obtained from the large-sized electrode structure with that obtained using the

proposed method, it was conﬁrmed that the
self-energy matrices can be reproduced without deterioration in the accuracy.
For demonstration of the proposed method,
the computational time in generating the selfenergy terms for several supercell models is examined. For generating the self-energy terms,
the computational time increases proportional
to N 3 where N means the number of the total grid points in the supercell. In some cases,
the computational eﬃciency exceeds the theoretical value (the square of the supercell size)
because the order of the computational time
for the recursive iteration to generate the selfenergy terms is slightly larger than N 3 . On theother hand, the computational time for reproducing the self-energy terms is notably reducedby the proposed method, and this beneﬁt becomes more remarkable as the supercell size
increases. These works have been performed
on System B and System C.

References[1] Y. Egami, S. Tsukamoto and T. Ono:
Phys. Rev. B 100, 075413 (2019).

119

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of Reaction Mechanism of d-sorbitol Dehydrationin High Temperature Water with Metadynamics
1

Tomomi Kondo1,2，Chang Yong Lik1，Takehiko Sasaki1，Motoyuki Shiga2
Department of Complexity Science and Engineering, Graduate School of Frontier Sciences,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8561
2 Center for Computational Science and E-Systems, Japan Atomic Energy Agency
148-4 Kashiwanoha Campus, 178-4 Wakashiba, Kashiwa, Chiba, 277-0871

1 Introduction
Chemical reactions in high temperature pressurized water
without organic solvent or poisonous materials such as metals
are worthy of attention with respect to environmentally friendly
chemistry, i.e., Green Chemistry.

In this study metadynamics

calculation was achieved to elucidate the reaction mechanism
for the cyclodehydration of sorbitol (SBT) [1] (Fig. 1) in highFig. 1. The dehydration reaction of d-sorbitol (SBT).

temperature water (HTW). Reaction pathways were searchedon the free energy surface (FES) and the activation barriers were𝑁𝑁

𝑉𝑉ℎ𝑖𝑖𝑖𝑖𝑖𝑖𝑖𝑖 (𝑡𝑡, 𝒔𝒔) = � � ℎ exp �−compared with the experimental values.

𝜏𝜏<𝑡𝑡 𝑘𝑘=1

(𝒔𝒔𝑘𝑘 (𝑡𝑡) − 𝒔𝒔𝑘𝑘 (𝜏𝜏)) ∙ 𝒘𝒘−1
�
2

(1)

We used PIMD [2] to achieve MTD simulations associated with

2 Methodthe Density Functional based Tight Binding (DFTB) method

In Metadynamics (MTD) simulations chemical reactions
that do not happen in a regular time scale of molecular dynamics
simulations are induced by adding a bias potential proportional
to the appearance frequency on the FES defined with collective
variables (CV).

Bias potential at time t is expressed by aGaussian function (equation (1)) with height h and width wi,

Fig. 2. The reaction pathway and the collective variables (1,4-AHSO6).

where 𝒘𝒘−1 = {1/𝑤𝑤𝑖𝑖 } .

dependent term given by the sum of Gaussian functions (hills)

using DFTB+ [3]. The present system contains one molecule

deposited along the path followed by the fictitious particle (sk)of SBT, 30 molecules of H2O, one proton and one Cl- anion.

on the FES until time t. Sampling is effectively achieved by

The other system containing H2CO3 instead of H+ and Cl- wassumming over N fictitious particles (walkers) which are allowed

also examined. The thermodynamic condition at 573 K andto move simultaneously on the FES. The point corresponding

20 MPa was the same as the experimental results [1]. Fig. 1

to the maximum accumulated potential and the point at the onset

shows structures of SBT molecule and three products (1,4-of the reaction correspond to the minimum point and the saddle

AHSO, 2,5-AHSO and 1,5-AHSO) for the cyclodehydration ofBias potential is the history-

point on the FES, respectively.

120

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

SBT. Considering the reaction pathway of cyclodehydration,
there are two pathways for each product. CV is chosen foreach pathway [4].

For example, there are two reaction

pathways (1,4-AHSO3 and 1,4-AHSO6) for 1,4-AHSO
depending on the position of OH group and the carbon atom
involved in the reaction. Fig. 2 illustrates the pathway 1,4AHSO6 and the associated CV.

Fig. 3. The dehydration reaction of SBT to 1,4-AHSO6.

Here, the oxygen atom O3

in OH group on the carbon atom C3 attacks the carbon atom C6.
In order to describe this reaction pathway the dihedral angleφ（O6-C6 -C5-C4）defined by the O6-C6 bond and the bond C5C4, the difference in the O-C bonds d（= 𝑟𝑟𝑂𝑂3 −𝐶𝐶6 − 𝑟𝑟𝑂𝑂6 −𝐶𝐶6 ）between the O3-C6 bond and the O6-C6 bond, and thecoordination number n of hydrogen atoms toward O6 areselected as CV. The height of the Gaussian function was set as
h = 500 K, and the step width of the variables are set as follows:
wφ= 10.0°, wd = 0.10 Bohr , wn = 0.10 and time step = 0.25 fs.
Fig. 4. The dehydration reaction of SBT to 1,4-AHSO6.

The activation energy with H+ and Cl- was lower than that

3 Results and Discussion

with H2CO3, indicating the activation energy has a negative

Over 3.6 ns of MTD simulations with DFTB along thepathway 1,4-AHSO6 the dehydration reaction was observed

correlation withacidity.

However, relative relationship ofwith the CV atφ= 155°, d = 0.0 and n = 2.1. Fig. 3 shows

calculated activation energies of products was not in agreement

the calculated FES, where the shallow path was observed,

with the experimental results [1]. In order to overcome thisleading to the transition state marked as the red arrow. Withproblem, a method for smoothing FES was developed to

the Molecular Dynamics calculation started from this transition

decrease the sampling error and the calculation with this method

state as the initial state it was found that after the addition ofis under way.

proton to the oxygen atom （Fig. 4 ①）the dehydration （Fig.
4 ②） and the formation of a five-membered ring (C-O bond

References

formation Fig. 4 ③) happened almost simultaneously. Hence,[1] A. Yamaguchi et al. Green Chem., 13, 873 (2011).

it is concluded that the hydroxyl group of SBT is protonated, the[2] http://ccse.jaea.go.jp/ja/download/pimd/index.jp.html.

five-membered ring is formed via SN2 mechanism, and finally[3] https://www.dftbplus.org.

the excess proton is released（Fig. 4 ④）. This mechanism[4] Y. L. Chang, et al., J. Phys Chem. B, 23, 1662 (2019).

is the same as that for our previous study for the
cyclodehydration of polyalcohol [4].

121Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio molecular dynamics study of stability of artificial
retina molecule
Satoshi Ohmura
Research Center for Condensed Matter Physics / Department of Environmental and Civil
Engineering
Hiroshima Institute of Technology, Hiroshima, Hiroshima 738-5193
By means of ab initio molecular-dynamics

spectra are different from that of non-substituted

simulations, we have investigated the lightsystem in a sense that there are small peaks at

absorption properties in a photoelectric dye (2-[2-longer wavelength region. In addition to halogen[4-(dibutylamino)phenyl]-3-

atoms, we also substitute Br with [(CF3SO2)2N]−

carboxymetheylbenzothiazolium bromide ) (retina(TFSI) molecule, and investigated the stability andmolecule) coupled to polyethylene. We adopted thelight-absorption properties. Our simulation foundTime-Dependent

Linear-that substitution for TFSI molecule has the

Response Theory (TDDFRT), proposed andpotential for increasing stability of the artificial

formulated by Casida, for calculating light-

retina. For absorption spectrum, the main peak isabsorption spectrum. The absorption spectrum of

maintained, and no additional peak appears at

retina molecule obtained by the simulation have alonger wavelength region. Moreover, we havemain peak at approximately 550, which is ininvestigated effects of the water. Our simulationagreement

indicated that water stabilize the energy around the

with

]

eheny

Density-Functionaltheexperimental

result.

Counterion substitution is considered one of thecounter ion.

effective methods to improve the performance ofretinal molecule. Figure 1 shows absorption
spectra of the non-substituted retina molecule(counter ion = Br-) and substituted retina molecules(counter ion = F-, Cl-, I-). The absorption spectra of
the substituted system also have the main and small
peak, and the profile of spectrum of I-substituted
system is almost the same as non-substituted
Fig1. Light-absorption spectra, inset shows
spatial distribution of wavefuctions for HOMO
and LUMO of non- and F-substituted systemsystem. On the other hand, for F- and Clsubstituted system, the profiles of the absorption

122

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio molecular dynamics study of structural properties
and immiscibility of liquid Fe-Si-O mixtures under highpressure
Satoshi Ohmura
Research Center for Condensed Matter Physics / Department of Environmental and Civil
Engineering
Hiroshima Institute of Technology, Hiroshima, Hiroshima 738-5193
Liquid iron is a major constituent of Earth’s

atoms is stronger than those between other atoms,

outer core, but the core density is approximately

which means that a covalent like interactions exists

10 % lower than that of pure iron. Therefore, lightbetween Si and O under outer core conditions.

elements (LE) such as hydrogen, carbon, oxygen,

Moreover, our simulation found that liquid Fe-Si-silicon, and sulfur are expected to exist in the core.

O ternary systems shows immiscible tendency

Under this circumstance, we have studied theunder outer core conditions. Figure 1 shows atomic

effects of light element on the structural andconfiguration of liquid Fe-Si-O at about 140 GPa

transport properties of liquid iron mixtures byobtained from our simulation. As shown in figuremeans of ab initio molecular-dynamics simulations.

1, oxygen atoms confined to the narrow area (redFor Fe-LE binary systems, we clarified thearea in Fig. 1).

structural properties and interactions between LE
atoms at core-mantle boundary condition [1]. The
C–C interactions are stronger than those of otherlight elements. The S–S interactions depend on the
S concentration, in the sense that the shape of pair
distribution functions for the S–S correlation
change with increasing S concentration. In
addition to the binary systems, we haveinvestigated the structural properties of liquid FeFig1. Snapshot of the atomic configuration.
Gray, yellow and red ball show Fe, Si and O
atoms. Red area shows the area in which oxygen
atoms exist.

Si-O ternary systems. From the radial distributionfunction obtained from our simulations, it is foundthat Si and O atoms shows “substitutional” andReferences“interstitial” behavior even in liquid Fe-Si-O[1] S. Ohmura, T. Tsucniya and F. Shimojo:
Physica Status Solidi B, accepted for publication

ternary system. The interaction between Si and O

123

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Construction of Neural Network Force Field for Molecular
Dynamics Simulation in Multicomponent System
Kohei Shimamura
Department of Physics,
Kumamoto University, 2-39-1 Kurokami, Chuo-ku, Kumamoto 860-8555
In this study, we aimed to development of an

Even if the interatomic distance approaches

interatomic potential using an artificial neuralduring ANN-MD simulation, the ANN potential

network (ANN) applicable to multicomponent

does not learn such a state, thereby failingsystems such as life systems. This is one of thecontinuing the calculation. For long-term MD

data-driven interatomic potential that takes

simulations,advantagefunctionoversample such rare FP data and let ANN

approximation, and automatically constructs alearn. (Actually, FP data for the relaxation

functional form that represents the input dataprocess from the state where the atoms arethrough training. Since first-principles (FP)close to each other is also needed.)

of

ANN's

universal

it

was

thus

necessary

to

Next, we tried whether the key findings

calculation data is mainly used for the training,molecular dynamics (MD) simulations withobtainedthrough

ANN potentials (ANN-MD) are expected to beconstruction for α-Ag2Se can be applied to theaccessible to large-scale systems or long-term

multicomponent

calculations while maintaining FP accuracy.

glycine taken as an example is a system in

However, the current construction method may

which glycine molecules composed of four

yield less robust ANN potentials, making long-elements H, C, N, and O are irregularly

term MD calculation difficult. Therefore, weaggregated,first have investigated the factors affecting the

between the molecules. In the case of ANN

robustness of ANN potential [1], where the ion-

potential without training rare FP data, the MD

conducting phase of α-Ag2Se is employed as ansimulation cannot be continued for a few fs.

example system.

When it is learned, at least ns order is possible.

and

the

systems.

protonANN
The

potential
amorphoustransport

occursThe most important factor was found in

Although the glycine amorphous system is nottraining data. Generally, it is difficult to preparea living system, we consider that this result is ahighly diverse FP data due to its large

great step forward.

calculation cost. However, minority data can be

Referencephysically very important. That is the FP data

[1] K. Shimamura, et al.: J. Chem. Phys. 151,

with the interatomic distance approaching.

124303 (2019).

124

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Manipulation the cross-plane thermal conductivity of the 2D
hetero-junction materials
Hu Shiqian
Department of Mechanical Engineering,
The University of Tokyo, Hongo, Bunkyo City, Tokyo 113-8654
We have studied the two-path phonon-

packetmolecular-dynamics

simulation.

interference resonance which induces a stop

Compared with thetraditionalband in silicon crystal matrix by embedded

formation(single-path

nanoparticles array [1] and the coherent phonon

scattering), the two-path resonance mechanism

transport in van der Waals graphene-MoS2

has a significant advantage in not requiring thehetero-structure, using the massive parallel

strict periodicity in nanostructures, due to thecomputer simulations.

local origin of the phonon resonance.

mechanismstop-band
Bragg

Massive efforts have been devoted toMoreover, there are growing efforts tocontrol phonon transport in the phononic

control thermal transport via coherent phonons

crystals utilizing phonon interference and in thein the one-dimensional superlattice. However,phononic metamaterials (local nanostructures)in general, the difference in the intrinsic latticeutilizing local phonon resonance. However,structures

since the phononic crystals require strict global

inevitably generate interface disorder during

periodicity and the local resonances in thethe fabrication process, greatly limiting direct

metamaterials only affect phonons with specificexperimental observation of the coherent

discrete frequencies, further development ofphonon transport. The flexible integration andphonon engineering has been a pressing andatomistic interlayer smoothness of van derbaffling challenge. A new mechanism that can

Waals

mitigate the strict requirement of the globally

platform for the coherent phonon transport

periodic nanostructure and can influence a

manipulation. Thus, in the second work, using

broader and continuum range of frequencies

the(the stop band) is urgently needed.

simulations,

of

the

constituent

hetero-structure

non-equilibrium
we

providemolecular

investigate

thematerials

an

ideal

dynamics
coherent

We have studied a new stop-band formation

phonon transport in van der Waals graphene-

mechanism that is the two-path phonon-

MoS2 hetero-structure with different stacking

interference resonance by using the atomistic

order at room temperature. The histogram ofGreen’s function calculation and the wave-

the

125

phonontransmissionsindifferentActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

disordered structure exhibits a log-normal
distribution, which reveals a localization of thecoherent phonons. Furthermore, the optimal
stacking order of the graphene and MoS2 isefficiently identified from tens of thousands ofcandidatesbymachinesignificantly

suppressedlearning.
of

the

The

phonontransmission in the low frequency (<5THz)
phonons of the optimized structure lead to asignificant reduction (~95%) of the thermal
conductancecompared

with

the

pristinegraphite. Finally, the effects of the temperatureand strain effect on the thermal conductivity ofgraphite and optimized structures are also
discussed. Our work provides a deep insight
into the coherent phonons transport behavior in
the atomistically smooth van der Waals
structure, which is beneficial for further
development of phononics.

References[1]

Hu, Shiqian, et al. arXiv preprint

arXiv:2001.10321 (2020)

126

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of algorithms in crystal structure
prediction
Tomoki YAMASHITATop Runner Incubation Center for Academia-Industry Fusion,
Nagaoka University of Technology
1603-1 Kamitomioka-machi, Nagaoka, Niigata, 940-2188

We have developed a crystal structure prediction tool, CrySPY as an open source
software [1].
CrySPY is interfaced with
VASP[2], Quantum ESPRESSO[3], soiap[4],and LAMMPS code for structure optimization.
Several searching algorithms are available in
CrySPY, such as random search (RS), evolutionary algorithm (EA), Bayesian optimization(BO), and LAQA. RS is a basic algorithm andwidely used. EA[5, 6, 7] is currently very popular. We have implemented implemented EA
into our CrySPY code. Previously we havedeveloped selection-type algorithms with machine learning. BO can efficiently select potential candidates from a large number of candidate structures by machine learning[8]. LAQA
is one of the refinforcement learning, which can
reduce the computation time[9]. The key point
here is that the selection-type algorithms are
not exclusive with EA. In this study, we develop a hybrid algorithm of BO and EA. Thishybrid algorithm could be the most promising way to find the global minimum structure
in large and complicated systems. Moreover,
we compare searching efficiency among the RS,
EA, BO, and hybrid algorithm.
Searching efficiencies of RS, EA, BO, andthe hybrid algorithm have been investigatedin two systems of Si16 and Si32 . The former isa relatively easy system to find the most stable structure, and the latter is slightly difficult.
For the system of Si16 , we optimized a hundred
structures using interatomic potential calcula-tions with the soiap code in each algorithm.
Here, a hundred structures were selected fromthree hundred structures particularly in BO
and the hybrid algorithm. A hundred structures were obtained by random structure generation and the remaining two hundred structures were generated by EA in the hybrid algorithm. To statistically investigate searchingefficiencies, we carried out simulations of crystal structure prediction 50 times. The successrates to find the most stable structure were64%, 58%, 70%, and 82% for RS, EA, BO,
and the hybrid algorithm, respectively. The
success rates of RS and BO were slightly better
than that of EA. Random structure generation
is sufficiently effective to find the most stablestructure in this small system. The number ofsearching trials (100 structures) might be too
small for EA. The success rate of the hybridalgorithm was the highest in which we generated 200 structures by EA. This is because EA
was able to generate good candidates and BO
efficiently selected the good ones. For the system of Si32 , three hundred structures were optimized in each algorithm. In BO and the hybrid algorithm, three hundred structures wereselected from six hundred structures. Three
hundred structures were obtained by random
structure generation and the remaining half ofthe structures were generated by EA in the hybrid algorithm. The success rates were 46%,
60%, 54%, and 74% for RS, EA, BO, and the
hybrid algorithm, respectively. The success127

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

rate of RS was lower than others since thesystem became complex. Although the success rate of BO was better than that of RS,
BO was not as good as EA. Random structure
generation is no longer effective in this system.
However, the success rate of the hybrid algorithm was still the highest. These results show
the hybrid algorithm is superior to EA and BO
and could be the most promising method forthe crystal structure prediction.

References[1] https://github.com/TomokiYAMASHITA/CrySPY.
[2] G. Kresse and J. Furthmüller, Phys. Rev.
B 54, 11169 (1996).
[3] P.
Giannozzi
J.Phys.:Condens.Matter(2009).

et
21,

al.,
395502[4] https://github.com/nbsato/soiap.
[5] A. R. Oganov and C. W. Glass, J. Chem.
Phys. 124, art. 244704 (2006).
[6] A. R. Oganov, A. O. Lyakhov and M.
Valle, Acc. Chem. Res. 44, 227 (2011).
[7] A. O. Lyakhov, A. R. Oganov, H. T.
Stokes, and Q. Zhu, Comp. Phys. Comm.
184, 1172 (2013).
[8] T. Yamashita, N. Sato, H. Kino, T.
Miyake, K. Tsuda, and T. Oguchi, Phys.
Rev. Materials 2, 013803 (2018).
[9] K. Terayama, T. Yamashita, T. Oguchi,
and K. Tsuda, Npj Comput. Mater. 4, 32(2018).

128

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Large scale ab initio calculations on the fundamental
processes of solar energy convergence devices and on
designing principles for new materials
Koichi YAMASHITA
Elements Strategy Initiative for Catalysts and Batteries (ESICB),
Kyoto University, Nishiｋyo-ku, Kyoto 615-8510, Japan
1. Electron-phonon interactions in tungsten

calculations. An integral approach utilizing 500

oxide photocatalysts

random Q points was used for the electron-

Water-splitting

photocatalysts,

whichphonon interaction calculations. �e results

decompose water into hydrogen and oxygen by

showed that the bandgap of the direct transition

sunlight, are promising for a clean andat the Γ point is larger than the bandgap of therenewable energy source for the next generation

indirect transition. It is suggested that theof hydrogen production. A considerable amountbandgap of the indirect transition is moreof literature has been published on thepreferred and reduce carrier recombination.

photoexcited state of tungsten oxide, and long-

Next, the Eliashberg function was calculated to

lived trapped photocarriers have been found to�nd the phonons that contribute signi�cantly toplay a key role in photocatalytic reactions. Using

the electron-phonon coupling. �e transition

XAFS techniques, Uemura et al. found that thedipole moment on the Γ point of the structure,

photoexcited electrons stay on the tungsten atomwhich is displaced in the direction of the strain

and the local structure is changed [1,2]. However,caused by the phonon, was calculated. It isthere has been no detailed investigation of thesuggested that the strain caused by the phonon,

structural changes caused by photoexcitedwhich is strongly coupling with the electrons onelectrons and the changes in electronic states

the CBM, reduces the transition dipole moment,

associated with these structural changes. In thisand also reduces the recombination of thework, electronic states, phonon, and electron-

photocarriers.

phonon interaction calculations for tungsten
oxide were performed by using �rst-principles

2. Device-Scale Simulations of Organic

calculations based on density functional theory

Photovoltaics for Performance Improvement

in order to discuss the lattice distortions caused

Organic photovoltaics, OPVs, are promisingby photoexcited electrons. �ese calculations

energy harvesting devices, but their power

were performed by using Quantum ESPRESSO

conversion efficiencies are lower than traditional

6.3 and Yambo 4.2.4. GGA-PBE and “on thesilicon ones. For performance enhancement, it ismass shell” approximation were used for theseimportant to control properties of donor and129

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

acceptor materials, such as HOMO and LUMO

and end groups—from SMILES. HOMO andlevels,Fullerene

LUMO levels of indacenodithiophene, IDT,

derivatives, e.g., phenyl-C61 butyric acid methyl

derivatives were evaluated at ωB97X-D/def2-

ester, PCBM, have been used for acceptors, but

SVP level

recently non-fullerene acceptors are attracting

dependence

attentions because of easiness of LUMO level

electronegativities of end groups. In future work,tuning and light harvest. A non-fullerene

it is planned to evaluate other properties such as

acceptor is composed of three units: π-electron mobilities, absorptions spectra, andconjugated core; alkyl side chains, which control

exciton lifetimes.

bymolecular

design.

ofoftheory, which
LUMO

reproduceslevelsonsolubility; and electron-withdrawing end groups,
which control LUMO level. It is however

References

challenging to synthesize and evaluate device[1] Y. Uemura, H. Uehara, Y. Niwa, S. Nozawa,

performances for combinations of donors and

T. Sato, S. Adachi, B. Ohtani, S. Takakusagi, K.

acceptors.

Asakura, Chem. Lett. 43 (2014) 977.

In this work, density functional theory, DFT,

[2] Y. Uemura, D. Kido, Y. Wakisaka, H. Uehara,code as implemented in NTChem was employed

T. Ohba, Y. Niwa, S. Nozawa, T. Sato, K.

to evaluate material properties of donors andIchiyanagi, R. Fukaya, S. Adachi, T. Katayama,non-fullereneWe

T. Togashi, S. Owada, K. Ogawa, M. Yabashi, K.

implemented programs to generate NTChem

Hatada, S. Takakusa, Y. Yokoyama, B. Ohtani, K.

inputs—Cartesian products of cores, side chains

Asakura, Angew. Chem. Int. Ed. 55 (2016) 1364.

acceptorcandidates.

130

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Computational physics and chemistry approach todevelop the artiﬁcial photosynthesis and fuel cell
catalysts
Kazume NISHIDATE
Faculty of Science and Engineering, Iwate University
Ueda 4-3-5, Morioka, Iwate 020-8551

TiO2 is well known as an eﬃcient photo catalytic material and has a wide range of application area from air-puriﬁer to antimicrobial
coating. However, TiO2 uses only the ultraviolet ray which is less than 3 % of the whole
sunlight pouring on the earth surface. Therefore extensive studies have been devoted to develop photo-catalytic materials sensitive to visible light that makes up 50 % of the sunlight.
A large number of double-perovskite oxides, A2 B ′ III B ′′ V O6 , have been studied dueto their intriguing physical and chemical properties originating in their mixed valence nature.
Above all, Ba2 PrBiO6 was foundto show an eﬃcient photo catalytic activity to dissolve water molecules into oxygen and hydrogen gases under the visible
light. However, detailed theoretical analysis on the electronic structures and the crystal geometries of the double-perovskites has
not been performed. In this work, we study
the structural and electronic properties of
Ba2 BiIII BiV O6 , Ba2 PrBiO6 , and Ba2 PrSbO6
double-perovskites using the ﬁrst-principles
density functional theory [1]. The HeydScuseria-Ernzerhof hybrid functional was applied to the calculations to handle the strong
electron-correlation.
First of all, we evaluate the structuraland electronic properties of Ba2 BiIII BiV O6 as
it gives the basis in analyzing the double
perovskite crystals. Unit cell contains fourBaBiO3 chemical units where the BiIII octahe-

dra and the BiV octahedra are arranged alternately forming the B-site ordering. Where thedistortions of octahedra caused by the mixed
valencies are characterized by breathing distortion and tilting angle as depicted in Figure 1.
We ﬁnd that the BiIII 6s states at the top of

Figure 1: Distorted octahedra of Ba2 BiIII BiV O6 .
valence band of Ba2 BiIII BiV O6 vanish on the
Pr substitution for Bi at B ′ III -site. When Sb
is substituted for Bi at B ′′ V -site, the BiV 6s
states at the bottom of the conduction band
vanish causing additional widening of the bandgap. Further, our calculation suggests thatthe Ba2 PrPrBi O6 is a possible candidate as asource of the PrIV signal observed in the experiment. We ﬁnd that the anti-B-site atomic
conﬁgurations, Ba2 B ′′ V B ′ III O6 , are easily restored to those of the original structures. This
demonstrates the stability of the B-site ordering in the double-perovskite framework.

References[1] K. Nishidate: submitted.

131

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Reveal the mechanism of thermal transport in PbS
quantum dot system
Cheng SHAO
Depart of Mechanical Engineer, University of Tokyo
Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656 JAPANColloidal quantum system has attracted a
lot attention recently due to their controllable
electronic and optoelectronic properties.[1]Therefore, the colloidal quantum dot systems
are promising for a wide range of applications
from solar cells, thermoelectric devices, photodetectors, and many others. [2] Understanding the thermal properties of such quantum
dots system is crucial for the thermo-stability
and the performance of the above-mention application. However, due to the large unit
cell size and complex inter-atomic interaction,
the thermo properties for such system is stillless understood. In this project, we applied
the molecular dynamics simulations to systematically investigate the thermal transport
in PbS quantum dot system. The large-scale
molecule dynamics simulations is carried out
by the open source software LAMMPS withthe computational resource from The Institutefor Solid State Physics (ISSP) of the Universityof Tokyo.

The simulation model used for thermal properties calculations is shown in Fig.1. The sizeof the PbS dots is about 3 nm, which contains
about 600 atoms. C5 H10 S2 ligands are used
to bridging the connection between the quantum dots. The length of the system range from
20-100 nm, while are cross-section of 10 nm ×
10 nm with periodic boundary is used in the
direction perpendicular to the heat flux. The
simulated thermal conductivity from the nonequilibrium molecular dynamics simulations is
as lower as ∼0.1 W/mK at temperature of 300
K. As a reference, the thermal conductivity ofbulk PbS is about ∼5.0 W/mK based on thesame interatomic potential.

Figure 2: Illustration of the non-equilibrium
molecular dynamics simulation for thermal
conductivity calculation in PbS ligand system

Figure 1: Illustration of the non-equilibrium
molecular dynamics simulation for thermal
conductivity calculation in PbS ligand system

To understand the origin of the lower thermal conductivity in such system, we calculated the spectral-resolved thermal conductivity at different temperature and the results
are shown in Fig. 2. From this figure, we132Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

can clearly see that thermal transport in PbS
quantum dots system is dominated by low
frequency phonon in the frequency range of
0.2∼5 THz, while the high frequency vibrational modes are mainly scattered at the PbSligand interface. This explained the ultra-law
thermal conductivity in such quantum dot system.

References[1] Ellingson, Randy J., et al. Nano letters
5.5 (2005): 865-871.
[2] Cao, Yiming, et al. Nature Energy 1.4(2016): 1-6..

133

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Exploration of surface reactions on model real catalyst II
Wataru Mizukami
Center for Quantum Information and Quantum Biology, Institute for Open andTransdisciplinary Research Initiatives,
Osaka University, Toyonaka, Osaka 560-8531, Japan
This year, as in the previous year, we studied

performed a detailed analysis of the reaction. It

two chemical reactions on inorganic surfaces

was found that the adsorption character

using density functional theory (DFT) utilizing

transforms from the chemisorption with theparallel computational resources of ISSP's

physisorption at the reactant and product into thesupercomputer system and the Vienna Ab initio

physisorption at the transition state during the

Simulation Package (VASP) version 5.4.4. On

diffusion.
In addition to the above two studies, we

top of that, we worked on the development of anelectronic

structure

theoryfordeveloped a new quantum chemical method forquantumquantum computing based on the variational

computing.

quantum eigensolver (VQE). The VQE is a

The first reaction was the industriallyrelevant Ziegler–Natta catalysis for olefin

quantum-classicalpolymerization, which is based on titanium

optimized wave-function, where quantum-

chlorides supported by MgCl2. In the previous

circuit parameters are determined variationally.

year, we had revealed that two alkyl aluminum

Our method, called orbital-optimized unitary

molecules are involved during the active-site

coupledformation process. This year, we examined threequantum circuit parameters and molecularpossible reaction paths of the active-siteorbitals

formation in detail, and found a new possible

computing first-order molecular properties

transition state.

easily in the framework of the VQE. Taking

clusterhybriddoubles,simultaneously,

algorithm

optimizes
which

to

both
allowsadvantage of this property, we realized the first

The second reaction was a diffusion of
3,4,9,10-perylene-tetracarboxylic-dianhydride

geometry

optimizations(PTCDA), which is an organic semiconductor

molecules

using

molecule, on the Ge(001) surface. In thederivatives of the VQE.[1]previous year, we had located the transition state

Referencesof this reaction using the climbing-image[1] W. Mizukami, et al., arXiv:1910:11526

nudged elastic band method. This year, we

134

the

of

polyatomic

analyticalenergyActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

DFT calculation of atomic displacements captured by energy
dissipation of noncontact atomic force microscope
Toyoko ARAI1, Taichi Shikichi1, Jun-Ichi Iwata2, Atsushi Oshiyama3
1

Graduate school of Natural Science and Technology, Kanazawa University, Kanazawa,
Ishikawa, 920-1192
2
3AdvanceSoft Corporation, Tokyo 101-0062

IMaSS, Nagoya University, Nagoya, Aichi 464-8601
Si(111)-(7×7)

In the last two decades the conservative andsurface,thesimultaneously

non-conservative (dissipative) force interactions

obtained energy dissipation signal increased in

between a tip and a sample in proximity haveclose proximity over the hollow sites surrounded

been examined by non-contact atomic force

by a Si adatom and a Si rest atom with a dangling

microscopy (nc-AFM). In particular, the channelbond per each (Fig. 1) [1]. Based on theof nc-AFM to measure the energy dissipation

experimental results, the dynamic atomic

through the non-conservative force interactions

processes responsible for the dissipation had

has been regarded to have great potential tobeen discussed in regard to breaking of the

explorethe

backbonds of the Si adatom and subsequentdissipation channel gives the change in thebond formation in an alternative atomic

amount of mechanical energy to maintain theconfiguration of the Si surface atoms, including

constant oscillation amplitude of an AFM

the Si atom at the apex of AFM tip. In this study,

cantilever. We had experimentally found that,to elucidate the phenomena, the surface

when the nc-AFM image showed the highdiffusion potentials of a Si adatom wereresolution for the individual adatoms on a

calculated using real-space density functional

nano-mechanicalphenomena;

theory (RSDFT) [2] when the Si tip was broughtcloser to the Si(111)-(7×7) surface. RSDFT is a
first-principles program developed by Oshiyama
and Iwata, which uses a real-space difference
method and a pseudopotential method.
First, we optimized the structure of Si(111)(7×7) reconstructed surface consisting of 298 Si

Fig. 1: Simultaneously obtained nc-AFM
image and the energy dissipation image, withthe structure model of Si(111)-(7×7).

atoms and 49 H atoms by RSDFT, as shown in
Fig. 2. Then, the surface diffusion potential for a

135

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

corner Si adatom was calculated from its

from the adatom site to the hollow site. Thisoriginal position to the neighboring hollow siteenergy of less than 1 eV could be captured as a

(Fig. 3). The hollow site seems metastabledissipation energy in the nc-AFM experiment.

because of a diffusion barrier from the hollow
site to the adatom site, the barrier height ofReferences

which was several tenth of 1 eV. Our preliminary[1] T. Arai, R. Inamura, D. Kura, and M.

calculations anticipated that the diffusion barrier

Tomitori, Phys. Rev. B 97, 115428 (2018).

is lowered and the adatom can move to the[2] J.-I. Iwata, D. Takahashi, A. Oshiyama et al.,hollow site, when the tip is in close proximity to

J. Comput. Phys. 229, 2339 (2010).

the surface [3]. It is deduced that the oscillating[3] B. Enkhtaivan, Y. Sugimoto, and A.

nc-AFM cantilever can provide the Si adatom

Oshiyama, Phys. Rev. B 96, 155417 (2017).

with the kinetic energy to overcome the barrier

Fig. 3: Surface diffusion potential of the Si
adatom from the original position (x = 0,
denoted by Co (corner adatom site)) to theneighboring hollow site (x = 2.25 Å) without
the Si tip.

Fig. 2: Optimized atomic structure of Si(111)(7×7). (a) top view. (b) side view.

136

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Hybrid Ab-Initio/Machine-Learning Computation for Designing
Nano/Molecular Structure
Kenji TSURUTA, Kyosuke SATO, Md. Abdullah Al ASAD, Tadahiro MIMURA, andSatoshi OHMURAa
Graduate School of Natural Science and Technology, Okayama University, Okayama 700-8530aDepartment of Civil and Environmental Engineering, Hiroshima Institute of Technology,
Hiroshima 731-5193
Designing and developing functional
materials/molecules often require vast searchingof target properties from extra-large data set,
which is far out of the capability of conventional
computing algorithms. In recent years, theDeep-Learning (DL)-based molecular design
methods have been extensively studied. One of
the recent studies has reported [1] a machinelearning method for predicting molecularproperties by mapping a graph representation ofa molecule to a latent variable space and bylinking the variable to physical property of themolecule. Representing molecules in the latent
space enables an efficient property search within
existing data, because the DL model transforms
the discrete representation of a molecular graphinto a continuous variable space suitable forvarious numerical algorithms.
In the present study, we have developed ahybrid algorithm that combines the continuous
representation of molecules with an
optimization algorithm to predict physicalproperties of organic molecule [2]. Here theGrammar Variational Autoencoder (GVAE) [3]algorithm was adopted for transforming discrete
representation of a molecular graph into
continuous representation. The optimum valueof the HOMO-LUMO gap obtained by an abinitio quantum-chemical calculation waspredicted by searching a molecular structure
within the latent space.
The input of GVAE is a Simplified
Molecular Input Line Entry System (SMILES)
string, which represents a molecular graph. The
GVAE consists of two neural networks: An
encoder and a decoder. The encoder converts
SMILES into latent variables z, whereas the
decoder converts z back to the original SMILES
string. These neural networks are trained so thatan input SMILES coincides with the output
SMILES. The distance between molecules withcloser SMILES is mapped to a closer point in thelatent variable space. By using this method,molecular design with desired characteristics
can be treated as an optimization problem in acontinuous variable space. We have examined
the algorithm for predicting molecules using the
Quantum Machine 9 (QM9) as a training dataset.

Fig. 1 The molecule and its properties predicted by
the present method

Figure 1 shows the molecule possessing atargeted HOMO-LUMO gap among possible
molecular structures with atomic species of C, O,
N, F, and H, predicted by the present algorithm.
In this case, CF4 was predicted to have thewidest gap of 0.62151 hartree among thepossible molecular formula in the QM9 [2].
Parallelly, we have performed an ab-initio
molecular dynamics study on water-molecule
dissociation in a nanostructured perovskite
material (MAPbI3) [4]. These computations
have been done in part by using the Supercomputing System at SCC-ISSP
References[1] R. Gómez-Bombarelli et al, ACS Cent. Sci. 4(2018) 268–276.
[2] K. Sato and K. Tsuruta, Mater. Sci. Forum,in press.
[3] M. J. Kusner, B. Paige, J. M. HernándezLobato, http://arxiv.org/abs/1703.01925.
[4] M.A.A. Asad, K. Sato, and K. Tsuruta, MRS
Adv. 4, 1965 (2019).

137

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis of ion conduction in materials of proton-conducting solid electrolyte
and application to catalytic surface reaction with proton conductors
Fumiya Murase, Hiroki Matsuo, Junichiro Otomo
Graduate School of Frontier Sciences,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8561
hydrogen atom dissociate the nitrogen bondstep by step. However, the roles of the cathodic
polarization of the catalyst and protons
supplied from the electrolyte on the nitrogendissociation reaction in the ammonia
electrosynthesis process are still unclear.
In this study, the roles of the cathodepolarization of the catalyst and protons fromthe electrolyte are investigated by theoretical
calculations based on density functional theory(DFT) to reveal the mechanism of theelectrochemical promotion effect of ammonia
formation reaction.

1. Introduction
Ammonia has been regarded as one of theattractive energy carrier for storage andtransport of hydrogen because of its highhydrogen content and high energy density.
Electrosynthesis of ammonia from nitrogen
and water has been studied as a novel processreplacing the conventional Haber-Boschprocess which consumes a lot of energy.
We reported electrosynthesis of ammonia
using an electrolyzer cell with a protonconducting electrolyte and cathode catalyst of
Fe and Ru. We found the ammonia formation
rate is remarkably enhanced with increasing
cathodepolarization(electrochemical
1
promotion effect) . Since dissociation of
nitrogen triple bond is a rate-determining stepin the ammonia formation reaction, we
consider that the application of the cathodic
polarization promoted the dissociation
reaction of nitrogen triple bond.
As for the dissociation reaction of nitrogenmolecule on the metal catalyst, previous
studies based on theoretical calculations
suggested majorly two different mechanisms
for the N2 dissociation reaction on a surface ofthe cathode catalyst metals2,3. One is the direct
dissociation mechanism in which nitrogenmolecule adsorbed on the surface of thecatalyst directly dissociate into two adsorbed
nitrogen atoms. The other is associative
mechanism in which hydrogen atom initiallyreacts with the adsorbed nitrogen molecule toform N2H species and successive reaction with

2. Computational methods
For the calculation of the surface reaction,a slab-and-vacuum model was employed. We
chose BaCeO3 (BCO) with a BaO2-terminated(001) plane as a proton-conducting oxide slab
and a Ru cluster on the surface of the BCO
surface as a catalyst. DFT calculations were
performed

with

VASP5.5.4

code.

The

generalized gradient approximation proposedby Perdew, Burke, and Ernzerhof (GGA-PBE)
represented the exchange-correlation energyfunctional4. Plane-wave cut-off energy of
400 eV was adopted. Monkhorst-Pack k-meshof 2 × 2 × 1 centered at the  point for thegeometry optimized supercells.

138

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

To reveal the effect of the cathodic

configuration

of

the

adsorbed

nitrogenpolarization on the nitrogen dissociation,

molecule was stabilized in the dissociative

density of states (DOS) of the systems withmodel by the addition of an electron. This

one nitrogen molecule apart from the catalyst

result allows us to expect that the dissociationand that with nitrogen molecule adsorbed onmechanism can be promoted by the cathodic

the catalyst were calculated. Moreover, one

polarization.

electron was added to the system withadsorbed nitrogen molecule to reproduce thecathodicpolarization

in

the

ammoniaelectrosynthesis.
Fig. 1. The Ru cluster and the adsorbed N2

3. Results

molecule on the BCO (001) surface withIn the calculation for the model without

BaO2-termination.

adsorbed nitrogen, electron-occupied Ru 4d
state was emerged at around Fermi level after

Table 1. Calculated charges normalized by

the addition of an electron, which suggested

elementary charge for constituent atoms of thethat the cathodic polarization activates an

Ru cluster and the adsorbed nitrogen molecule

electron-donating property of the Ru catalyst.

before and after the addition of an electron

Moreover, the calculation for the model withnormalized by elementary charge.

adsorbed nitrogen showed that an anti-bonding
orbital of the adsorbed nitrogen located aroundthe Fermi level after the electron addition.
Then, charges of constituent atoms of the Rucluster and the adsorbed nitrogen molecule(Fig. 1) were calculated for the system before
and after the electron addition. As summarizedin table 1, the N2 atom and the Ru atoms were
negatively charged after the electron addition.
These results suggested that back donation of

Atom

BeforeAfter

Variation

N1

−0.36

−0.35

0.01

N2

−0.05

−0.15

−0.10

Ru1

−0.42

−0.51

−0.09

Ru2

0.16

0.07

−0.09

Ru3

−0.03

−0.09

−0.06

Ru4

0.09

0.04

−0.05

References

electron from the Ru catalyst to the adsorbed[1] F. Kosaka et al., Sustainable Chem. Eng.,

nitrogen molecule can be promoted by the5, 10439–10446 (2017).

application of the cathodic polarization.

[2] S. Back and Y. Jung, Phys. Chem. Chem.

To clarify the possible nitrogen dissociation

Phys. 18, 9161–9166 (2016).

mechanism, the reaction activation energies[3] D. Bao et al., Adv. Mater., 29, 1604799

for the two mechanisms were calculated with(2017)

the nudged elastic band (NEB) method.

[4] Perdew, J. P. et al., Phys. Rev. Lett. 77, 3865

Though the apparent difference in the(1996).

activation energy was not observed, side-on

139

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Transport and reaction properties of nanographene
Koichi KUSAKABE
Graduate School of Engineering Science, Osaka University
1-3 Machikaneyama, Toyonaka, Osaka 560-8531

1. A cross-correlation transport eﬀect ofa magnetic Ni/h-BN/Ni junction
We found that a thin magnetic Ni/h-BN/Nijunction allows a novel magnetoresistance effect controllable by the external electric-ﬁeld,
i.e. a cross-correlation eﬀect. The eﬀect comesfrom realization of local pyramidal B-N3 structures of the h-BN monolayer. When the antiparallel spin conﬁguration of two ferromagnetic Ni layers is ﬁxed, the spin-polarized tunnel current is reversed in its spin-moment direction by the electric ﬁeld whose ﬁeld strengthis within a realizable range. Switching uprightpyramids to inverted pyramids, the electronic
polarization direction in the h-BN layer andthe spin-moment direction are reversed.[1]2. The strong-correlation eﬀect in anelastic property of defect-free graphite
We developed new DFT-based simulation
methods, i.e. LDA+U+RPA and ACFDTRPA+U, for the explanation of unexpectedly
large elastic constant C33 of the defect-freemonocrystalline graphite by KANEKA, whichis measured by the microscopic picosecond ultrasound method.[2] The short-range correlation eﬀect described by the U term causes unharmonic potential proﬁle raising C33 from thevalue by ACFDT-RPA by more than 20%.
3. Hydrogen production catalyzed bygraphene with vacancies
We found that hydrogenated graphene vacancies promote dehydrogenation processes ofseveral alkane molecules in simulations. Basedon these results, we can propose that creation of atomic vacancy becomes the activa-

140

Figure 1: Calculated C33 by LDA+U+RPA(solid line) and LDA+U.[2]tion of the dehydrogenation catalytic propertyof graphene, which is shown to be realized inexperiments.[3]4. Zero modes in PTM molecules
The counting rule of zero modes by Morishita holds generally in a set of phenalenyl
tessellation molecules (PTM).[4] Based on theruled creation of zero modes, we can constructa certiﬁed ferrimagnetic Hubbard model in two
dimensions. An eﬀective low-energy model becomes a Kondo-lattice model, where extending
orbitals causes the Kondo screening in localized spins of arrayed zero modes.
Acknowledgement
This work was partly supported by KAKENHI (Nos. JP18K03456 and JP19H00862).
References[1] H. Harfar, et al., ACS Appl. Elec. Materials, in press. [2] K. Kusakabe, et al., Phys.
Rev. Materials, 4, 043603 (2020). [3] K.
Kusakabe, et al., Japan patent appl. JP2019135780 [4] N. Morishita and K. Kusakabe, J.
Phys. Soc. Jpn. 88, 124707 (2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyovan der Waals density functional study of image-potential
states at organic-metal interfaces
Yuji HAMAMOTO
Department of Precision Science and Technology, Graduate School of Engineering,Osaka University, Yamada-oka, Suita, Osaka 565-0871
Recent progresses in observation techniques

1
Interaction energy / eVenable us to elucidate the transport properties ofunoccupied states on solid surfaces. Amongthem, image-potential states (IPSs) are ofparticularimportance,

since

they

appearubiquitously on metal surfaces, exhibiting a

0
ï1
ï2
ï3
4.0

Rydberg series with parabolic dispersions. From

top
bridgehollow

4.5

5.0
5.5
6.0
Distance / Å

6.5

7.0

an applicational point of view, IPSs could

Fig. 1: Determination of the equilibrium dis-

influence the properties of molecular-basedtance between PbPc and graphene

electronic devices such as organic light-emitting

as shown in Fig. 1. Experimentally, IPSs of PbPc

diodes, interacting with unoccupied molecularadsorbed on HOPG has been investigatedorbitals of adsorbates. Recently, we have applied

intensively using two-electron photoemission

van der Waals density functional (vdW-DF)

spectroscopy [3-5]. Unlike naphthalene, PbPc

method [1] to naphthalene physisorbed on

has a non-planar shuttlecock structure due to thegraphene and revealed that IPSs are induced onaclose-packed

naphthalene

central lead atom, which results in a dipole

monolayer,

moment. To understand the influence of thehybridizing with graphene IPSs [2]. The

dipole moment on hybrid IPSs, we investigate

resultant hybrid IPSs show an anisotropic

the band structure of PbPc on graphene andeffective mass that reflects the molecularanalyze the effective mass of the IPSs. Our

structure of naphthalene, demonstrating that theresults reveal that the dipole moment reduces thetransport properties of IPSs of metal surfaces

overlap of wave functions between neighboring

can be fine-tuned by molecular adsorption.

molecules, which enhances the effective mass ofAs an extension of our previous study on

the hybrid IPSs. Moreover, unlike the IPSs ofhybrid IPSs at molecular-metal interfaces, we
heretheoreticallyinvestigate

graphene, the hybrid IPSs in PbPc on grapheneleaddisplays an anisotropic effective mass withphthalocyanine (PbPc) physisorbed on graphene141

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

nearly C4 symmetry, which prominently reflects[3] M. Shibuta, K. Miyakubo, T. Yamada, and T.

the molecular structure of PbPc [6].

Munakata, J. Phys. Chem. C 115, 19269 (2011).
[4] N. Kawakita, T. Yamada, M. Meissner, R.

References

Forker, T. Fritz, and T. Munakata, Phys. Rev. B[1] M. Dion, H. Rydberg, E. Schröder, D. C.

95, 045419 (2017).

Langreth, and B. I. Lundqvist, Phys. Rev. Lett.

[5] T. Yamada, N. Kawakita, C. Okui and T.

92, 246401 (2004).

Munakata, J. Phys.: Condens. Matter 31, 044004[2] S. A. Wella, H. Sawada, N. Kawaguchi, F.

(2019).

Muttaqien, K. Inagaki, I. Hamada, Y. Morikawa,[6] Y. Hamamoto, H. Sawada, S. A. Wella, K.

and Y. Hamamoto, Phys. Rev. Materials 1,

Inagaki, I. Hamada, and Y. Morikawa, in

061001(R) (2017).

preparation.

142

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

STM simulations for Fe-adsorbed Si(111) surfaces
Kei TANIMOTO and Ken HATTORI
Graduate School of Science and Technology, Nara Institute of Science and Technology
Takayama, Ikoma, Nara 630-0192

Using scanning tunneling microscopy(STM), author’s group has been studied
iron-silicides formation on Si(111) [1] prepared in ultra-high vacuum. In the initialstage of Si(111)7×7 with isolated Fe atoms,
we observed 5 diﬀerent adsorption types inexperimental STM images [2]. In order tounderstand (meta) stable actual structures of
Fe/Si(111)7×7, we carried out ﬁrst principles
calculations using the super computing systemin the institute for solid state physics.
We utilized the calculation package of Simulation Tool for Atom TEchnology (STATE)Senri [3] for 17 models of Fe single-atom adsorption including atop, ins, T4 , and H3 sites,
based on a Si(111)4×4 surface-substrate model[4]. The 4×4 model (i.e., 4 Si adatoms on
2×2 T4 sites, and 2 of 4 restatoms terminatedwith H atom, in a unit) has an advantage offast calculation, because of smaller number ofatoms compaired to that in the 7×7 model,
maintaining the speciﬁc Si surface property of
the 7×7 model of the dimer–adatom–stackingfault, though the 4×4 model is not equal to
the 7×7 model.

The clean Si(111)4×4 model consisting of a
Si adatom-layer, six Si-layers, and a bottom
H-terminated layer has 118 atoms, while 7×7
has 347 atoms. The top-view and side-view
schematics in Fig. 1 show the atomic structure of the clean 4×4 model; upper adatom(brawn ball) corresponds to center adatom(CEA) with two neighbored restatoms (purple
ball, note another restatom is terminated by Hatom), and lower adatom corresponds to corner adatom (COA). The bottom panel represents STM simulation images of ﬁlled (empty)
states at -0.5 (+0.5) V in bias voltage, displaying clear adatom images.
In the simulation, the atoms in the top six
layers were relaxed with the spin polarization,from the converged conﬁgurations without the
spin polarization.

Figure 2: A model of Si(111)4×4 surface withFe atom near a H3 site and STM simulation
results.

Figure 1: A model of Si(111)4×4 clean surface
and STM simulation results.

143

During the 17 models, the stable conﬁguration was Fe atom close to H3 site as shown in
Fig. 2; Fe atom (pink ball) locates between
CEA and restatom, with the formation energyof -7.59 eV. The STM images showed darken
adatom at ﬁlled states at -0.5 V while no drastic change at empty states at +0.5 V. The sec-

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoond (meta) stable conﬁguration was also nearH3 site COA and restatom with the formationenergy of -7.55 eV. The third meta-stable conﬁguration group was near T4 sites with -6.87
eV to -6.35 eV in formation energy. The fourthgroup was ins sites with -6.34 eV to -6.28 eV,
and the last (much unstable) group was atop
sites with -5.32 eV to -5.28 eV.
The authors thank Profs.
Morikawa,
Hamada, and Inagaki in Osaka University, andProf. Yanagisawa in Ryukyu University for
their great support in STATE-Senri calculations.

References[1] K. Kataoka, K. Hattori, Y. Miyatake,and H. Daimon, Phys. Rev. B 74 (2006)
155406.
[2] K. Kataoka, Dr.. Thesis, Nara Institute of
Science and Technology, Nara (2006).
[3] Y. Morikawa, Phys. Rev. B 63 (2001)
033405, and references therein.
[4] Guo-Xin Qian and D. J.Chadi, Phys. Rev.
B 35 (1987) 1288.

144

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis on atomic and magnetic structure in magnetic
molecular complex, crystal and interface and investigation of
external field effectMasao OBATA1,2
1

Institute of Science and Engineering, Kanazawa University, Kanazawa, Ishikawa 920-1192
2

Graduate School of Natural Science and Technology, Kanazawa University, Kanazawa,
Ishikawa, 920-1192
We have investigated the weak-boundproportional to minus cube of distance. It canmagnetic material systems such as magnetic

be estimated using spatial spin density obtained

molecular

fromcrystalandmagnetic-layered

DFT calculation.

Weappliedthismaterial. They have received a lot of attention

approach to antiferromagnetic molecular crystal

due to their unique physical properties, such as[1] (monoclinic crystal solid oxygen 𝛼𝛼 phase:external field-controllable its magnetization andcrystal structure. Since prediction of structural

𝛼𝛼 -O2) and ferromagnetic thin film and chain

and energic properties with high accuracy is

MA is comparable to those of Spin-Orbit

essential

for weak-bond magnetic materials,

Interaction. Moreover, the spatial distribution

we have enhanced the computational accuracyof intra-atomic spin density occasionallyof density functional theory (DFT) by including
physical interactions, e.g. van der Waals (vdW)

contributes to MDI energy. For solid oxygen 𝛼𝛼-interaction and magnetic dipole-dipole (MDI)

DF method, which developed in our previous

energy, which were neglected in standard DFT

work [2], was employed. External magnetic

calculation. While MDI energy is often

field effect due to Zeeman interaction can beconsidered as weak, it plays important role formagnetic anisotropy (MA) and diamagnetic

considered for oxygen 𝛼𝛼-phase case, in order tofield. Moreover, we also attempt to build a[3].

framework to investigate the external magnetic

References

field effect.

[1] M. Obata et al., AIP Adv. 8, 10149 (2018).

We developed

the method(Fe, Co, Ni). We found that its contribution tophase case, noncolinear spin-dependent vdW-

investigate the effect towards its magnetization[2] M. Christivana et al., JPSJ 88, 104601

for eachmaterial dimensionality (chain, film, bulk) to(2019).

estimate[3] A. R. Rio et al., JPSJ 89, 035002 (2020)

their

MDI

energy,

since

MDI

interaction is basically long-range interaction

145

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Eﬀects of electron-phonon scattering on electronic
structure of half-metallic Heusler alloys
H. Akai
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

In some Heusler alloys, despite the fact that
there exists a band gap in one of spin channels
expected, established through ﬁrst-principles
calculations, the half-metallicity of the materials often turns out fragile under realistic situations such as in device structures. It has
been pointed out that chemical disorders anddefects might easily degrade the half-metallic
nature of such materials. These degradations
are structure oriented, and therefore, static.
This means, once a perfect structure is attained, there exists no reason of this kind of
degradation for the half-metallicity. However,there still exist another source of degradation,i.e., dynamical eﬀects. The main sources ofsuch eﬀects are phonons and magnons at ﬁnite
temperature. In the present research, we discuss the eﬀects of electron-phonon scatteringon the half-metallicity of Co2 MnSi, as a typicalexample, on the basis of ﬁrst-principles calculations. The phonons are treated as giving local and static (adiabatic) eﬀects [1], where correlations of the displacements between neighboring sites as well as dynamical eﬀects are neglected, i.e. we take a quasi-dynamical treatment. The phonons are expressed as random
displacements of atoms from their equilibrium
positions. Using the distribution of the atomic
displacements, the electronic structures of thesystem at ﬁnite temperature are calculated byregarding the system as a disordered systemwith randomly distributed atomic positions.
This kind of randomness can be treated using KKR-CPA code [2]. The results show

146

that even at 300 K, the perfect half-metallicity
is lost (Fig.1), showing that the eﬀects ofphonons are important at usual operating temperatures of devices. The eﬀects on the GMR
is also discussed. It turns out that, though
the half-metallicity is lost at ﬁnite temperature, the conductivity of the spin-down stateis much lower than that of the spin-up state
by virtue of the strong electron-phonon scattering. Thus, the system can still be used in
GMR devices at ﬁnite temperatures.

Figure 1: DOS of Co2 MnSi with an average
displacement hu2 i = 0 (left) and 0.046 (right)
in units of Bohr2 .

References[1] S. Kou and H. Akai, Solid State Commun.
276, 1 (2018).
[2] H. Akai, AkaiKKR, http://kkr.issp.
u-tokyo.ac.jp/ (2002).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Systematics of Curie temperature in rare earth
permanent magnet materials
H. Akai
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

References

Calc.
Calc. lmd
Expt.

R2Fe14B

TC (K)

1000

500

0
La

Ce

Pr

Nd Sm Gd Tb Dy Ho Er
Rare-earth elements

Tm Yb

Lu

Y

Figure 1: Calculated TC of R2 Fe14 B comparedwith experiments.
R2Co14B

Calc.
Calc. lmd
Expt.

TC (K)

1000

500

0
La

Pr Nd Sm Gd Tb
Rare-earth elements

Y

Figure 2: Calculated TC of R2 Co14 B comparedwith experiments.
Calc.
Calc. lmd
Expt.

R2Fe171000

TC (K)

Curie temperatures TC ’s of permanentmagnet materials R2 (Fe,Co)14 B, R2 (Fe,Co)17 ,and RFe11.5 Ti0.5 (R = La, Ce,. . . , Lu, Y),
are calculated within the mean field approximation using the exchange coupling constants Jij ’s that are obtained by first-principles
KKR–Green’s function method[1]. While theagreement between the calculations and experiments is rather well for the Co-based systems,
there arise some discrepancies in the case of
Fe-bases systems. Despite these discrepancies,
however, the systematic changes seen in TC
as the rare earth element R changes acrossthe lantanoid are fairly well reproduced by thecalculation. In the case of R2 Fe14 B, the discrepancies can be largely diminished by using
Jij ’s that are calculated for local-moment disordered states (LMD), which is considered tocorrespond to the paramagnetic state above
TC , as is shown in Fig.1 and 2. However, this is
not the case in general: the discrepancies seenin R2 Fe17 (FIg. 3), cannot be remedied. From
the analyses of calculated and experimental
data, it is concluded that data assimilations
are possible and necessary to make reasonablepredictions of TC for rare earth permanentmagnet materials, in particular, the Fe-based
ones.

500

0
Ce

[1] H. Akai, AkaiKKR, http://kkr.issp.
u-tokyo.ac.jp/ (2002).

147

Pr

Nd Sm Gd Tb Dy Ho Er
Rare-earth elemets

Tm Yb

Lu

Y

Figure 3: Calculated TC of R2 Fe17 comparedwith experiments.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electronic state of water under various environments
Ryosuke YAMAMURA, Kento AKIHIRO, Nozomu FUTAMATA, and Osamu
TAKAHASHI
Graduate School of Science, Hiroshima University, kagamiyama, Higashihiroshima,
Hiroshima 739-8526
We have studied aqueous solution using
massive parallel computer simulations. This
year, we focus on aqueous oxalic and malonicacid observed by X-ray absorption and

Fig. 1: (a) XAS and (b) XES spectra ofemission spectroscopy [1]. To obtain the

aqueous oxalic acid (solid line: experiment,

theoretical spectra of an aqueous solution, adash: theoretical, black: pH 1.1, red: pH

molecular dynamics (MD) simulation based

2.7, green: pH12.9).

density functional theory (DFT) was adopted toemission spectra. The core excited dynamics

simulate the structure of the solution. The MD

and relative peak intensities of the spectra were

simulations ware performed using the Vienna

calculated within the framework of DFT using

ab initio simulation package (VASP). The MD

deMon2k code.

simulations ware performed for 5 ps, with 0.2-

We found that the theoretical XAS and XES

fs time steps. Cluster sampling was performed

spectra of cluster models reproduced theusing python and fortran code for the results oftrends of the experimental spectra with

the MD simulations. From the cluster obtained

respect to emission energy compared withby structure sampling, a carboxylic acidsingle molecular models. We found that themolecule at the center of the cluster was used todependence of XAS and XES spectra on pH

model the OC=O,1s and OC-O-,1s core-holeis different from monocarboxylic acid.

and core excited state dynamics. The time steps

Referencesused for these simulations were 0.25 and 20 fs,[1] R. Yamamura, T. Suenaga, M. Oura, T.

respectively. During the core excited state

Tokushima, and O. Takahashi: Chem. Phys.

dynamics, each snapshot was used to calculate

Lett. 738 (2020)13689

the relative line intensities of the X-ray

148

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Temperature-Dependent Optical Properties in Rare-earth
Sesquioxides and Related Phonon Calculations
Takayuki MAKINO
Department of Electric and Electronics Engineering,
University of Fukui, Fukui 910-8557, JapanThe natural oxide of Si, amorphous SiO2, isFigure 1 shows temperature dependences of theimportant for the CMOS technology. Due to theband-gap energies. Alloted symbols are open

problem related to its fundamental size limits,

circles for ytterbia and open squares in lutetia,

reduction of the gate-oxide thickness in devices

respectively. We here use Pässler model to fit tois strongly demanded. As one of the expected

the experimental data. the detailed values ofcandidates satisfying these properties, attention

deduced parameters have been given elsewhereis paid on rare-earth metal sesquioxides. Their[1]. We could reduce of the number of running

optical properties are almost far from the fullparameters in the regression analysis which are

understanding. It is expected that such aantemperature-dependent optical study can yield

abovementioned

in several insights not only on electronic or

discussion.

advantage

andsignificance

of

the

phonon-property-related

excitonic properties, but also on phononic
properties. In this activity report, we report theReferences

optical[1] T. Makino et al.: Jpn. J. Appl. Phys. 59

properties

andrelatedphononcalculations of ytterbia (Yb2O3) and lutetia(2020) SCCB13.

(Lu2O3) thin films.

[2] R. Pässler, Phys. Rev. B 66, (2002) 085201.

The phonon properties of the structure are
obtained by a frozen phonon method: The
forces acting on the ions are calculated upon asmall displacement of each ion by using
Quantum ESPRESSO package. The set offorces can be converted into the force constants,
which are required to construct the dynamical
matrix. We used the PHONOPY package togenerate a set of 2×2×2 supercells with

Fig. 1: Temperature dependences of band-gap
Eg in Yb2O3 (circles) and Lu2O3 (squares).

displaced atoms, to compute the phonon
dispersion and density-of-states (DOS) spectra.

149

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation of organic modified metal oxide
nanoparticles
Akira YOKOWPI-Advanced Institute for Materials Research,
Tohoku University, Katahira 2-1-1, Sendai, Miyagi 980-8577
We have studied an interface system ofbasis was set at 500 eV for all the calculations.

organic molecules on metal oxide surface.

Monkhorst–Pack k‐point set of 4 × 4 × 1 wasFrom the experiments, it is known that surface

used for the a slab model. Convergence criteria

stability of metal oxide greatly changes

was set at less than 0.01 eV/Å for the force.
Figure 1 shows the adsorption,

depending on the environment, resulting in the
difference in the properties. For example, CeO2

deprotonation, and dehydration of octanoic acidis ordinary stable with (111) surface, but it turns

on CeO2 (100) surface considered in this study.

to be stable with (100) facet when

From the results, energy stabilization washydrothermally treated with carboxylic acid. As

calculated as -26.63 kJ/mol for adsorption anda result, catalytic activity is greatly enhanced-26.57 kJ/mol for deprotonation. Deprotonation

with (100) facet exposure of CeO2 [1]. In thisdoes not contribute stabilization. Dehydration

year, we studied the interaction betweenof octanoic acid and hydroxide on CeO2 surface,octanoic acid and CeO2 surface using first-

much larger stabilization as -43.20 kJ/mol was

principles simulation.

observed.

Plane-wave basis density functional theory
simulations were conducted with VASP code.
Simulations were The generalized gradientapproximation proposed by Perdew, Burke, andErnzerhof (PBE) represented the exchange‐
correlation energy functional. The DFT+U
method introduced by Dudarev was used totreat electron localization. The parameter U-J

Figure 1 Adsorption, deprotonation, andwas set to 5.0 eV for Ce4f state. The valence

dehydration of octanoic acid on CeO2 (100)configurations of the pseudopotentials wereReferences

5s25p64f15d16s2 for Ce, 2s22p4 for O, and 2s22p2[1] X. Hao, A. Yoko, C. Chen, K. Inoue, M. Saito, G. Seong, S.

for C. The energy cutoff for the plane‐wave

Takami, T. Adschiri, Y. Ikuhara: Small 14 (42), (2018) 1802915

150

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles study on leaking current at a
dislocation in doped semiconductors
Yosuke HARASHIMA
Institute of Materials and Systems for Sustainability, Nagoya University
Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8601

In the second half fiscal year of 2019, we haverevealed the following results related with theperformance of gallium nitride (GaN) powerdevices [1].
• The threading screw dislocations attract
Mg impurities, and the electronic levels in
the energy gap induced by the threading
dislocations elevate towards the conduction band as the Mg approaches the dislocation line.
This results suggest that the leakage current
which degrade the performance of the devices
is induced by the presence of the Mg and thescrew dislocation complexes.
GaN is one of the most promising compounds for the power devices since it has alarge band gap. For the realization of the device, suppressing the leakage current is an important issue. The leakage current has been
observed at the position of the threading dislocation. Recent experimental study suggeststhat the Mg impurities are condensed aroundthe dislocation. The electronic structure of
the Mg-dislocation complexes should be related with the origin of the leakage current,
and it is important to guarantee the device reliability.
In this study, we systematically perform
first-principles total-energy calculations forpossible 16 core structures of the screw dislocations as shown in Fig. 1. The core structures are expressed as D(n | m) or S(n | m).
The first capital letter denotes the position of
the dislocation line. One is called single core,

Figure 1: The 16 core types of the screw dislocations. A red cross in the top panel denotes
the position of the dislocation line. The left
is for D(n | m) and the right is for S(n | m),where n is the number of removed Ga and mis that of N.
in which the dislocation line is at the centerof the single hexagon; Another is called double core, in which the dislocation line is at the
middle of the bond of hexagon. n and m represent the numbers of Ga and N atoms removed
from the fully filled structures. An example ofD(0 | 0) is shown in Fig. 2
Those first-principles calculations are doneby using the Vienna Ab initio Simulation
Package (VASP) [2] which is based on the
projector augmented-wave (PAW) method.
The exchange-correlation energy is treatedwithin the generalized gradient approxima-

151

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fictitious hydrogen

Dislocation line
41Å
GaN
49Å

Figure 2: The core structure D(0 | 0). Greenand blue spheres denote Ga and N, respectively. The atoms surrounding the dislocationline are enlarged to emphasize the position.

tion (GGA) with the Perdew-Burke-Ernzerhof
functional. We also use the Heyd-ScuseriaErnzerhof (HSE) hybrid functional to evaluate more accurate electronic levels in the bandgap. The unit cell contains about 800 Ga
and N atoms in total. The GaN pillar issurrounded by the vacuum on the lateral directions perpendicular to the [0001]. We expect that this vacuum relaxes artificial straincaused by rounding the lateral surfaces. The
dangling bonds on the lateral surface of the
GaN pillar are terminated by ≈ 100 fictitioushydrogens. The schematic picture of the unit
cell on the [0001] plane is shown in Fig. 3. The
integration over Brillouin zone is taken with
4 sampling points along the [0001] direction.
The structural optimization is performed foreach core structures.

VacuumFigure 3: A schematic picture of the [0001]
plane of the unit cell. The green region denotes GaN and it is terminated by the fictitioushydrogen atoms. The outermost region is thevacuum. A red cross denotes the position of
the dislocation line.

References[1] T. Nakano, Y. Harashima, K. Chokawa,
K. Shiraishi, A. Oshiyama, Y. Kangawa,S. Usami, N. Mayama, K. Toda, A.
Tanaka, Y. Honda, and H. Amano: arXiv,
2004.06876 (2020).
[2] G. Kresse and J. Furthmuller: Phys. Rev.
B 54, 11169 (1996).

We found that D(0 | 2), S(0 | 3), and S(0 | 6)
are stable. Then we replace one Ga atom inthese three core structures with an Mg atom.
The relative position of the Mg from the dislocation line is sampled. The resultant binding
energy of the Mg shows that Mg is attracted
by the screw dislocation and the electronic levels in the gap elevate towards the conduction
band, as mentioned above.

152

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab Initio Band Structure Calculation of InSb Using VASP
Based on Hybrid Density Functional Theory
Hiroki I. FUJISHIRO, Yoshitaka MATSUMOTO, Takahiro SUZUKI, and Akira ENDOH
Department of Applied Electronics,
Tokyo University of Science, Niijuku, Katsushika, Tokyo 125-8585
Terahertz-wave frequency range (0.1 to 10

of unstrained and compressively strained InSb

THz) will be the major resources in futureusing Vienna Ab initio Simulation Package

communication and sensing systems. InSb

(VASP) based on the method in the local density

channel high electron mobility transistors

approximation to obtain band parameters [3].

(HEMTs) are one of the most promising devices

We obtained nonzero bandgap energy Eg values

that can operate in the terahertz band. Although

by using PBE0 (Perdew-Burke-Ernzerhof 0) as

InSb has the lightest electron effective mass ina functional. In this work, we investigated

III-V semiconductors, the lattice constant offunctionals used for band structure calculation in

InSb is the largest. Therefore, compressive strain

order to obtain the Eg values close to theis always applied to the InSb channel.

literature ones.

In our previous work [1], we carried out

We studied the hybrid coefficient of theMonte Carlo (MC) simulations of InSb channel

density functional [4]. The hybrid functional

HEMTs to predict device performance. We used

used in this work was a modification of PBE0.

the band parameters calculated by the empirical

The functional is constructed by the mixing of apseudopotential method [2]. However, the band

fraction 𝛼 of the Fock exchange with a fraction

structure obtained from the first-principles

1

calculation seems to be preferable. In 2018, we

correlation energy 𝐸

carried out ab initio band structure calculations

following equation:

𝛼 of the PBE exchange. The exchangecan be expressed by the2Bandgap energy [eV]

1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0

0.05

0.1

0.15

0.2

0.25

0.3

0.35

0.4

0.45

Mixing coefficient, Fig. 1 Calculated bandgap energy as a function of mixing coefficient, .

153

0.5

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

𝐸

𝛼𝐸

(1)

However, the increase in the value of m* for theis the PBE-1.32% compressively strained InSb also

is the PBE correlation [4].

appears to be small. Furthermore, there is room

1

𝛼 𝐸

𝐸

where 𝐸 is the Fock exchange, 𝐸
exchange, and 𝐸

In PBE0, the mixing coefficient 𝛼

0.25 . In

for reconsideration of the energy difference

our previous work [3], we obtained the bandgap
energyEgvaluesofunstrained

between  and L valleys, 𝐸

andvalleys, 𝐸

compressively strained InSb. However, the Eg
values are too large when using 𝛼

and  and X.

Regarding the mixing coefficient of the

0.25

density functional, further work is necessary(PBE0). We calculated the bandgap energy

considering the correspondence with various

values as a function of 𝛼 . Figure 1 shows theliterature and experimental values.

calculation results of bandgap energy. We
obtained the closest bandgap energy Eg to theReferences

previous work [5, 6] with 𝛼[1] T. Takahashi, S. Hatsushiba, S. Fujikawa,

0.21.

and H. I. Fujishiro: Phys. Status Solidi A 214

Table 1 summarizes the band parameters of
InSb in Refs. [3, 5, 6] and in this work. In our(2017) 1600599.

previous work [3], we obtained the bandgap[2] H. Nishino, I. Kawahira, F. Machida, S. Hara,

energy Eg of 0.34 and 0.48 eV for unstrainedand H. I. Fujishiro: Proc. 22nd Int. Conf. on(0%) and compressively strained (-1.32%) InSb,

IPRM (2010) p. 156.

respectively. The Eg value for unstrained InSb in[3] H. I. Fujishiro, Activity Report 2018,[3] is much larger than that in [5, 6]. In the

Supercomputer Center, Institute for Solid State

present work, the Eg value was relatively

Physics, The University of Tokyo, p. 137.

reasonable because the mixing coefficient 𝛼 was[4] T. Garwood, N. A. Modine, and S. Krishna:

set to match the “general” bandgap value of InSb

Infrared Physics & Technology, 2017.

[5, 6]. On the other hand, the increase in Eg when

[5] M. Levinshtein, S. Rumyantsey, and M.

compressive strain is applied seems to be small

Shur: Handbook Series on Semiconductor

for 𝛼

0.21. The electron effective mass in the

Parameters in 2 Volumes, World Scientific, 1996.

 valley m* of unstrained InSb is almost same

[6] H. Rodilla, T. González, D. Pardo, and J.

as the values in the previous results [3, 5, 6].

Mateos: J. Appl. Phys. 105 (2009) 113705.

Table 1 Main band parameters of InSb.
0%[5, 6]
𝐸 eV)
𝑚∗
𝐸
eV)
𝐸
eV)

0.18
0.014
0.76
0.46

0%
(VASP)
[3]
0.34
0.015
1.04
2.64

-1.32%(VASP)
[3]
0.48
0.022
1.06
2.69

154

0%
(VASP)[This work]
0.151
0.012
1.05
2.64

-1.32％(VASP)[This work]
0.154
0.013
1.05
2.64

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles investigation of electronic propertiesof carbon nanotubes and graphene
Yoshitaka FUJIMOTO
Depertment of Physics, Tokyo Institute of Technology
Ohokayama, Meguro, Tokyo 152-8551

Graphene and carbon nanotubes (CNTs)
show high charge mobility at room temperature, and therefore they are expected to be a
promising device material to be used in nanoelectronics such as field-eﬀect transistors. Substitutional doping is one of the eﬀective ways
to tune the electronic properties of graphene
and CNTs, and is also shown to improve thechemical reactivity to adsorbates. Therefore
dope graphene and doped CNTs are a goodcandidate for future sensor device materials.
We here present the adsorption propertiesof toxic NO and NO2 molecules on the borondoped graphene and (8,0) CNT using a firstprinciples density-functional calculation [1, 2,
3]. It is found that the NO and NO2 molecules
can be adsorbed strongly with short distancesand large adsorption energies on the B-dopedmonolayer graphene [2]. For the AB-stacked
bilayer graphene, NO and NO2 molecules canbe also strongly adsorbed [1, 3]. It is also
found that the adsorption energies of NO andNO2 molecules on the B-doped (8,0) CNTs aremuch larger than those of monolayer and bilayer graphenes.
Table 1 lists the adsorption energies and the

distances between the B atom in the doped
graphene layer and the adsorbed molecules for
NO and NO2 molecules on the B-doped monolayer and AB-stacked bilayer graphenes. The
NO and NO2 molecules are found to be adsorbed strongly with short distances and large
adsorption energies on the B-doped monolayer
graphene. For the case of the AB-stacked bilayer graphene, it is interesting that the adsorption energies as well as the binding distances for the adsorptions of the NO and NO2
molecules are comparable to those of the Bdoped monolayer graphene.

Table 1: Adsorption energy Ea (eV) and distance d (Å) between adsorbed molecule andB atom for molecules adsorbed on B-dopedmonolayer and AB-stacked bilayer graphenes.

In summary, we have studied the adsorption properties of the toxic NO and NO2
molecules on the B-doped graphene and Bdoped (8,0) CNT, based on first-principles
density-functional calculations. The NO andNO2 molecules strongly bind on the B-dopedmonolayer and bilayer graphenes. The adsorption energies of NO and NO2 molecules on the
B-doped (8,0) CNTs are larger than those on
the B-doped graphene layers.

NO
NO2

Monolayer
Ea
-1.23
-1.16

d
2.15
1.59

Bilayer
Ea
-1.19
-1.13

d
2.14
1.60

155

We also study the adsorption energies
and the binding distances of NO and NO2
molecules on the B-doped (8,0) carbon nanotubes (CNTs).
Like monolayer and bilayer graphenes, the NO and NO2 molecules
are found to strongly bind on the B-doped(8,0) CNTs with the large adsorption energies and the short binding distances. Furthermore, the adsorption energies for NO andNO2 molecules on the B-doped (8,0) CNTs
are considerably larger than those on the Bdoped monolayer as well as the B-doped bilayer graphenes due to the curvature eﬀects.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] Y. Fujimoto and S. Saito, Chem. Phys.
478, 55 (2016).
[2] Y. Fujimoto and S. Saito, Jpn. J. Appl.
Phys. 58, 015005 (2019).
[3] Y. Fujimoto and S. Saito, to be published.

156

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study of appearance of ferromagnetism by electric field
application to Pt thin film
Tatsuru Yamada1, Hiroyuki Kageshima2, and Tetsuya Sato1
1Department of Applied Physics and Physico-Informatics, Keio University, 3-14-1 Hiyoshi,
Kohoku-ku, Yokohama 223-0061, Japan
2Graduate School of Natural Science and Technology, Shimane University, 1060
Nishikawatsu-cho, Matsue 690-8504, Japan
Recently, It was reported that ferromagnetism

that

the

ferromagnetism

appearedinappears in an oscillatory manner in the Pt(100)oscillatory manner with a period of 6 ML only

thin films depending on the film thickness[1][2].

when spin-orbit interaction (SOI) was not

This property suggests that magnetism inincluded (Fig.1). This oscillatory behavior

Pt(100) thin film can be controlled by electricagrees with the experiment[2]. These results

field. In order to clarify the magnetism changesuggest that magnetism in Pt(100) thin film iswith application of electric field, we performed

intrinsically unrelated to SOI. For the next

first-principles calculation using the PHASE/ 0

step, we calculate magnetism in Pt(100) thinprogram.

film under application of electric field.

The first-principles calculation based on the
DFT within the GGA was performed, where
Vanderbilt type pseudopotential and a planewave basis set were used to evaluate electric
structure and magnetization of Pt(100) thinfilm. We used 88×88×1 k points (based on
Monkhorst-Pack) and a cutoff energy of 36
Rydberg.

Fig. 1: Thickness-dependent magnetic

We calculated lattice constant that minimizes

moment per Pt atom.

the energy. Using the obtained lattice constant,
we calculated the Pt layer thickness dependence

Referencesof the magnetic moment of Pt slab. Calculations[1] A. M. N. Niklasson et al.: Phys. Rev. B 75,

of electronic structure for the free-standing

172402 (2007).

Pt(100) thin films from 2 monolayers(ML) up[2] K. Ochiai et al.: JPS2019, Gifu, 10aPS27

to 17 ML were performed and it was clarified(2019).

157

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab Initio Calculation of High-Rate Deposition of Copper
Film by Low-Pressure Chemical Vapor Deposition with CuI
on Ru Substrate
Tatsuya JOUTSUKA
Institute of Quantum Beam Science,
Graduate School of Science and Engineering, Ibaraki University, Hitachi, 316-8511 Ibaraki,Japan
We have studied low-pressure chemical

integration metallization.

vapor deposition of Cu on Ru substrate using

Based on this study, we are now extending

CuI [1] using VASP program package (MPI

our calculations to analyze the dynamicalparallelization with multiple threads). This year,

properties in more detail. In addition, new sets

we focused on the molecular mechanism ofof precursor and substrate are explored for ultra

adsorption, migration and desorption. This is alarge scale integration metallization together

collaborative work with the experimentalist [2]with experiment.

(Prof. Satoshi Yamauchi at Ibaraki University),
who conducted the LPCVD experiment.
In this study, we elucidated the molecularmechanism of Cu deposition using copper(I)iodide (CuI) on Ru substrate by low-pressurechemical vapor deposition through electronic
structure calculations. Using density functional
theorycalculations,molecules

adsorb

we

show
and

that

CuI

decompose

exothermically due to a strong adsorption ofFig. 1: Molecular mechanism of LPCVD of Cu.

iodine atoms onto the Ru(001) surface. The
rate-limiting step of the Cu deposition is found

References

to be the desorption of iodine molecules from

[1] T. Joutsuka, S. Yamauchi: Chem. Phys. Lett.

the Cu(111) surface, suggesting that the741 (2020) 137108.

removal of iodine species is necessary to[2] T. Nishikawa, K. Horiuchi, T. Joutsuka andachieve the high-rate deposition of highly-

S. Yamauchi: submitted.

conductive copper films for ultra large scale

158

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Analysis of Photocatalytic Reaction Mechanism atTitanium Dioxide Interfaces
Tatsuya JOUTSUKA
Institute of Quantum Beam Science,
Graduate School of Science and Engineering, Ibaraki University, Hitachi, 316-8511 Ibaraki,Japan
We have studied photocatalytic reaction

adsorption and the photogenerated hole can bemechanism at anatase TiO2 surfaces [1] using

trapped not on the neat surface but on the

cp2k program packagehydroxylated surface better at the (112) and(MPI parallelization

with multiple threads). This year, we focused(001)

surfaces.

The

experimental

andon the energetics and structure during the holetheoretical findings elucidate that the (112)

migration. This is a collaborative work with thefacet shows the larger stabilization of absorbed

experimentalist [2] (Prof. Satoshi Yamauchi atwater and trapped holes than other facets by

Ibaraki University), who conducted the LPCVD

larger structural relaxation at the surface.

experiment.
Anatase TiO2 shows a high photocatalytic
activity to decompose organic compounds andplays a crucial role in chemistry and physics.
To enhance the photocatalytic activity, proper
control of surface properties is crucial and themolecular-level mechanism can offer valuable
insight. We herein clarify the facet dependenceof hole trapping at the anatase TiO2 surface bydensity functional theory (DFT) calculations

Fig. 1: Molecular mechanism of hole migration.

using the constrained DFT method with thehybrid functionals. The photocatalytic activity

References

by UV irradiation around 365 nm in methylene[1] T. Joutsuka, H. Yoshinari, K. Yamamoto

blue aqueous solution is significantly high,and S. Yamauchi: in preparation for submission.

which is two-order larger than that on the[2] S. Yamauchi, K. Yamamoto, and S.

multi-oriented TiO2. The DFT calculations

Hatakeyama: J. Chem. Eng., 3 (2015) 28–38.

show the (112) surface can stabilize water

159

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Search and realization of novel electronic properties ofsolid surfaces and interfaces and of small particles
Takeshi INAOKA

Department of Physics and Earth Sciences, Faculty of Science,
University of the Ryukyus, 1 Senbaru, Nishihara, Okinawa 903-0213(1) Application of the tight-binding method
to a novel single-layer structure of carbon
atoms [4]The above-stated electron pocket andthe hole pocket are formed by-orbital-derived bands around the Fermi
level EF. Therefore, we can expect that thetight-binding method in terms of pz orbitalsof C atoms is effective for this system.
Figure 2 exhibits the band dispersion on
the  - M line for the hybrid density-functional method (Hyb) and the tightbinding method (TB). The transfer integral
for a diagonal nearest-neighbor pz pair and160

that for a lateral nearest-neighbor pz pair
were chosen to be -2.9 eV and -3.2 eV,
respectively. In view of band dispersions onother symmetric dispersion lines as well,
we found that the tight-binding method
can reproduce adequately the band
dispersions around EF, and consequently
the electron and hole pockets. The
tight-binding method provides a useful toolfor evaluating electronic properties of thissystem arising from -orbital-derived
bands.

Fig. 1 Carbon monolayer structure
considered here

E(k)-EF (eV)We mention two subjects which we
addressed this year.
Graphene is a very popular single-layer
structure of carbon (C) atoms arranged ina hexagonal lattice. However, we explore
different monolayer structures of C atoms.
Previously, we showed that the monolayer
structure in Fig. 1 is stable, and that theelectron system is a semi-metal which ischaracterized by the electron pocket
around the M point and the hole pocket
around the  point. We applied thetight-binding method to this system andclarified its utility and limitation for thissystem.
In scanning tunneling microscopy (STM)
light emission spectra of Ni(110)-(2x1)-O
surface emerge stepwise structures dueto oxygen (O) atom vibration parallel tothe surface [1]. These structures are
considered to arise from the change in thelocal density of states (LDOS) below the
STM tip owing to the vibration [1]. Using
first-principles calculations, we examinedthe variation in LDOS due to adiabaticin-plane displacement of an adsorbed O
atom.
We employed the program package‘Vienna Ab initio Simulation Package’(VASP) [2,3] on systems B and C.

5

0

TB
Hyb

-5

-10



M

Fig. 2 Band dispersions on the  - Mline for the hybrid density-functional method (Hyb) and thetight- binding method (TB).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

161

Fig. 3 Optimized slab structure of Op(2x1) Ni(110) surface. The slab iscomposed of 21 Ni atom layers and anadsorbed O atom at each surface.

0.15

O atompy-projectedEF

Majority spin

0.3Å disp.

0.1

opDOS

(2) Electronic structure of Ni(110)-(2x1) O
surface [5]Last year, by means of the generalized
gradient approximation, we investigated
the ground state of a proposed promising
structure, namely, the missing-row
reconstructed O p(2x1)/Ni(110) surface.
We optimized a slab composed of 11 Ni
atom layers and an O atom adsorbed ateach surface. This year, for a 21 Ni atom-layer slab, we treated phonon vibration
adiabatically, and examined the change inthe orbital-projected DOS (op-DOS) at
each atom when O atoms are displaced inthesurface-parallel
direction.
We
optimized the structure when the distance
between the O atom and the Ni atom
numbered 40 (see Fig. 3) in the y direction
is reduced by a certain length and fixed.
The height of the O atom measured fromthe No.40 Ni atom is 0.29Å in the groundstate. As the O atom gets closer to theNo.40 Ni atom by 0.3Å, this height rises
to 0.71Å. We pay attention to p orbitals of
the O atom and d orbitals of Ni atoms. We
analyzed the variation in the op-DOS ateach atom due to O-atom displacement.
Here, we present a part of our results for
majorityspin
originatingfromferromagnetic Ni. Figure 4 exhibits thepy-projected DOS at the O atom which isquite important in the STM experimentwith the tip placed right above the O atom.
The broken curve marked ‘GS’ and thefull curve labelled as ‘0.3Ådisp’ display
the results for the ground state and for 0.3Å displacement in the y direction,
respectively. The peak around the Fermi
level EF shifts to the higher energy side,and the peak intensity increases with
O-atom displacement. The peak position
reaches EF at 0.3Ådisplacement. The peakin the py-projected DOS for minority spin
also shows a similar shift to the higher
energy side. Our analysis including
d-orbital-projected DOS at Ni atoms
indicated that approach of the O atom to
the No.40 Ni atom leads to stronger
hybridization between the py orbital of the
O atom and the dyz orbital of the Ni atom.
The above peak shift implies that thephonon vibration affects the STM lightemission through the change in opDOS.

GS

0.05

0
-3

-2

-1

0

1

2

3

E (eV)
Fig. 4 py-orbital-projected density ofstates at the adsorbed O atom for the
ground state and for O-atom
displacement by 0.3Å.
References[1] Y. Uehara, T. Inaoka, T. Nishio, and
S. Katano: J. Appl. Phys. 123 (2018) 224302(8 pages).
[2] G. Kresse and J. Hafner: Phys. Rev. B 47
(1993) 558-561.
[3] G. Kresse and J. Furthmüller: Comput. Mat.
Sci. 6 (1996) 15-50.
[4] T. Inaoka and M. Furugen: unpublished.
[5] T. Inaoka and Y. Uehara: to be prepared.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Atomic and electronic structures of intermetallic
compound catalysts
Kazuki NOZAWA
Department of Physics and Astronomy, Kagoshima University
1-21-35, Korimoto, Kagoshima 890-0065

In this fiscal year we have studied theinitial stage of oxidation of Ni3 Al(210) and
PdZn(111) surfaces. All calculations are caried
out using VASP with the PAW method and the
PBE exchange-correlation functional.
It was reported that Ni3 Al is highly active
for hydrogen production from methanol andmethane, and its catalytic performance is considered to be attributed to the selective oxidation and hydroxylation of Al and the formation of metallic Ni particles at low oxygen
partial pressures[1]. An X-ray photoelectron
spectroscopy study shows Al oxide is formed
preferentially in the beginning of the oxidation process, and Ni oxides start to form at
1.6 ML oxygen coverage[2]. We first searched
for the stable adsorption sites at 0.25 and 0.5
ML. In both cases, it turned out that the moststable adsorption site is a pseud-threefold sitesurrounded by two Al atom at the top layer
and one Ni atom at the second layer. The adsorption geometry is similar to the result reported for NiAl(110)[3], but this structure isnot consistent with the XPS experiment showing no sign of Ni oxides formation at this coverage. Inspired by the previous study[3], we introduced some antisite defects in the oxidized
surface, and it is found that antisite defect stabilizes the surface when they form a specificstructure. According to the simulated STM
images using the Tersoﬀ-Hamann approximation, this structure shows a unique image easily
distinguished from other structures with diﬀerent antisite arrangement or without the defect.

Although pure Pd is not active for methanol
steam reforming (MSR), PdZn exhibits comparable catalytic activity and selectivity to theconventional Cu catalyst in MSR. Recently,
some groups reported that ZnO formed during
the reaction is essential for the catalytic performance of PdZn. However, this is not straightforward because Zn has no d-state around the
Fermi level implying the chemical inactivity of
ZnO. We first determined the stable adsorption
structure of oxygen on PdZn(111), and investigated the electronic structure of this system.
We previously reported that bulk PdZn has asimilar electronic structure to Cu[5], but thePd 4d-band of PdZn is broadened when oxygen is adsorbed. It was also found that Zn-dstates appear below the Fermi level when oxygen adsorbs on the most stable site.

References[1] D. H. Chun et al., J. Catal. 243 (2006)99,
Y. Xu et al., J. Phys. Chem. C 114(2010))6047.
[2] Y. Xu et al., Appl. Surf. Sci., 39 (2017)18.
[3] A. Y. Lozovoi et al., Phys. Rev. Lett., 85(2000)610.
[4] K.
Yamaguchi,
Master(Kagoshima University, 2020).

Thesis[5] A. P. Tsai et al., Acc. Chem. Res. 50(2017)2879.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Switching of magnetism via modifying phase shift ofquantum-well states by tailoring the interface
electronic structure
Shunsuke SAKURAGI
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

In this project, we expanded Phase modelfor the Quantum-well states (QWs), and suggested the method to control the QW induced
ferromagnetism in Pd(100) by changing scattering phase shift. Then, we verified this theory using density functional theoretical (DFT)
calculation [1].
The following Phase model, describing the
QWs, indicates the conditions under which astanding wave can exist:

electrons, phase shift Φ of the QWs might depend on kx , ky , and ϵ. Thus, it is necessary to
expand the phase model to include kx and ky(i.e. the wave number of the in-plane directionk∥ ) dependencies.
First, kz (n) = (2πn − Φ) /2d is defined fromeq. (1). Then, the n-th energy level of()
Pd(100) film quantum well ϵQW n, k∥ can beobtained from the Pd bulk energy band structure ϵ(kz , k∥ ) as

2kz d + Φ = 2πn,()()ϵQW n, k∥ = ϵ kz (n), k∥ ,(1)where kz is the confined wave number, d is thefilm thickness, Φ is the scattering phase shift at
surface and interface, and n is an integer quantum number. Previous experiments and DFT
calculations showed that the period of oscillation by modification of magnetic properties
via QWs is expressed as p = 1/kF z , where pis the period of oscillation (where thickness ofthe film is d) and kF z is the vertical Fermi wave
number i.e. the Fermi wave number of the confined band. This and eq. (1) indicate that theconfined wave number kz reaches Fermi energy
periodically depending on the film thickness dand the phase shift Φ is unrelated to the periodof oscillation.
Previous DFT calculations and experiments
predicted that dxz,yz electrons are confined at
the QWs of Pd(100) films, and this induces ferromagnetism in Pd(100) ultrathin films. These
orbital characters express one dimensional dispersion in the in-plane direction. For these

163

(2)

where k∥ = (kx , ky ) is the in-plane wave vector
because the band dispersion of the QWs is a
projection of the specific bulk band. Then, thebinding energy of the quantum-well state ϵQW
in Pd(100) can be described by expanding ϵQWaround the Fermi energy as
(
)
)
∂ϵ (
ϵQW n, k∥ ∼ ϵF + [kz (n) − kFz ]kFz , kF∥
∂kz
)
∂ϵ (
+ ∆k∥ ·
kFz , kF∥ ,∂k∥(3)
where kF∥ is the in-plane Fermi wave vector,()∆k∥ = k∥ − kF∥ , and ϵF = ϵ kFz , kF∥ .
Considering Pd bulk band dispersion, dispersion of dxz,yz has a flat shape around Γpoint and zone edges. Therefore, in Pd(100)film, the following relation is satisfied:)∂ϵ (kFz , kF∥ ∼ 0.
∂k∥

(4)

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

According to eq. (5), this means that()ϵQW n, k∥ almost coincides with the Fermi
energy ϵF being independent of k∥ , if kz (n)matches kFz . Then the density of states at the
Fermi energy D(ϵF ) diverges and induces ferromagnetism from the standpoint of the Stonercriterion. The condition kz (n) = kFz leads tooscillatory appearance of ferromagnetism withthe periodicity p depending on the film thickness d.
Now we extend the theory above as shallbe discussed later, the phase shift Φ generally depends on k∥ . If we permit such k∥ dependence for Φ, kz (n) also depends on k∥ .
()
Since kz (n, k∥ ) = 2πn − Φ(k∥ ) /2d eq. (5)must be modified into()ϵQW n, k∥ ∼ ϵF[] ∂ϵ ()+ kz (n, kF∥ ) − kFz
kFz , kF∥
∂kz
(
)
∂ϵ
(5)
kFz , kF∥
+ ∆k∥ ·
∂k∥
)
∂kz
∂ϵ (
+ ∆k∥ ·
kFz , kF∥ ,(n, kF∥ )∂k∥∂kztransition metals on Pd(100) films. In addition, if the d-electron band of a stacking layer
appears near the Fermi energy at S-point, magnetic change via modifying phase shift might
be clearly observed, as indicated in eq. (5).
The present DFT calculation using Phase/0
code [2] well verified the above theory [1]. The
electronic states of Au stacked Pd film weremodified by changing the Au-Pd layer distance, and the QW induced ferromagnetism
was controlled. Contrastingly, we observedthat stacking of Al, which contains only selectrons around Fermi energy, cannot modify the shape of the band dispersion of delectron QWs because there is no hybridization between the s- and d-electrons. We see
above behaviour from the calculated band dispersion and the shape of wave function. Ourfindings suggest a mechanism for controllingmagnetism using modification of interface electronic states in metal-nano structures.

Because of the fourth term on the right hand()
side of eq. (7), ϵQW n, k∥ is no longer theconstant for k∥ and the divergence of D(ϵF )does not occur often, even when kz (n, kF∥ )matches kFz and eq. (6) is satisfied. Furthermore, the divergence of D(ϵF ) can be promoted
if we appropriately modify the k∥ -dependenceof Φ even when kz (n, kF∥ ) does not match kFz
or eq. (6) is not satisfied. Thus, we can expect that a fine control of the k∥ -dependenceof phase shift Φ can reduce the magnetism in asimilar way to induce the magnetism for nonmagnetic materials.
In the case of quantum confinement of Pd
dxz,yz electrons, which we discussed in this paper, the hybridization between the d-electron
wave function of the stacking layer and Pd atthe zone edge (S-point) is intrinsically important for producing a flat band. Because typical 3, 4, 5d transition metals forming fcc structure have d-electron bands around the S-point,
this eﬀect generally occurs by stacking of these[1] Shunsuke Sakuragi, Hiroyuki Kageshima,
and Tetsuya Sato : Phys. Rev. B. 101(2020) 014410.

164

References[2] https://azuma.nims.go.jp/software/phaseActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Stability of vacancy cluster and interaction with impurities intungsten lattice
Kazuhito Ohsawa
Institute for Applied Mechanics,
Kyushu University, Kasuga-koen, Kasuga, Fukuoka 816-8580

Introduction

Simulation method

The study of lattice defects in tungsten (W)The binding energies of the vacancy clusters

are important issue in the field of fusion reactor

were calculated in terms of first-principle

because W is one of the plausible plasma facing

calculations based on density functional theory.

materials (PFMs). Usually, hydrogen (H) and H

We used the Vienna ab-initio simulation package

isotopes seldom dissolve in W. However, H(VASP). A large simulation cell, composed of

atoms are trapped in the vacancy-type lattice

6x6x6 bcc lattice (432 atoms), were used in

defects (vacancy clusters etc.) created in theorder to reduce the effects of periodic boundary

irradiation circumstance. In particular, tritium

condition imposed on the simulation cell. The(T) retention in the PFM is one of the serious

cut-off energy of plane wave was 520eV.

problem associated with fusion reactor because

The

T is radioisotope whose half-life is 12 years. So,

composed of n mono-vacancies Vn was defined

the stability and binding energy of the vacancy

Eb(Vn)=nE[V]-{E[Vn]+(n-1)E[P]},clusters in the bulk W were investigated bywhere E is cohesive energy of the supercell andsimulations and experiments.

P indicates perfect lattice of W. Positive binding

bindingenergyofvacancycluster

Small vacancy clusters in the W lattice has

energy corresponds to attractive interaction.

been reported to be unstable by the first-

Similarly, the binding energy of vacancy cluster

principle calculations. On the other hand, suchcontaining an oxygen VnO issmall clusters and their growth to larger clusters

Eb(VnO)=

were observed in positron annihilation lifetime

E[VO]+(n-1)E[V]-{E[VnO]+(n-1)E[P]}.

measurements. In the present work, we

Results

investigate the reason why the small vacancy
clusters exist in the W lattice. The vacancy

We investigated the most stable structure ofclusters are stabilized by impurities. In particular,

vacancy clusters composed of n mono-vacancies

they are greatly stabilized by the presence of

without and with an oxygen ( n ≤ 6 ). We

oxygen.

examined di-vacancy V2 in the first (1nn),

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Discussion

second (2nn), and third (3nn) nearest neighborconfigurations. The di-vacancy in the 1nn

Growth of vacancy cluster in W lattice wasconfiguration is the most stable among them.

observed in the positron annihilation lifetime

However, small vacancy clusters, V2 and V3, aremeasurements but the vacancy clusters wereenergetically unstable compared with isolated

expected to be energetically unstable in the first-

mono-vacancies, as shown in Fig. 1. On theprinciple

other hand, larger vacancy clusters, Vn ( n ≥ 4 ),stabilization effects by impurities contained inare stable. Therefore, if V4 were nucleated in thethe W specimen. Even if high purity metalbulk W, the vacancy cluster growth would

specimen were prepared, some kinds ofspontaneously occur.

impurities would be inevitably contained.

calculations.

We

examinedtheThe presence of impurities in W lattice

Carbon, nitrogen, and oxygen are the typicalcontributes to the stabilization of vacancy

inevitable impurities in the actual metals.

clusters. Fig. 2 shows the most stable structure

Actually, vacancy clusters are greatly stabilizedof vacancy clusters with an oxygen VnO. The

by the presence of such impurities. Besides, themost stable structure of V2O is the 2nn

diffusivity and binding energy to a mono-configuration, which is different from thatvacancy of oxygen in the W lattice arewithout an oxygen V2. According to Fig. 1, allremarkably

vacancy clusters trapping an oxygen are stable

impurities. The presence of oxygen is the mostand the binding energy increases as a function ofplausible candidate to explain the vacancy

the number of vacancies composed of thecluster growth observed in the positron

vacancy clusters.

annihilation lifetime measurements.

larger,compared

with

other

Fig. 2: Schematic view of the most stable structure of
Fig. 1: Binding energies of vacancy

vacancy clusters trapping an oxygen (VnO). The doted

clusters without and with an oxygen,circles indicate positions of mono-vacancies in bcc W(Vn and VnO).

lattice.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principles study on static structure of glass materials
Akihide KOURA
Student Affairs Department,
Kumamoto University, Kurokami, Kumamoto, Kumamoto 860-8555
Cu2GeTe3 (CGT) is one of fast phaseof number of ring to that from the experimenttransition materials. This material changes[1] was obtained [3]. This result shows that the

between crystalline and amorphous phases

distribution of six-membered ring is higher thanquickly like Ge2Sb2Te5. In order to clarify thethat by Chen et al. [2]. The coexistence of 3+5

phase

many

and distorted 6 membered rings would enhance

experimental and theoretical studies were

the fast phase transition between crystal andcarried out so far. From results of anomalous x-

amorphous phases.

transition

mechanism,ray scattering and extended x-ray absorption
fine structure experiments, the local andReferencesintermediate range structures of glass were

[1] J. R. Stellhorn, B. Paulus, S. Hosokawa, W.-

preserved structural motifs of the crystal [1].

C. Pilgrim, N. Boudet, N. Blanc, and Y. Sutou:

However, the ring structure from theoreticalarxiv:1908.07297v1 [cond-mat.mtrl-sci] (2019).

study [2] was different from the experimental[2] N.-K. Chen, X.-B. Li, X.-P. Wang, M.-J.

result [1]. In order to clarify the structure of

Xia, S.-Y. Xie, H.-Y. Wang, Z. Song, S. Zhanga,

amorphous CGT, we have performed ab initio

H.-B. Suna: Acta Matter. 90 (2015) 88.

molecular dynamics simulations.

[3] A. Koura and F. Shimojo: J. Phys.: Condens.
Matter 32 (2020) 244001.

In this study, we made two amorphousstates, which were called a1 and a2 amorphousstates. Figures 1 shows the distribution of
number of M-membered ring 𝑃𝑃(𝑀𝑀) [3]. In the
crystalline state, there are only six-memberedrings. In the amorphous state, some sixmembered rings are distorted from 6 to 3+5rings, and distorted six-membered rings also
remain in the amorphous state [1]. Using ring

Fig. 1 The distribution of number of M-memberedanalysis method for our ab initio molecularring 𝑃𝑃(𝑀𝑀) [3].

dynamics simulations, the similar distribution

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Graphene-based Symmetric and Non-Symmetric
Magnetoresistive Junctions
Arqum Hashmi
Center for Computational Sciences,
University of Tsukuba, Tsukuba, Ibaraki 305–8577, Japan
We have studied the structural, magnetic, andspectraspin-dependent transport properties of Graphene

indicating

lowcontact resistanceirrespective of the electrode material.

based MTJs using massive parallel computer
simulations. Gr layer is sandwiched between
ferromagnetic

electrodes.

Typical Dirac cone feature of Gr is not preserved
upon the formation of MTJ and Gr derived 𝜋Furthermore, the influence of different

states near the Fermi level was strongly

stacking of electrode layers on transport

hybridized with the 𝑑𝑧 2 orbital of the Ni and Co

properties is also checked although not muchsurfaces. APC was found to be stable in the Gr-

difference is observed in conductance spectra.

based ML junctions and distinct hybridization ofBoth symmetric and non-symmetric junctions

the Gr 𝜋 states are observed with symmetric andexhibit distinctive selection rules due to thenon-symmetric junctions. Spin filtering is quite

incompatibility of wave functions of electrodes.

sensitive to the electrode materials. The

Our comparative study reveals the effect ofsymmetric junction has higher TMR ratio

various electrode materials on spin transportcompared to non-symmetric junction.

property that can help to develop Gr-based highThe

highest TMR ratio

observed in

TMR ratio devices.

symmetric junction is 13.60%, while it is 8.26%

Referencesin non-symmetric Gr based junction. Gr based[1] A. Hashmi, K. Nakanishi, T. Ono: J. Phys.

junctions displayed the higher transmission

Soc. Jpn. 89, 034708 (2020).

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Local physical quantities analysis based on thequantum field theory in material surface
Masahiro FUKUDA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

region between the surface and the Si tip are
positive (tensile stress) and the eigenvectors
form the spindle structure [1], which visualizes
a covalent bonding. In the future work, moredetail analysis will give a deep understandingof chemical bond formation between a material
surface and a molecular cluster.
14

0.001

13

0

12
−0.00111y (Å)

The local physical quantities, which is defined in the framework of quantum field theory (energy-momentum tensor density, current
density, chiral current density, and so on), aresignificant to understand the fundamental aspect of nature of materials. In particular, since
surface materials and two dimensional materials may have physical or chemical properties
which cannot be explained by bulk feature insolids, it is important not only to evaluate theenergy of the whole system and band structures but also to investigate the local physicalproperties.

10−0.0029−0.0038

In the previous work, the local physicalquantities in molecular systems have been investigated by using a post-process calculationfrom wave packets obtained by molecular orbital method [1].
In this project, we developed a program code
which enables us to calculate local physicalquantities as a post-process calculation from
OpenMX [2] (DFT calculation program code)in order to evaluate the local physical quantities in large periodic systems. It supports
OpenMP/MPI parallelization to handle large
system calculations.
The physical and chemical nature around√√the interaction region between a 7 × 7
Si(111) surface and a Si cluster (a model ofatomic force microscopy tip), were investigatedas a demonstration. The system is a periodic
system including 402 atoms in a unit cell. The
Fig. 1 shows that the maximum eigenvalues ofthe electronic stress tensor density around the7−0.0046−0.005
0

2

4

6

8
x (Å)

10

12

14

Figure 1: Distribution of maximum eigenvalues and eigenvectors of the electronic stresstensor density and zero surface of the electronic kinetic energy density in the region be√√
tween Si tip and 7 × 7 Si(111) surface.

References[1] A. Tachibana, Journal of Chemical
Physics, 115, 3497 (2001); A. Tachibana,“New Aspects of Quantum Electrodynamics”, Springer (2017); M. Fukuda,
K. Soga, M. Senami, and A. Tachibana,Int. J. Quant. Chem., 116, 920 (2016).
[2] OpenMX, http://www.openmx-square.org/.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First principle simulation on reactions and electronic
structures of new material synthesizedfrom organic molecules
Toshihiro SHIMADA, Wei LIU, Ichiro YAMANE, Taro NAGAHAMA, Takashi YANASE
Division of Applied Chemistry, Faculty of Engineering
Hokkaido University, Kita-ku, Sapporo, Hokkaido 060-8628
We have experimentally synthesized newi]phenazine (DDQP) under pressure[4].

Itcarbon materials by applying high temperatureshows Diels-Alder type intermolecular reaction.

and / or high pressure to organic molecules.

The electronic band structures showed three-

Using this ISSP supercomputer time, we havedimensional dispersion (Fig.3).

studied the reactions and electronic structuresof these materials[1-3]. We present some of theexamples.
Figure 1 shows optimized structure of
Fig. 2: Pressure-induced bond formation
reaction of DDQP revealed by calculation.

graphitic carbon nitride (g-C3N4) and a nitrogenmolecule.
based

We developed a liquid nitrogenquenchingprocesstopreparephotocatalyst materials with atomic layer
separated. This process greatly improved thephotocaltalytic activity of the material. This
calculation supports N2 molecule can beintercalated to g-C3N4, which assists exfoliationof the layers.
Fig.3 Band dispersion of pressure-polymerized
DDQP.
References[1] W. Liu, T. Shimada et al.: Journal of Colloid& Interface Science 567 (2020) 369.
[2] W. Liu, T. Shimada et al.: International J. of
Hydrogen Enegry 44 (2020) 8444.
[3] W. Liu, T. Shimada et al.: Applied Surface
Science499(2020)
143901.

Fig. 1: Optimized crystal structure of twolayered g-C3N4 and N2-inserted interlayer of gC3N4.
Figure 2 shows optimized structure ofdibenzo[a,c]dibenzo[5,6:7,8]quinoxalino[2,3-170Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Developments of a derivation method of a low-energy
models in ﬁrst-principles
Hirofumi Sakakibara
Department of Applied Mathematics and Physics, Tottori university, Tottori 680-8552, JapanFirst principles calculation is useful method
to determine the electronic structure. Most of
the ﬁrst-principles assumes local density approximation(LDA) in density functional theory, however, LDA usually underestimatesband gaps of semiconductor. This underestimation is overcome by the consideration of theeﬀect of particle excitation. The quasiparticle
self-consistent GW method (QSGW) is a ﬁrstprinciples method to determine the one-body
Hamiltonian H0 taking into such excitation effects account.
However, even QSGW improves the size ofband gaps compared to LDA, there still havesome errors. For example, QSGW systematically overestimates the size of band gaps [1].
This overestimation is investigated from theviewpoint of vertex correction on the proper
polarization P by Shishkin et al.. Their work
has shown that such vertex corrections improve the dielectric constant very well. However, their method is somewhat ambiguous andconsuming for computing resource.
To solve this problem, we introduced amethod to numerically estimate the vertex
correction[3]. Our method is to determine thevertex correction by a self-consistent calculation applying static electric ﬁelds to obtainthe linear response of electronic density. On
this purpose, we implemented the combination of QSGW and eﬀective screening medium
method (ESM, Ref. [4]). Namely, we calculate a slab model applying an external electrostatic potential varying along z axis. Fig. 1 isa schematic picture of ESM method applied to

MgO slab. Then, it is better that slabs are as
thick as possible because we intend to estimate
the vertex correction of bulk materials.
To access the eﬀectiveness of our method, we
calculate optical dielectric constant ϵ∞ , where
ϵ∞ is measured by the slope of the electrostatic potential. In Tab.1, we compare ϵ∞ ofbulk calculation in the random phase approximation (RPA) and the QSGW+ESM method.
Here we applied generalized gradient approximation(GGA) instead of LDA. We have chosen ﬁve simple ionic materials LF, KF, NaCl,
MgO, and CaO for the examination system.
We can ﬁnd that QSGW+ESM is in an extremely good agreement with experiments. It
is interesting that LDA(GGA)+ESM method
does not necessarily improve the value of ϵ∞ .
This may because that the exchange eﬀect
taken in the exchange correlation functional of
GGA is not accurate.
In Tab.1, the underestimation of ϵ∞ of bulk
system corresponds to the overestimation ofband gaps. It is also found that the material
dependence of the vertex corrections is not solarge. From this result, some hybrid methods
between QSGW and GGA may be applicable
instead of present QSGW+ESM method as acompromise. In the previous work by Deguchi
et al., a hybrid method named QSGW80 (hybridization between QSGW and GGA at theratio 8:2) has shown good agreements with experiments. Therefore, the systematic overestimation of QSGW may be improved by considering vertex corrections, which are eﬀectively
taken into account in QSGW80.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1: Calculated optical dielectric constant
ϵ∞ . ‘RPA’ are in bulk calculations. ‘Slab’ arecalculated from the slab models in the settingof Fig.1.
RPA Slab Experiments
GGA
1.95 2.01
LiF
1.96
QSGW 1.67 1.94
GGA
1.96 1.94
KF
1.85
QSGW 1.68 1.86
GGA
2.33 2.42
NaCl
2.34
QSGW 1.92 2.31
GGA
2.96 3.09
MgO
2.96
QSGW 2.50 2.37
2.91
GGA
3.59 3.68
CaO
3.33
QSGW 2.88 2.68
3.31

References[1] D. Deguchi, K. Sato, H. Kino, and T.
Kotani, Jpn. J. Appl. Phys. 55, 051201(2016).
Figure 1: Schematic picture of ESM method.
The upper panel shows the electrostatic potential when the diﬀerence bias voltages at
z = 30, −30 are 0.0 Ry and 0.2, respectively.
The lower panel shows the diﬀerence between
the potentials among these to cases. The optical dielectric constant ϵ∞ is measured from theratio of the slope between vacuum and slab region, as indicated in the lower panel.

[2] M. Shishkin, M. Marsman, and G. Kresse,
Phys. Rev. Lett. 99, 246403 (2007).
[3] H. Sakakibara, T. Kotani, M. Obata. andT. Oda, Phys. Rev. B (2020)(in press).
[4] M. Otani and O. Sugino, Phys. Rev. B 73,
115407 (2006).

To summarize,
we have developed
QSGW+ESM method to determine thevertex correction in QSGW. Our method
can calculate dielectric function in a good
agreement with experimental observation.
The future problem is to derive a low-energy
model Hamiltonian based on the one-body
Hamiltonian H0 derived from QSGW or
QSGW80.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation of
the higher-order phonon-phonon scattering strength
Haruhiko DEKURA
Geodynamics Research Center
Ehime University, 2-5 Bunkyo-cho, Matsuyama 790-8577, Japan
Phonon-phonon interaction is a key parameter that describes thermal transport properties insolids [e.g., 1]. First-principles calculation of lifetimes of phonon quasiparticles owing to theinteraction is computationally demanding for precise determination of phonon thermal conductivity.
From the theoretical point of view for the many-body interacting systems, the phonon-phonon
scattering rate is approximately inversely proportional to the imaginary part of the phonon selfenergy [1]. Most density-functional theoretic calculations for determining phonon thermal
conductivity is limited to the lowest order phonon-phonon interaction. The higher-orderanharmonicity is likely to contribute to the conductivity particularly at temperatures higher than the
Debye temperature as would be seen in the deep Earth’s interior [2]. The primary purpose of thisproject in this period is to try to establish a roadmap as a first step for the accurate determination ofphonon thermal conductivity at high temperature considering the effect of higher-order phononphonon scattering. Silicon was selected for this purpose for its simplicity.
We have performed the density-functional theoretic calculations based on the plane-wave basis
pseudopotential method within the local density approximation. In order to extract harmonic andanharmonic force constants (AFC), the higher-order derivatives of the adiabatic potential surface
were determined by the self-consistent field calculations for the structures in which some atoms areslightly shifted from the equilibrium positions. The 3×3×3 cubic supercell containing 216 atoms in
total was primarily adopted in this study to capture the anharmonic interaction.
During this period, by the use of supercomputer (system B) in ISSP, we have launched test
calculations to check the computational conditions regarding the size dependency in the AFC,
convergency in the with respect to the simulation cell size of the mesh to sample the phonon wave
number vectors. Also, the self-consistent field calculations to extract AFC using the optimum
condition have been almost finished. In parallel, post-processors to calculate the total phononphonon scattering rate including up to the fourth-order anharmonicity and thermal conductivity
based on the Boltzmann transport equation have been almost developed. Using the complete data set

173

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoobtained in this study, we will make a thorough examination of the effect of the higher-orderscattering on the lattice thermal conductivity at high temperatures. After the establishment of theprocedure to compute the thermal conductivity, we plan the application of the developed technique
to Earth’s minerals under very high-temperature conditions [2].

References[1] G. K. Horton, A.A. Maradudin, eds., Dynamical Properties of Solids: Crystalline solids,
fundamentals (North-Holland, Amsterdam), (1974).
[2] 出倉春彦, 高圧力の科学と技術, (2020), in press.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Study on the Aggregation-Induced Emission
Norifumi YAMAMOTO
Department of Applied Chemistry,
Chiba Institute of Technology, 2-17-1 Tsudanuma, Narashino, Chiba 275-0016
In this study, the mechanism of aggregation-states are degenerated at a conformation withinduced emission (AIE) of diphenyldibenzo-

the twist angle of 90° around its ethylenic C=C

fulvene (DPDBF) was studied theoretically.

bond,

The DPDBF has been known to exhibit

which

can

lead

the

fluorescencequenching of DPDBF molecule in dilute

the AIE, which is non-emissive in dilute

solutions.

solutions but becomes highly emissive in solid

The free-energy profile of the photoor aggregates [1]. In this study, the AIE of

isomerization of DPDBF in condensed phase

DPDBF was investigated by using ab initio

was computed using MD simulations based onelectronic structure calculations, together with

an empirical force field representation. All MD

molecular dynamics (MD) simulations.

simulations of DPDBF presented herein wereIn order to elucidate the characteristics ofthepotential

for

the

The results of MD simulations revealed

DPDBF,

thethat DPDBF tends to assemble in close contact,

minimum energy paths for the photo relaxation

where the ethylenic C=C bond rotation isprocess of DPDBF in an isolated phase weremarkedly restricted in aggregates, preventing

investigated using ab initio electronic structure

the fluorescence quenching via the S0/S1

calculations. The spin-flip approach within theconical intersection; DPDBF in acetonitrile

time-dependent density functional theory (SF-solution, however, proceeds a barrierless non-

TDDFT) method was used to compute theradiative transition. These results gave a clear

potential energies and analytical gradients for

picture of the AIE of DPDBF, which is agree

the electronic ground (S0) and first excited (S1)with that of a cyanostilbene derivative [2].

photochemicalenergyprofilesprocessesofcarried out using the GROMACS program.

states of the molecule. All electronic structure
calculations of DPDBF presented herein wereReferences

performed using the GAMESS program.

[1] Tong, H, et al., J. Phys. Chem. C, Vol. 111,

The results of SF-TDDFT calculations

pp. 2287−2294 (2007).

showed that the potential energies of DPDBF[2] Yamamoto, N., J. Phys. Chem. C, Vol. 122,for electronic ground (S0) and first excited (S1)

pp. 12434−12440 (2018).

175

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Benchmark of density functional theory forsuperconductors in elemental materials
Mitsuaki Kawamura
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

1

introduction

The first-principles calculation of the superconducting properties, such as the transition
temperature (Tc ) and the gap function, isof great interest to explore new materials aswell as to understand the physical mechanism of known superconductors. Density functional theory for superconductors (SCDFT)
is one of the frameworks for such calculations; this method enables us to perform fully
non-empirical simulations in the superconducting phases at a reasonable computationalcost. In SCDFT, we can treat the electronphonon interaction, the electron-electron repulsion, the spin-orbit interaction (SOI) [1],and the spin-fluctuation (SF)-mediated interaction in a first-principles manner.
However, the accuracy of the current approximated functional of SCDFT and the effects of SOI and SF have not been verified
systematically, although such verification ishighly desirable before applying this method
to a wide range of materials. Such a highthroughput calculation was performed, forexample, in the exploration of low-thermalconductivity compounds using first-principles
calculations together with the materials informatics. A benchmark is also a useful tool used
to find a guideline for improving the theory andapproximations of the superconducting density
functional. For this purpose, in this project,
we are presenting the benchmark calculationsof SCDFT [2]. As benchmark targets, we havechosen the simplest superconducting, and non-superconducting materials, i.e., elemental materials; each material in this group comprises asingle element. The particular computational
cost is relatively low because most materials
in this group contain only one or two atoms in
the unit cell. Moreover, we can see the eﬀects
of the chemical diﬀerence and the strength of
the SOI of each element.

2

methodWithin SCDFT, Tc is obtained as a temperature where the following Kohn-Sham superconducting gap ∆nk becomes zero at all theband n and wavenumber k:
1 ∑ Knkn′ k′ (ξnk , ξn′ k′ )2 ′ ′ 1 + Znk (ξnk )
nk
√

2
2
ξ
+
∆
′
′
′
′
′
′
∆n k
nk
nk
,
×√
tanh 
2T
ξ 2 + ∆2

∆nk = −n′ k′

n ′ k′(1)
where ξnk is the Kohn-Sham eigenvalue measured from the Fermi level (εF ) at the band index n and wave-number k. ξnk is obtained bysolving the spinor Kohn-Sham equation. The
integration kernel Knkn′ k′ (ξ, ξ ′ ) indicates thesuperconducting-pair breaking and creating interaction and comprises the following threeterms:
ep′ee′Knkn′ k′ (ξ, ξ ′ ) ≡ Knkn
′ k′ (ξ, ξ ) + Knkn′ k′ (ξ, ξ )sf′+ Knkn′ k′ (ξ, ξ ),

176

(2)

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

namely, the electron-phonon, Coulomb repulsion, and spin-fluctuation kernel, respectively.
However, the renormalization factor Znk (ξnk )comprises only the electron-phonon and spinfluctuation terms as follows.
epsf
Znk (ξ) ≡ Znk(ξ) + Znk
(ξ),

(3)

because the Coulomb-repulsion contribution tothis factor is already included in the KohnSham eigenvalue ξnk .

3

Result and Discussion

We have plotted the computed- andexperimental-Tc in Fig. 1 to visualize theeﬀect by SOI and SF; we can detect thefollowing trends by inspecting this graph: SF
always reduces Tc s for the elemental systems.
This reduction becomes significant for thetransition metals and is crucial to reproduce
the experimental Tc quantitatively. In thetransition metals, the eﬀect of SF weakens
with the increasing of the period numberin the periodic table. The eﬀect of SOI issmall in most cases, excepting Tc, Sn, Re,
Tl, Pb. In these elements, the Fröhlich’s
parameter λ changes drastically by turning on
the SOI. We can reproduce the absence of thesuperconductivity in alkaline, alkaline earth,and noble metals, excepting Pt and Au with
SOI and SF; we have observed small finite Tc
for these two elements; we can reproduce thenon-superconductivity also in Sc by including
SF while we observe Tc = 2.711 K by ignoring
SF. Since Sc has highly localized 3d electrons,
the SF largely reduces Tc . For the group 12
elements (Zn and Cd), Tc s are overestimatedeven if we include SF. For these materials, theSF eﬀect is small because the d orbitals are
fully occupied.

0

1

2 Be
1 Na
2 Mg
13 Al
1K
2 Ca
3 Sc
4 Ti
5V
11 Cu
12 Zn
13 Ga
1 Rb
2 Sr
3Y
4 Zr
5 Nb
6 Mo
7 Tc
8 Ru
9 Rh
10 Pd
11 Ag
12 Cd
13 In
14 Sn
1 Cs
2 Ba
3 La
4 Hf
5 Ta
6W
7 Re
8 Os
9 Ir
10 Pt
11 Au
12 Hg
13 Tl
14 Pb
2
0

3rd row
4th row
SOI+SF :SOI :SF :no SOI/SF :Exp. :

5th row

6th row2

4 6
Tc [K]

8 10 12 14 20 22

Figure 1: Theoretical and experimental Tc s [2].
The vertical axis is the atomic symbol together
with the group of the periodic table. Downward (upward) triangles indicate the Tc s computed with (without) SF. Filled (empty) triangles indicate the Tc s computed with (without)
SOI. “+” indicates the experimental value of
Tc . The plot which ranges from zero to two
Kelvin in the upper panel is magnified into thebottom panel.

M. Kriener, Y. Taguchi, and Y. Tokura,Phys. Rev. B 101, (2020) 014505.
[2] M. Kawamura, Y. Hizume, and T. Ozaki,
Phys. Rev. B 101, (2020) 134511.

References[1] T. Nomoto, M. Kawamura, T. Koretsune, R. Arita, T. Machida, T. Hanaguri,

177

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulation of scanning tunneling microscopy
images of graphene ribbons with edges
Junhuan LI, Kenta ARIMA
Graduate School of Engineering, Osaka University, Yamadaoka, Suita, Osaka 565-0871
We are aiming at elucidating local electronic

STATE is based on the density functional

structures of finite-size graphene sheets and their

theory. The exchange and correlation potential is

impact on scanning tunneling microscopy (STM)

described

images. For this purpose, we have started first-

approximation

principles calculations of single-layer graphene(GGA-PBE). We also used both a plane-wave

ribbons possessing either zigzag or armchairbasis set and pseudopotentials. When runningedges by the use of a simulation package named

STATE, we first defined the atomic structure of

STATE (Simulation Tool for Atom TEchnology).

a finite-size graphene. This model as well as

by

the
by

generalized

gradient

Perdew-Burke-Ernzerhof

other parameters were placed as an input file ona supercomputer. The self-consistent field
method was employed, which is an iterative
method that involves selecting a Hamiltonian,solving the Kohn-Sham equation to obtain amore accurate set of orbitals, constructing thepotential for each wave function, and solving the
Fig. 1(a) Structure of single-layer graphene

Kohn-Sham equation again with these until the
results converge. In order to draw a map of local
density of states, an electron density was
integrated over an energy window of 0.05 eV
below the HOMO (Highest Occupied MolecularOrbital). At each (x, y) coordinate, a z-height
possessing the same electron density (1×10-4

Fig. 1(b) Simulated STM image of single-layer/Bohr3) was investigated and its contour map

graphene

was depicted, which is regarded as a simulated
STM image at the sample bias of -0.05 V. We

178

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

used the module (intel/18.0.5.274) for theimage of the surface in Fig. 1(a) at the sample

compilers and mpt/2.16 for MPI library. The set

bias of -0.05V. A brighter area in Fig.1(b)of calculation was usually executed on F4cpu orindicates a higher corrugation, which is caused

F36cpu with suitable nodes in ISSP.

by a higher density of the occupied states. It is

To check both the validity of our parameters

apparent that a hexagonal pattern is formed inin the input file for STATE calculations and thewhich the position of a bright dot coincides withperformance of STATE itself, we first modeledthat of a carbon atom comprising the graphene

an infinite, single-layer graphene. The creatednetwork. Figure 1 insists that the combination ofmodel is shown in Fig.1(a). The cutoff energies

our modeling and parameters with the STATE

were

Ry

software works well. In the next fiscal year, we(GMAXP=20) for the wave functions and theare going to characterize the distribution of local

augmentation charge, respectively. Then we

charge densities near the edges of a graphene

conducted first-principles calculations withinribbon and to unveil its relationship with an

STATE to get the electronic structure of the

STM image around the Fermi level.

36

Ry(GMAX=6)and

400model. Figure 1(b) shows a simulated STM

179

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

An open source code for QUANTUM ESPRESSO to compute
irreducible representations of Bloch wave functions
Seishiro ONO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
indicators has been extended to magnetic spacegroups and superconductors [2].
As seen in the preceding paragraphs, it is
helpful to compute irreducible representations
by using DFT. Although the authors of Refs.
[3,4] implemented programs for WIEN2k and
VASP to calculate irreducible representations,these packages need paid licenses. In contrast,
QUANTUM ESPRESSO, a free package for abinitio calculations, can obtain irreducible
representations only for symmorphic spacegroups.
In this work, we developed an open-sourcecode for QUANTUM ESPRESSO to getirreducible representations for all space groups.
In addition to this function, we implemented afunction to automatically compute the ℤ" index
that can diagnose various topological phasessuch as higher-order topological insulators.
Furthermore, we also apply our program toabout 40 magnetic materials. Then, we used thefacilities of the Supercomputer Center to get
wave functions for these materials. We are stillsearching for new topological materials byusing our program and DFT calculations.

Since the remarkable discovery of ℤ!
topological insulators, topological materials
have attracted researchers around the world.
Topological materials host robust surface statesand exhibit unique bulk responses, which could
be leveraged for new low-power devices.
Therefore, discovering various topologicalmaterials is one of the important tasks forengineering.
Given a symmetry setting, establishing
topological invariants that characterize all
possible topological phases is a pending
problem. Furthermore, it is sometimes difficult
to compute topological invariants even when
we know the mathematical definition of
topological invariants. However, when spatial
symmetries exist, it is effortless to diagnose
topological phases by using information of
spatial symmetries. A prototypical example ofthis relation is the Fu-Kane formula, which canevaluate the topological invariant of insulatorsfrom eigenvalues of the inversion symmetry. In
recent years, this idea has been generalized to
all combinations of crystalline symmetries byusing irreducible representations of wave
functions instead of eigenvalues, and thegeneralized theory is called symmetry
indicators [1]. While it does not bring thecomplete classification, this theory is suitable
to discover realistic topological materials. In
fact, this method is a basis of recent
comprehensive surveys of topological materials
among existing databases of inorganic
substances. As a result, thousands of candidatesof topological (crystalline) insulators andsemimetals have been discovered. In addition
to these developments, the theory of symmetry

References[1] H. C. Po, A. Vishwanath, and H. Watanabe,Nat. Commun. 8, 50 (2017).
[2] S. Ono, H. C. Po, and H. Watanabe, Sci.
Adv. 6, eaaz8367 (2020).
[3] F. Tang, et al., Nature, 566, 486-489 (2019).
[4] M. G. Vergoniry, et al., Nature, 566, 480485 (2019).

180

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First Principles Calculation of 2-Dimensional Silicides
Formed on Nickel Surfaces
Tsuneo FUKUDA1 and Ippei KISHIDA2*
1

Department of Physical Electronics and Informatics, Graduate School of Engineering,Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-Ku, Osaka 558-8585
2
Department of Mechanical and Physical Engineering, Graduate School of Engineering,Osaka City University, 3-3-138 Sugimoto, Sumiyoshi-Ku, Osaka 558-8585
Metal silicides are indispensable materials
foradvanced

microelectronics.

We

have

recently proposed a new route to form a robust
two-dimensional (2-D) silicide [1,2]. Unlike
conventional thin film silicide formed by

1 nm

depositing metal on the silicon surface, Si was
deposited on a clean metal surface to form

Fig. 1 Typical STM image for a 0.39 ML Si deposited
surface. White square corresponds to the 1×1 unit cell.

silicide. Our recent studies show that robust 2-

top layer. Since the STM image is reflected by

D silicides are formed on Ni(110) and Ni(100)the surface local density of states (LDOS) nearsurfaces due to the large diffusion asymmetry

EF, the embedded Si reduces the tunnelingbetween Si in bulk metal and metals in bulk Si

current without the large LDOS due to Ni 3d[1,2]. However, the lack of theoretical support

bands, making it a dark site. Therefore, theclearly undermines the significance of ourdiscrimination between individual Si and Ni is

research findings.

fairly straightforward, but the relationshipbetween Si and Ni is unsolved.

First-principles calculation code VASP wasexperimentally

Therefore, the first principle calculation was

obtained 2-D atomic structure with theoretical

performed in this system. The calculation

simulations. A typical scanning tunnelingparameters are shown in Table 1. Before

microscope (STM) image of a Si-deposited

performing

Ni(100) surface is shown in Fig. 1 [2]. The

evaluated the ground state energies of Ni and Si

initial clean surface was essentially a 1×1

atoms, and bulk Ni and Si, respectively.

structure, but many dark sites were formed after

Because of the slow convergence of self-

Si deposition. These dark sites are not due toconsistent electronic states in the surface

structural defects, but Si replaced by Ni in the

structure, we adjusted the mixing parameters as

adoptedtocomparethe181

surfaceslab calculations,weActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Table 1 Parameters for present calculation

shown in Table 1 (so-called linear mixing, see

VASP Version
slab geometry

VASP manual). First, all atoms except for the
middle layer has been completely relaxed. Thenvacuum region
k-points
potential
cut off energy
Fermi level smearing

0-8 surface Ni atoms in the top layer were
replaced by Si, and the top 5 layers were fully
optimized. A total of 36 different surface

convergent condition
ion cordinationelectronic states
mixing parameters

configurations were evaluated for 0-1 ML Si
coverage.
In order to compare the formation energy
for different numbers of surface species, we

5.3.5
Ni(100) 2×4 unit
11 layers
2.12 nm16×8×1
PBE [3]350.39 eV
Methfessel & Paxton
σ = 0.12 eV0.01 eV/Ang.
10-5 eVspin-resolved
AMI = 0.02
BMIX = 0.0001
AMIX_MAG = 0.08
BMIX_MAG = 0.0001

evaluated chemical potential as,
𝐸𝑡𝑜𝑡𝑎𝑙 = 𝐸𝑠𝑙𝑎𝑏 − 𝑛𝑁𝑖 𝐸𝑏𝑁𝑖 − 𝑛𝑆𝑖 𝐸𝑏𝑆𝑖 ,N
S

where 𝐸𝑠𝑙𝑎𝑏 is a total energy of a particular slab
structure, 𝑛𝑁𝑖 and 𝑛𝑆𝑖 are respectively numbersof Ni and Si atoms in the slab, and 𝐸𝑏𝑁𝑖 and 𝐸𝑏𝑆𝑖
are respectively bulk cohesive energies for Ni
and Si.
As shown in Fig. 2, the relative energies ofFig. 2 Relative formation energies of Si-embedded
Ni(100) surfaces with various configurations of Si
coverage between 0-1 ML. Inset: The most stableconfigurations with Si coverage of 0.125, 0.25, 0.375,
and 0.5 ML.

various configurations referenced from that for
the Ni(100) surface are plotted as a function of
Si coverage. Negative formation energy meansthat energies of Si embedded structures are

results. As a future study, the displacement

lower than that of the Ni(100). There is aprocess, so-called depressive adsorption, should

negative slope for Si coverage from 0 to 0.5

beML, indicating that Si substitution with Ni issimulations.

revealedbymolecular

dynamics*present address: Nagamori Institute of Actuators,
Kyoto University of Advanced Science, 18
Yamanouchi, Gotanda-Cho, Ukyo-Ku, Kyoto 6158577, Japanenergetically favorable. On the other hand, apositive slope above 0.5 ML means that Si will
be ejected from the structure, which is in good

References

agreement with experimental observations.

[1] T. Fukuda, I. Kishida, and K. Umezawa,
Surf. Sci. 659 (2017) 1.
[2] T. Fukuda, I. Kishida, and K. Umezawa,
Jpn. J. Appl. Phys. in press.
[3] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys. Rev. Lett. 77, (1996) 3865.

In conclusion, the first-principles study of
two-dimensional Ni silicide formed on Ni (100)is in good agreement with the experimental

182

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles Study of Defects of Magnesium Alloys
Daisuke Matsunaka
Department of Mechanical Systems Engineering,
Shinshu University, 4-17-1 Wakasato, Nagano 380-8553
interatomic potentials.

Magnesium (Mg) has been of increasingly
viewpoint,

One way for improving the limited ductility

because of its low density and relatively highof Mg at room temperature is to activate non-

specific strength. Despite intensive researchbasal slips. In particular, Mg-Y alloy has shown

efforts, there remain various problems to bea significantly enhanced ductility. It has been

overcome; low ductility and low toughness atsuggested that the improvement of ductility wasroom

activeattributed to the reduction of the intrinsic I1

deformation mode under an applied load, thestacking fault (SF) energy by Y addition. We

Schmid factor and the critical resolved shear

investigated defect nucleation in the vicinity ofstress (CRSS) for each deformation mode areahelpful. However, several studies showed thatsimulations. While formation of (11-21) twin

the activated deformation mode under various

was observed under shear stress on (0001)

uniaxial loadings deviated the Schmid’s law

along [11-20], <c+a> partial dislocations were

and their CRSSs were not uniquely determined.

generated with SFs for higher resolved shear

In order to investigate influences of non-glide

stress for pyramidal slips. The dissociationstress on deformation modes, we carried out

reactions of the dislocations at the side ends ofmolecular dynamics (MD) simulations for slips

the I1 SF were energetically evaluated, and itwith <a> Burgers vector under several normal

was implied that nucleation of the <c+a>stress conditions. For basal slip, extended

dislocations on the first-pyramidal planes isdislocations were generated and glided on the

more favorable than on the second-pyramidal

basal planes, irrespective of the applied normal

planes.

stress conditions. In MD simulations of shear

References

deformation for first-pyramidal slip, distinct[1] S. Yoshikawa and D. Matsunaka: Mater.

dislocation gliding was not observed andTrans. 61 (2020) 127.

alternatively (10-11) twin was generated. For[2] S. Yoshikawa and D. Matsunaka: Comp.

prismatic slip, deformation behavior depended

Mater. Sci. 179 (2020) 109

interest

from

the

temperature.

engineeringTo

understandon the applied normal stress as well as

183

pre-existing

intrinsic

I1

SF

by

MD

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles study of magnetoresistance ratios and magnetic anisotropy
in magnetic tunnel junctions
Keisuke MASUDA, Tsuyoshi SUZUKI, and Kenji NAWA
Research Center for Magnetic and Spintronic Materials,
National Institute for Materials Science, Sengen, Tsukuba, Ibaraki 305-0047
Magnetic tunnel junctions (MTJs), where an

barrier is around 10 Å, which is consistent withinsulating tunnel barrier is sandwiched between

experiments. We found that the low RA is

two ferromagnetic electrodes, are the mostattributed to a small band gap in the MGO

practical spintronic devices. The MTJs havebarrier. In addition, our detailed analysis of thevariousnonvolatileelectronic structure clarified that the obtained

magnetic random access memories (MRAMs)

high MR ratio can be understood from theand many types of magnetic sensors includinginterfacial resonance effect [2].

read heads of hard-disk drives. For these

As a second topic, we tried the calculation of

applications, we have several requirements in

MR ratios in unconventional (111)-oriented

the physical properties of MTJs. In the present

MTJs, which have not been examined well sowork, we studied such properties using thefar owing to the successful history in the (001)-

first-principles calculations.

oriented MTJs. By using the first-principles

The spinel oxides AB2O4 can be hopeful

approach mentioned above, we calculated ainsulating tunnel barriers in MTJs. Among

MR ratio of Co/MgO/Co(111) and obtained athem, MgGa2O4 (MGO) has recently attracted

quite high value (>2000%). We found that suchattention because the MGO-based MTJs havea high MR ratio also comes from the interfacial

low resistance-area products (RA) and highresonance effect [3].

applications

such

as

magnetoresistance (MR) ratios [1], both ofwhich are necessary for MRAM and read-head

References

applications. To understand the mechanism of[1] H. Sukegawa et al., Appl. Phys. Lett. 110,such properties, we calculated RA and MR(2017) 122404.

ratiosby[2] K. Nawa, K. Masuda, and Y. Miura, 第 24

combining the density-functional theory (DFT)

回半導体スピン工学の基礎と応用, 東北大学,

and the Landauer formula. As a result, a low

2019 年 12 月.

RA (~0.5 Ωμm2) and a high MR ratio (~200%)[3] K. Masuda, H. Itoh, and Y. Miura, Phys.

were obtained when the thickness of the MGO

Rev. B 101, (2020) 144404.

in

the

Fe/MGO/Fe(001)

MTJ

184

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Carrier Dynamics in Nano Scale Semiconductor
Devices with Machine Learning
Masakazu Muraguchi
Faculty of Engineering, Hokkaido University of Science,
Maeda, Teine, Sapporo 006-8585
We have studied a Machine Learning(ML) approach to make a model of electrontransport process in nanostructures. The
transmission coefficients and timedevelopment of electron density in thenanostructures are computed by timedependent schrödinger equation to provide
training and test datasets to the machinelearning [1,2]. Calculations are performedon the motion of electron wave packets ofdifferent energies in a two-dimensional
nanostructure under random impurity
distribution.
We work on the creation of two
types of predictive models; thetransmission probability of electron
wave packet from the impurity
distribution; the impurity distribution
from the image sequence of electron
density
distributioninthetransmission process. By combining
these predictive models, we expect toachieve a more efficient device design
methodwithtime-dependentcalculation than ever before.
As the ML methods, a Random
Forest (RF) and a Neural Network(NN) are employed for modeling therelationship between the impurity
distributions and the transmission
coefficients of electron. The mean
absolute error is compared to eachmodel. In both methods, it is foundthat the approach of capturing theimpurity distribution as an image
could build a better model than using
simple impurity coordinates as input.
In addition, we investigate thepredictive model for the impurity
distribution from the image sequenceof the time evolution of electron
density as shown in Fig.1. Modelingby convolutional NN is performed,
and the accuracy is compared when
the image sequence is individually
inputted, when the mean of the image
sequence is inputted, and when theimage sequence is inputted with arecurrent network.
x

Propagation Direction
Propagation Directionyxy

Impurity
Potential

Modeling

Electron Density

Impurity Distribution

Fig.1
Modeling
theimpurity
distribution from the image sequence ofthe time evolution of electron density.

References[1] N. Watanabe and M. Tsukada: Phys. Rev.
B 62 (2000) 2914.

[2]. T. Okunishi, Y. Ohtsuka, M. Muraguchi, K.
Takeda, Phys. Rev. B, 75, 24 (2007), 2453141~245314-15.

185

Wavelength selection for the photocleavage of coumarin-caged Dluciferin via quantum chemical calculation
Junko Usukura a,†, Miyabi Hiyama b, Maki Kurata a, Yuji Hazama a,c, Xing-Ping Qiu d,Francoise M. Winnik e,f, Hidefumi Akiyama a,c, Nobuaki Koga gaInstitute for Solid State Physics, University of Tokyo, Kashiwa, Chiba, Japanb

Graduate School of Science and Technology, Gunma University, Kiryu, Gunma, Japanc

AIST-UTokyo OPERANDO-OIL, Kashiwa, Chiba, JapandDépartement de Chimie, Université de Montréal, Montréal, CanadaeDepartment of Chemistry, University of Helsinki, Helsinki, FinlandfInternational Center for Materials Nanoarchitectonics (MANA), National Institute for Materials
Science (NIMS), Tsukuba, Ibaraki,Activity
Japan
Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyog

Graduate School of Informatics, Nagoya University, Nagoya, Japan†

usukura@issp.u-tokyo.ac.jp

Keywords: firefly, bioluminescence,quantum chemical
calculation, absorption
spectrum
Analysisof absorption
spectrafor caged compounds

in aqueous solution
The firefly luciferin-luciferase system has been widely used as a bioluminescence-imaging probe.
MiyabiHIYAMAandrelease D-luciferins, are needed to
Photolabile caged D-luciferins, which cleave by light trigger
Graduate
Schoolof
ScienceandTechnology,
Gunma
control the initiation and the position of bioluminescent reaction. Recently,
we University,
synthesized a new
Tenjin-cho,
Kiryu,
Gunma
376-8515
photolabile caged D-luciferin, (7-diethylaminocoumarin-4-yl)methyl caged D-luciferin (DEACM-caged
D-luciferin), aiming at rapid photolytic cleavage1. Fig. 1 shows
the chemical structure of DEACM-caged D-luciferin. Its
Coumarin caged-luciferins, which can
genWe found that the peak near 384 nm of theoquantum yield (QY) after irradiation
by a 70 mWcm-2 higherate firefly luciferin (’luciferin’ in this ar- retical absorption spectrum corresponds to thenm) was only 6%, a value
pressure mercury lump (254-600
ticle) by UV photolytic reaction, would be absorption from the ground electronic statemuch lower than that of D-luciferin (41%). Higher QY may be
to understand the firefly biolumines- (S0 ) to the first excited state (S1 ) and that the
wavelengthis selected.
obtained if light of suitableusefulcence. We synthesized the new caged-luciferin(coumarin caged-luciferin) and obtained theabsorption spectra for this caged-luciferin itIn the present work, we studied
theoretically the equilibrium
self and irradiated caged-luciferin[1]. When we
structures and optical properties of DEACM-caged D-luciferin
use this caged-luciferin for spectroscopic studin neutral aqueous solution in order to predict the wavelengthies, we need the detail of electronic states ofof the irradiation light suitable for the photocleavage of DEACMthis molecule in aqueous solutions. In thiscaged D-luciferin2. 40 conformers were identified by scanning
year, we performed the density functional thethe potential energy surface. The conformers are similar inory (DFT) calculations for coumarin cagedterms of energies, oscillator
strengths and assignments of theluciferin .

lowest three excitations although their structures are different.
The theoretical absorption spectrum, which is the Boltzmann
The polarized
continuum
was usedin agreement
weighted average of the oscillator
strengths,
was model
1
for the description
solute inmolecules.
as shown
Fig. 2.
with the experimental absorption
spectrumof water
All calculations
usingbandthe
The theoretical analysis showedthat thewere
firstperformed
absorption
GAUSSIAN09[2]
programonsystemB
andat 384 nm is attributed to the S1 state, corresponding to the
C of caged
Super Computerin ISSP.
The
group Centerand thesecondelectronic excitation of thestates forto40
is attributed
theequilibrium
S2 and Sstructures
absorption band at 339 nmground3 states,forcoumarin
caged-lucifein
inaqueoussolucorresponding to the electronic excitations of the luciferin
tion
were
obtained.
The
time
dependent
moiety.

peak near 339 nm corresponds to the absorptions from S0 to the second (S2 ) and third (S3 )excited state[3]. We also found that the characteristics of 339 nm peak in the theoretical absorption spectrum of coumarin caged luciferin
is similar to that of the peak in the absorption
Fig. 1 Chemical structure of DEACM-caged Dspectrum
luciferin of luciferin.

Fig. 2 Absorption spectra of DEACM-caged D-

DFT (TDDFT) calculations for these strucluciferin and D-luciferin1
tures were poerformed to obtain the theoret- Figure 1: Absorption spectra for coumarin
ical absorption
spectra. T. Ito, Y. Hayamizu, X.-P.
caged
and luciferin[3].
solid[1] M. Kurata, M. Hiyama, T. Narimatsu,
Y. Hazama,
Qiu,luciferin
F.M. Winnik,
H. Akiyama,Black
Synthesis
line : Experimentalof
Photobiol. absorption
B (2018) spectrum
189:81-86.
and quantitative characterization of coumarin-caged D-luciferin, J. Photochem.
DOI:10.1016/j.jphotobiol.2018.10.002
Figure 1 shows the experimental and theo- coumarin caged luciferin, Red solid line: Theoabsorption
spectrumof coumarin
caged
Y. Hazama,
X.-P. of
Qiu,
F.M. Winnik,
Akiyama,
N. Koga,
Theoretical
study ofthe[2] J. Usukura, M. Hiyama, M. Kurata,
retical absorption
spectracoumarin
caged- H. reticalluciferin,Blackdashedline:
Experimental
abwavelength selection for the photocleavageof coumarin-caged
D-luciferin,
luciferin. The
experimental absorption
spec-Photochem. Photobiol. DOI:10.1111/php.13212
trum of luciferin is also shown in Figure 1. The sorption spectrum of luciferin, Orange dashedshape of the theoretical absorption spectrum line: the component of absorption from S0 toof coumarin caged-luciferin is quite similar to S1 , Green dashed line: the components of absorptions from S0 to S2 and S3 .
that of experimental spectrum.

186

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] Kurata et al. , J. Photochem. Photobiol.
B, 189 (2018) 81.
[2] Gaussian 09, Revision D.01, M. J. Frischet al.
[3] Usukura et al. Photochem. Photobiol.
(2020) in press

187

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Calculation of multication oxide surface properties forcatalyst informatics
Yoyo HINUMA
Center for Frontier Science
Chiba University, 1-33 Yayoicho, Inage, Chiba, Chiba 263-8522
Surface point defects of metal oxides, for[1,2] was expanded to allow automatic

instance O vacancies, have a dominant effectderivation of models where the topmost andon heterogeneous catalysis. The Mars-Van

bottommost surfaces need to be reconstructed,

Krevelen mechanism is one of the mostwhich is the case in the normal spinel surfaces

frequently encountered catalytic process. In one

in this study [3]. The surface energy was

example, O vacancies on a metal oxide catalyst

smallest in the (100) surface in all systems, andsurface act as reaction sites. The energy

EOvac was largest in the (100) surface in all

minimum required to remove O from a surface,systems except ZnCo2O4. The reactivity of awhich is denoted as the surface O vacancy

site is expected to be high if the site is unstable.

formation energy (EOvac), can be used to

In other words, a site with low EOvac is expectedrationalize and predict catalytic performance into have a higher reactivity and therefore cansuch a catalytic process. Calculation of EOvac

open up new capabilities in, for example,

requireswithcatalysis. The importance of finding unstablesufficient spacing between O vacancies, hence

sites, which roughly translates to having asome estimation of EOvac from less costly

lower EOvac for surface O sites, that arecalculations, such as slab-and-vacuum model

expected to have lower surface energy wascalculations with minimum cell size and even

identified in this study. Needless to say, thebulk calculations, will be effective in screening

surface must be proven to be experimentallymaterials for a given purpose.

accessible, which is a very important issue thataslab-and-vacuum

model

The EOvac of ZnM2O4, where M is one of Al,

need to be worked on.

Ga, In, V, Cr, Mn, Fe, or Co, was calculated.

References

These compounds take the normal spinel[1] Y. Hinuma et al.: Comp. Mater. Sci. 113

structure, and the (100), (110), and (111)(2016) 221.

surfaces[2] Y. Hinuma et al.: Phys. Rev. Mater. 2 (2018)

were

evaluated.

The

automated

nonstoichiometric and nonpolar slab-and-model

124603.

generation algorithm already by Hinuma et al.

[3] Y. Hinuma et al.: Mater. Trans. 61 (2020) 78.

188

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on physical properties of structural elementary
excitations of semiconductor surfaces and interfaces
Hiroyuki KAGESHIMA
Graduate School of Natural Science and Technology, Shimane University
1060 Nishi-Kawatsucho, Matsue, Shimane 690-8504

Our project has been focused on physicalproperties of structural elementary excitationsof semiconductor surface and interfaces. We
have performed three topics in this year. One
is the physical properties of SiO interstitials in
SiO2 at interface with Si [1, 2]. The second
is the physical properties of oxygen vacancies(VO ) in SiO2 at interface with Si. And thethird is the physical properties of vacancies ina two-dimensional material MoSe2 . The calculations were performed based on the ﬁrstprinciples calculation. Program package VASP
was employed for the ﬁrst and the third topics,
while program package PHASE0 was employed
for the second topic.
In the ﬁrst topic, we focus on the role of SiO
interstitials for the selfdiﬀusions in SiO2 undercompressive pressure. It is known that SiO interstitials are injected into the oxide when Si
is thermally oxidized. In addition, for Si pillar
oxidation, it is known that a large compressive
pressure as high as 5 GPa is induced in the oxide. We have calculated the pressure eﬀect for
temperatures 3000, 4000, 5000, and 6000 K,
and derived activation volumes as well as activation energies. We found that the SiO reallyacts as a unit for the diﬀusion mechanism. As
the result, the pressure dependence of Si diffusion is largely aﬀected by the SiO incorporation, while that of O diﬀusion is not muchaﬀected. [1, 2]
In the second topic, we focus on the strain
eﬀect on VO diﬀusion in SiO2 . As described
before, for the Si pillar oxidation, a large com-189

pressive pressure is accumulated in SiO2 . We
have calculated activation barriers as the function of modulated lattice constants. We havealso checked crystal polymorph dependence forQuartz, Cristobalite, or Tridymite. As theresults, we found that the barrier height increases with the Si density almost being independent of the polymorph type. The reason
comes from the fact that the initial Si-Si distance at VO controls the barrier height.
In the third topic, we focus on the supporting eﬀect on vacancy formation in monolayer
MoSe2 . The results are similar to our previous study on MoS2 . We found that the supporting eﬀect makes the charging more diﬃcult because the reduced quantum conﬁnement
shrinks the band gap. The hetero-stacking also
makes the charging more diﬃcult because thetype II band alignment also shrinks the bandgap. These lead to the reduction of charging
eﬀect on the vacancy formation.

References[1] H. Kageshima, Y. Yajima, K. Shiraishi,
and T. Endoh, Jpn. J. Appl. Phys. 58(2019) 111004 (11pages).
[2] Y. Yajima, H. Kageshima, K. Shiraishi,
and T. Endoh, 2019 International Workshop on Dielectric Thin Films for FutureElectron Devices – Science and Technology – (2019 IWDTF), Tokyo, Japan, p-7(Nov. 18, 2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical Study on Electronic Properties
in New Nanoscale Surfaces and Interfaces
Katsuyoshi KOBAYASHI, Yoko TANAKA
Department of Physics, Ochanomizu University
2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610

In 2019 we theoretically studied electron transport properties through higher-order
topological insulators. Higher-order topological insulators were recently proposed theoretically [1]. Higher-order topological insulators
are materials that have topologically protectedstates in two or more lower spatial dimensions.
There are several reports that higher-order
topological insulators are experimentally observed [2, 3]. We calculated electrical conduction properties through topological edge statesin a three dimensional crystal.
We used a tight-binding model of higherorder topological insulators given by Langbehn
et al. [4]. This model is a three dimensional
insulator and has one dimensional edge states
protected by mirror symmetry. Transmission
properties through the edge states are investigated. We consider a cubic structure of higherorder topological insulator. Two electrodes areattached to two corners of the cube. The electrodes are normal conductors. We solve scattering states of the Hamiltonian of the open
system. Electrical conductance is calculatedusing the Landauer formalism.
We consider several diﬀerent conditions ofcontact between the high-order topologicalinsulator and electrodes.
Calculated conductance depends strongly on contact conditions. Conductance increases with increasing
the strength of the contact for weak strengthof contact. But, it turns to decrease with further increase of the contact strength. There isa peak in conductance as a function of the contact strength. This result is due to a following
reason.
The incident electrons are transmitted to another electrode or reﬂected to the incident elec-

190

trode with conserved or inverted spin. The
reﬂection with conserved spin is dominant in
the region of weak contact strength. The spinconserved reﬂection decreases with increasing
the contact strength. The transmission to theother electrode increases in place of the decrease of conserved reﬂection. However, withfurther increase of the contact strength, thereﬂection with inverted spin increases and it
becomes dominant. Accordingly, the transmission turns to decrease. This result means that
there is moderate contact strength for highttransmission.
In addition to the study of electron transmission properties through the high-order topological insulators, we also developed the calculation method of spin and angle resolved
photoelectron spectroscopy. We extended themethod for obtaining time-reversed LEED
states from the results of repeated-slab calculations. It became possible to treat general cases
containing any number of bulk Bloch states byusing the singular value decomposition.

References[1] F. Schindler et al.:eaat0346.

Sci. Adv. 4 (2018)[2] F. Schindler et al.: Nat. Phys. 14 (2018) 918.
[3] S. N. Kempkes et al.: Nat. Mater. 18 (2019)1292.
[4] J. Langbehn et al.: Phys. Rev. Lett. 119(2017) 246401.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of First-principles calculations methodof Seebeck coeﬃcient in the framework of linear
response theory
Sonju KOU
Department of Materials Science and Engineering, Tokyo Institute of Technology J1-3,
KNagatsuta-cho 4259, Midori-ku, Yokohama 226-8502, Japanµ    

The study combines three approaches:
phonon density of state calculations, the CPA
method for static phonons, and linear response
theory in the framework of the KKR method.
The electrical conductivity and Seebeck coefficients at finite temperature were calculated
by using this method. Concretely, we first
calculate the phonon density of states assuming harmonic oscillations by the direct method
using the first-principles packages VASP[1] orQuantum-ESPRESSO[2] and ALAMODE[3] .
Next, the average displacement of the atoms ateach temperature is obtained from the phonon

density of states, and the eﬀect is incorporated
into the Green function in AkaiKKR, which
extends the CPA method to handle the effect of displacement. Finally, the Green function is substituted into the Kubo-Greenwood
equation[4] of the KKR-CPA method by Butlar to calculate the temperature-dependent
electrical conductivity, and the Seebeck coefficient is obtained from Mahan’s equation[5].
In the transition metal system, which is considered to be diﬃcult to calculate using theBoltzmann equation and the relaxation time
approximation, we calculate the Seebeck coefficients for the simplest single transition metals
using the above method, and confirm that thecoeﬃcients reproduce the experimental values
well[6].

 

The simulation of the Seebeck coeﬃcient ismainly calculated by using the relaxation time
approximation to the Boltzmann equation, but
this approximation is correct only if the relaxation time is constant, and it is not a good approximation method for transition metal systems where the band structure on the Fermi
surface is very complex. As a method to solve
this problem and calculate the Seebeck coeﬃcient in a non-semi-classical quantum mechanical way, a method to calculate the Seebeck
coeﬃcient from the energy dependence of electrical conductivity near the Fermi energy using
linear response theory has been proposed. In
this study, we deal with the temperature dependence of the phonon density of states andanharmonic oscillations, which are not considered in the method for obtaining Seebeck coefficients from electrical conductivities using linear response theory in previous studies.



 










  






Figure 1: (Color online) Calculated (closed
symbol) and experimental[7] (open symbol)
Seebeck coeﬃcients S of pure Cu, Mo, and W
as functions of temperature.

191

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] G. Kresse and D. Joubert, Phys. Rev. B
59, 1758 (1999)µ)K/V ( tneiciffeoc kcebeeS

0

-50
Ag

exp.

Au

exp.

Pt

exp.

Pd

exp.

[2] Paolo Giannozzi et al., Phys. Condens.
Matter 21 395502 (2009)

-100
0

500

1000

1500

2000

Tmeperature (K)[3] T Tadano et al., Phys. Condens. Matter 26,
225402 (2014)[4] W. H. Butler, Phys. Rev. B 31 3260 (1985)

Figure 2: (Color online) Calculated (closed
symbol) and experimental[7] (open symbol)
Seebeck coeﬃcients S of pure Ag, Au, Pt, and
Pd as functions of temperature.

[5] M. Jonson and G. D. Mahan, Phys. Rev. B
21, 4223 (1980)[6] S. Kou and H. Akai Solid State Communications 276 1-4 (2018)[7] N. Cusack and P. Kendall, Proc. Phys. Soc.
72, 898 (1958)

192

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculation of spin-density wave statein chromium metals
Yohei KOTA
National Institute of Technology, Fukushima College
Iwaki, Fukushima 970-8034

Chromium metal ﬁlms are one of practicalmaterials for strain gauge sensor due to showing the high-sensitive response of the electrical resistivity by strain eﬀect. [1] Though themechanism of the high sensitivity is still unclear, we consider a possibility that the electrical resistivity of chromium metal is greatly
inﬂuenced by lattice strain, through the modulation of the spin-density wave state. To
verify this possibility in the theoretical view
point, we analyze the strain eﬀect on the electronic structure in the spin-density wave stateof chromium metals by ﬁrst-principles calculations. For the calculation of the incommensurate spin-density wave state in chromium metals, large unit cells including more than 40
atoms were adopted, with reference to the previous works by Hirai and Hafner et al. [2, 3]
The Vienna ab-initio simulation package [4]was used for the calculations, where the exchange correlation functional was describedwithin the general gradient approximation.
Figure 1 shows the calculation result of thetotal energy in the nonmagnetic (NM) state,
the commensurate spin-density wave (CSDW)
state, and the incommensurate spin-density
wave (ISDW) state as a function of the lattice
constant a. Note that the wave-number in the
ISDW state was set to q = 0.95 · 2π/a [Å−1 ].
The equilibrium lattice constant in the ISDW
state is aeq = 2.845 [Å], which is approximately 1% smaller than the experimental value
aexp = 2.884 [Å]. We should mention here thatthe ground state is not the ISDW state but

Figure 1: Total energy per atom in NM (red),
CSDW (blue), and ISDW (green) states as afunction of the lattice constant a.
the CSDW state in the calculation, however,the similar result was obtained in the previous
works [2, 3]. On the other hand, it is remarkable that the magnetism of chromium metal
disappears for a ≤ 2.78 [Å]; this feature is qualitatively consistent with an experiment that
the Néel temperature of metallic chromium becomes zero for applying 15 GPa of hydrostaticpressure. [5] This result implies that the magnetism of chromium metal is sensitively variable by lattice strain, corresponding to the factthat the magnetovolume eﬀect is observed signiﬁcantly in chromium metal.

References[1] E. Niwa and Y. Sasaki, IEEJ Trans. SM
134, 385 (2014).

193

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[2] K. Hirai, J. Phys. Soc. Jpn. 66, 560(1997).
[3] R. Hafner et al., Phys. Rev. B 65, 184432(2002).
[4] G. Kresse et al., Phys. Rev. B 47, 558(1993); Phys. Rev. B 54, 11169 (1996).
[5] K. Shimizu et al., Physica B 378-380, 632(2006)

194

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development and application of the first-principles approach
Hiroaki IKEDA
Department of Physics,
Ritsumeikan University, Kusatsu, Shiga 525-8577
We have investigated unconventional super-model. In general, the conventional LDA /conductors in the strongly correlated electron

GGA calculations describe the overall featuresystems (SCES). The main theme is to developof the band structure. However, the size and

the

well

curvature of the Fermi surface and thedescribe the electronic structure of SCES. This

composed orbital characters are significantly

year, using a Class B, we have studied two

deviated from the experimental observations.

topics; superconducting gap anisotropy of thelayered Bismuth chalcogenide superconductors

This has a sizable effect on the gap structure. In(BiCh2) and the electron correlation effect ofgap structure. Emergence of propeller-type

the gap structure in iron-based superconductors.
The layered BiCh2 superconductors possess

Fermi pockets is well consistent with thenon-symmorphic structure. Locally inversion

orbital characters turns the gap structure fromsymmetry breaking and the strong spin-orbit

horizontal nodes to octet node structure. This

coupling (SOC) on a Bismuth site can lead tostudy was reported in MRM2019 [3].

first-principles

calculations

andFig. 1, we indicates the Fermi surface and theexperimental data. Furthermore, the change ofthe parity mixing between spin singlet andtriplet pairing. In addition, the observed charge/ orbital fluctuations potentially yield the gap
anisotropy even without strong repulsive
interactions. First, we performed the DFT band
structure calculations using Qunatum espresso[1] in Sekirei system, and made an effective
four-orbital models with the SOC using the
maximum localized Wannier functions. We

Fig. 1 Gap structure on the Fermi surface in
KFe2As2 obtained by GGA (left) and QSGW(right).

have solved the superconducting gap equationin multi-orbital attractive Hubbard model. In
the obtained phase diagram, we have found a
possibility of topological superconductivity.

References

This study was reported in the JPS autumn
meeting 2019 [2].

[1] P. Giannozzi et al., J.Phys.:Condens.Matter
21, 395502 (2009)

Next, in the iron-based superconductors, we[2] K. Suzuki, JPS Autumn meeting 10pB17-4

have applied the quasi-particle self-consistent
GW (QSGW) method to KFe2As2 and studied[3] K. Suzuki, MRM2019 D3-13(1)-l13

the gap structure in the effective Hubbard

195

3.3

Strongly Correlated

Quantum Systems

196

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Mechanism of quantum spin liquidand high-Tc superconductivity
studied by excitation spectra and nonequilibrium dynamics
calculation by variational Monte Carlo methods
Masatoshi IMADA
Toyota Physical and Chemical Research Institute41-1 Yokomichi, Nagakute, Aichi, 480-1192
andResearch Institute for Sicence and Engineering, Waseda University
3-4-1 Okubo, Shinjuku-ku, Tokyo, 169-8555
Understanding physics of high-Tc cupratemodel, namely Hubbard model on the squaresuperconductors remains one of the importantlattice

problems in materials science. In this project, wesuperconducting state is severely competing

have

phase

with the stripe ordered state, while most of the

diagram of HgBa2CuO4+y [1] by solving its abphase diagram in the parameter space of theinitio low-energy effective Hamiltonian without

carrier doping concentration is dominated by the

adjustable parameters [2].

It shows astripe order and the superconducting statesuperconducting phase in a wide range of holeremains an excited state [3,4]. Therefore, thedensity δ, and its competition with charge

Hubbard model does not properly account forperiod-4 plus spin period-8 stripe order near δ ∼the experimental phase diagram of the cuprate

0.1, in agreement with experimental results.

superconductors. However, it has also been

reproduced

theexperimental

hadclarified

that

the

d-waveA crucial role of off-site interactions inshown that the superconducting phase in the abstabilizing the superconductivity is elucidated

initio Hamiltonian is adiabatically connectedwith emphasis on charge fluctuations. It alsowith that found in the superconducting excitedclarifies

mainlystate of the Hubbard model. Therefore, it is

Coulomb

intriguing to understand the distinction of theinteraction. The present achievement will enablesuperconducting state in between the ab initio

deeper, predictable understanding on openand Hubbard cases. The method for dynamicalsuperconducting

properties newly developed offer useful insights

mechanism and promote ab initio studies on

into this issue as we describe in the next section.

strongly

Calculations of dynamical quantities are athecontributed

issuesofcondensation
from

the

the

on-sitehigh-Tc

correlated

energyelectrons

beyondparametrized model studies.

challenging subject for strongly correlated

In former studies on a simplified effective

electron systems even in the linear response

197

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

regime. Recently we have developed a method

method. The application of the method to larger-

to calculate the dynamical correlation functions

sized Hubbard model on the square lattice

based on the variational Monte Carlo method

correctly[3,4]. We first developed a method to calculate

behavior at half filling and gap structures of d -the charge dynamical structure factors for thewave superconducting state of the hole doped

ground states of correlated electron systems. Our

Hubbard model in the ground state optimized bybenchmarks for the one- and two-dimensional

enforcing the charge uniformity, evidencing a

Hubbard models show that inclusion ofwide applicability to strongly correlated electroncomposite-fermion excitations in the basis set

systems.

reproduces

the

Mott

insulating

greatly improves the accuracy, in reference to

From the obtained d-wave superconducting

the exact charge dynamical structure factors forgap of the charge uniform state, we find that theclusters. Together with examination for larger

gap amplitude at the antinodal point is several

systems beyond tractable sizes by the exact

times larger than the experimental value, when

diagonalization, our results indicate that thewe employ a realistic parameter as a model ofvariational Monte Carlo method is a promising

the cuprate superconductors. The effective

way for studies on the nature of charge dynamics

attractive interaction of carriers in the d-wave

in correlated materials such as the copper oxide

superconducting state inferred for an optimized

superconductors

composite-fermion

state of the Hubbard model is as large as theexcitations are properly included in the restricted

order of the nearest-neighbor transfer, which isHilbert space of intermediate states in the linear

far beyond the former expectation in the

response theory. Our results on the charge

cuprates. The nature of the superconducting

dynamical structure factor are consistent withstate of the Hubbard model in terms of thethe particle-hole excitations inferred from theoverestimate of the gap and the attractive

single-particle spectral function A(k,ω) in theinteraction in comparison to the cuprates are

literature. The importance of incorporating

clarified [4].

nonlocal composite fermion for a more accurate

Finding quantum spin liquids is anotherdescription is also pointed out [3].

important subject of the present research project.

This method can be extended to calculate theTopological properties of the strongly correlated

one-body Green's function by improving thesystems with strong spin-orbit interaction arevariational Monte Carlo method. We benchmark

one of such subjects. We have studied

against the exact diagonalization for the one-

Heisenberg model with spin-orbit interaction

and two-dimensional Hubbard models of 16 site

(Dyaloshinskii-Moriya

lattices, which proves high accuracy of the

pyrochlore lattice by using the variational Monte

if

the

198

interaction)

on

the

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Carlo method. This system has been proposed to

conductors

be a candidate of the quantum spin liquid in

Hamiltonian”.

earlier studies. We will report the result on thisand “Studies on Quantum Spin Liquids in

based

on

first-principles

Materials with Strong Spin-Orbit Interaction”

subject in the future.

This series of work has been done in

Another candidate of the quantum spin liquid

collaboration with T. Ohgoe, T. Misawa, M.

is found in a quantum Heisenberg model with

Hirayama, K. Ido, Y. Nomura, Y. Yamaji, R.

the geometrically frustrated square lattice, called

Pohle and M. Charlebois. The calculations were

J1-J2 model. By utilizing the machine learning

performed on computers at the Supercomputer

method, we have found a firm evidence for theCenter, ISSP, Univ. of Tokyo. The work is also

quantum spin liquid and clarified its excitation

supported by JSPS Kakenhi 16H06345, thespectra, which indicate the fractionalization of

RIKEN Center for Computational Science underspins into spinons. The subject has a closethe HPCI project (hp190145) and the MEXTHPCI Strategic Programs, CDMSI. This project

connection to the experimentally observed spin

has used the software HPhi and mVMC.

liquid state in molecular conductors. Studies on

References

the ab inito low-energy effective Hamiltonian[1] Motoaki Hirayama, Takahiro Misawa,

for a dmit compound are underway and will be

Takahiro Ohgoe, Youhei Yamaji, Masatoshi

reported elsewhere.

Imada, Phys. Rev. B 99 (2019) 245155.

This is a combined report for E project[2] Takahiro“Mechanism of quantum spin liquid and high-Tc

Ohgoe,

Motoaki

Hirayama,

Takahiro Misawa, Kota Ido, Youhei Yamaji,

superconductivity studied by excitation spectraand nonequilibrium dynamics calculation by

Masatoshi Imada, Phys. Rev. B 101 (2020)

variational

045124.

Monte

Carlo

methods”,“Development of methodology for analysis of[3] Kota Ido, Masatoshi Imada, Takahiro

nonequilibrium superconductivity in strongly

Misawa, Phys. Rev. B 101 (2020) 075124.

correlated systems via integration of electronic[4] Maxime Charlebois, and Masatoshi Imada,state theory and time-resolved experimental

arXiv:1912.09960.

data”, and shared project for post-K project“Studies on quantum spin liquids in molecular

199

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical studies on energy current correlations infrustrated quantum spin systems
Youhei YAMAJI
Department of Applied Physics, The University of Tokyo
Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656

Topological states of matters are often characterized by quantized transport properties.
As a prototypical example, two dimensional
Chern insulators are characterized by thequantized charge Hall eﬀect. In the Mott insulators, however, the quantization of thermal
Hall transports characterizes the topologicalstates, instead of the charge transports [1, 2].
The quantum spin liquid state of the Kitaev
model is a typical example of the topologicalstate that shows half-integer quantized thermal Hall transports [1]. The observation of thehalf-integer quantized thermal Hall coeﬃcientin a spin-orbit coupled Mott insulator α-RuCl3
has attracted broad attention [3].
We studied numerical methods to characterize the topological spin liquids. The thermal transport is calculated by correlations ofthermal currents and energy magnetization [4].
These quantities are formulated by energy current operators, which are given by the continuity equation of the energy density.
For the lattice hamiltonian, the energy density is represented by the bond energy as follows. Here, we show the continuity equation of
the energy density of the Kitaev-type magnets
on the honeycomb lattice as an example. The
nearest-neighbor bonds on the honeycomb lattice have three diﬀerent directions. When thethree bonds are labeled as x, y, and z, an effective hamiltonian of α-RuCl3 , the Kitaev-Γ

hamiltonian,
Ĥ =

∑

∑

(γ)

Ĥℓm ,(1)

γ=x,y,z ⟨ℓ,m⟩∈γ

is defined by the exchange coupling for the γ(= x, y, z) bond,
(
)
(γ)
γ
β
α
Ĥℓm = K Ŝℓγ Ŝm, +Γ Ŝℓα Ŝm, +Ŝℓβ Ŝm,(2)where (α, β, γ) is a permutation of (x, y, z) andK (Γ) is the Kitaev (oﬀ-diagonal symmetric)
exchange coupling. The bond energy of thehamiltonian is, then, introduced as the Fouriercomponents,
∑ ∑
Ĥq =
e+i(q /2)·(Rℓ +Rm )γ ⟨ℓ,m⟩γ

[
(
)]
γ
β
α
× K Ŝℓγ Ŝm+ Γ Ŝℓα Ŝm, +Ŝℓβ Ŝm, ,(3)
where ϵαβγ (α, β, γ = x, y, z). By using thesmall q limit of the continuity equation of thebond energy,dĤq∼ −iq · j E ,dt(4)

we determine the energy current operator j E .
When, for simplicity, K = 0 is chosen, theHeisenberg equation of motion,
]
dĤq
i[
=
Ĥ, Ĥq ,dtℏ
defines j E with the commutator,

200

(5)

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo]i[
Ĥ, Ĥq =
ℏ

(
)
i 2∑[
y y
y
x x
z
z y
y
Γ
q · δ xz,ℓ Ŝm
Ŝ
Ŝ
+
Ŝ
Ŝ
Ŝ
−
Ŝ
Ŝ
Ŝ
m
m
m
m
m
ℓ
ℓ
x
z
x
z
x ℓ
z
ℏ
ℓ
(
)
x
y
x
x
+q · δ zy,ℓ ŜmŜ z Ŝ z + Ŝm
Ŝ y Ŝ x − ŜmŜ x Ŝmz ℓ myz ℓ my
z ℓ
y
(
)]
y y
z
x
x z
z
z z
+ q · δ yx,ℓ Ŝm
Ŝ
Ŝ
+
Ŝ
Ŝ
Ŝ
−
Ŝ
Ŝ
Ŝ
my ℓ mx
my ℓ mxy ℓ mx
[
(
)
∑
i
x x
z y
y y
q · δ xz,m Ŝℓyx Ŝm
Ŝℓz + Ŝℓzx Ŝm
Ŝℓz − Ŝℓyx Ŝm
Ŝℓz
+ Γ2
ℏ
m
(
)
z z
y x
x x
+q · δ zy,m Ŝℓxz ŜmŜℓy + Ŝℓyz ŜmŜℓy − Ŝℓxz Ŝm
Ŝℓy
(
)]
y y
x z
z z
+ q · δ yx,m Ŝℓzy ŜmŜℓx + Ŝℓxy ŜmŜℓx − Ŝℓzy ŜmŜℓx ,(6)

where δ αβ,ℓ is the vector from the center of the α-bond terminated by ℓth site and to the centerof the β-bond terminated also by ℓth site.

The energy-current–energy-current correlations and energy magnetizaion for the KitaevΓ hamiltonian at finite temperatures are calculated by combining the Krylov subspace methods and typicalit approaches [5] and will bereported elsewhere [6].

References

The topological nature of the Mott insulating states will be destroyed by spontaneous
symmetry breakings. Therefore, to clarify the
topology, we need to examine whether the spin
liquid candidates show spontaneous symmetry
breakings or not. We have modified mVMC [7]to calculate higher-order spin correlations andcalculated the singlet-singlet correlatons of atypical frustrated quantum spin systems, theHeisenberg model on pyrochlore lattices. So
far, the inversion symmetry is spontaneously
broken in the lowest variational state.

[3] Y. Kasahara, et al.: Nature 559 (2018)
227.

[1] A. Kitaev: Ann. Phys. 321 (2006) 2.
[2] C. Wang, A. C. Potter, and T. Senthil:
Science 343 (2014) 6171.

[4] T. Qin, Q. Niu, and J. Shi: Phys. Rev.
Lett. 107 (2011) 236601.
[5] Y. Yamaji, T. Suzuki, and M. Kawamura:
arXiv:1802.02854.
[6] Y. Yamaji, et al.: in preparation.
[7] T. Misawa, et al.: Compt. Phys. Commun. 235 (2019) 447.

201

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of spin-orbit coupled phenomena
in correlated electron systems
Yukitoshi MOTOME
Department of Applied Physics,
The University of Tokyo, Bunkyo, Tokyo 113-8656
We have theoretically studied a variety ofthis topic in review articles [11,12,13].

intriguing phenomena in correlated electron(ii) Chiral magnets: We theoretically unveiled

systems with spin-orbit coupling, ranging fromthat a nonreciprocal spin transport, which is

Mott insulators to metals. During this fiscal

switchable by a magnetic field, can occur inyear, we have achieved substantial progress on

monoaxial magnets [14]. We also clarified thatthe following topics (project numbers: H31-

interplay between spin, charge, and orbital

Ca-0052 and H31-Cb-0032). We summarize

degrees of freedom plays a crucial role inthe main results below.

stabilizing the magnetic hedgehog lattices(i) Kitaev quantum spin liquids: By using ab

recently found in B20 chiral magnets [15]. We

initio based calculations, we theoreticallyalso showed that the magnetic monopoles andproposed new candidates for the Kitaev

antimonopoles associated with the magnetic

magnets with unconventional antiferromagnetic

hedgehogs annihilate in pair by magnetic fields

Kitaevand cause topological phase transitions [15,16].

interactions:Pr-basedf-electroncompounds [1,2] and polar asymmetric systems(iii)[3]. We also clarified real-time dynamics ofproposed that the successive phase transitions

fractional excitations in the Kitaev quantum

in a spin-orbit coupled metal Cd2Re2O7 arespin liquids [4], Majorana-magnon crossover indriven by electric toroidal quadrupoles [17]. We

an applied magnetic field [5], and exotic phasealso clarified that nonmagnetic impurities cantransitions in three-dimensional extensions of

induce magnetic and toroidal multipoles in

the Kitaev models [6,7]. In addition, we haveferromagnets [18].

collaborated with several experimental groups(iv) Spin current generation: We discovered afor identifying the signatures of Majorana

new mechanism of spin current generation,

excitations in the Kitaev magnets: nuclear

which can work even in the absence of thequadrupole and magnetic resonances [8],spin-orbit coupling [19]. We also developed theRaman scattering [9], and thermal Hall effectunderstanding of this phenomenon based on the[10]. We have summarized the recent results oncluster multipole picture [20].

202

Multipole

physics:We

theoreticallyActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References

preprint (arXiv:2001.01899).

[1] S.-H. Jang, R. Sano, Y. Kato, and Y.

[11] Y. Motome and J. Nasu, J. Phys. Soc.

Motome, Phys. Rev. B 99, 241106(R) (2019).

Jpn. 89, 012002 (2020), INVITED REVIEW[2] S.-H. Jang, R. Sano, Y. Kato, and Y.

PAPER.

Motome, preprint (arXiv:1912.03422).

[12] 求 幸年，那須 譲治, 固体物理 54, 217[3] Y. Sugita, Y. Kato, and Y. Motome, Phys.

(2019).

Rev. B 101, 100410(R) (2020).

[13] Y. Motome, R. Sano, S.-H. Jang, Y. Sugita,[4] J. Nasu and Y. Motome, Phys. Rev.

and Y. Kato, preprint (arXiv:2001.03731), in

Research 1, 033007 (2019).

press in J. Phys.: Condens. Matter, Special[5] J. Yoshitake, J. Nasu, Y. Kato, and Y.

Issue Article.

Motome, Phys. Rev. B 101, 100408(R) (2020).

[14] S. Okumura, H. Ishizuka, Y. Kato, J. Ohe,

[6] T. Eschmann, P. A. Mishchenko, T. A.

and Y. Motome, Appl. Phys. Lett. 115, 012401

Bojesen, Y. Kato, M. Hermanns, Y. Motome,(2019).

andS.

Trebst,

Phys.

Rev.

Research 1,[15] S. Okumura, S. Hayami, Y. Kato, and Y.

032011(R) (2019).

Motome, preprint (arXiv:1908.05044), in press[7] P. A. Mishchenko, Y. Kato, K. O'Brien, T. A.

in Phys. Rev. B.

Bojesen, T. Eschmann, M. Hermanns, S. Trebst,[16] S. Okumura, S. Hayami, Y. Kato, and Y.

and Y. Motome, Phys. Rev. B 101, 045118

Motome, JPS Conf. Proc. 30, 011010 (2020).

(2020), Editors' Suggestion.

[17] S. Hayami, Y. Yanagi, H. Kusunose, and Y.

[8] Y. Nagai, T. Jinno, Y. Yoshitake, J. Nasu, Y.

Motome, Phys. Rev. Lett. 122, 147602 (2019),

Motome, M. Itoh, and Y. Shimizu, Phys. Rev.

selected as a Cover Image.

B 101, 020414(R) (2020).

[18] S. Hayami, H. Kusunose, and Y. Motome,[9] Y. Wang, G. B. Osterhoudt, Y. Tian, P.

J. Phys. Soc. Jpn. 88, 063702 (2019).

Lampen-Kelley, A. Banerjee, T. Goldstein, J.

[19] M. Naka, S. Hayami, H. Kusunose, Y.

Yan, J. Knolle, H. Ji, J. Cava, J. Nasu, Y.

Yanagi, Y. Motome, and H. Seo, Nat.

Motome, S. Nagler, D. Mandrus, and K. S.

Commun. 10, 4305 (2019).

Burch, npj Quant. Mat. 5, 14 (2020).

[20] S. Hayami, Y. Yanagi, M. Naka, H. Seo, Y.

[10] T. Yokoi, S. Ma, Y. Kasahara, S. Kasahara,

Motome, and H. Kusunose, JPS Conf. Proc. 30,

T. Shibauchi, N. Kurita, H. Tanaka, J. Nasu, Y.

011149 (2020).

Motome, C. Hickey, S. Trebst, and Y. Matsuda,

203

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Studies on the Role of the Incipient Band Played in Two-band
Unconventional Superconductivity
KAZUHIKO KUROKI
Department of Physics, Osaka University
1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, Japanthe two-leg ladder Hubbard model, and made acomparison between the two models.
In Fig.2, we show for t′ = 0 the eigenvalue λplotted against t⊥ for the bilayer and tr for the
two-leg ladder. For each t⊥ or tr , the maximum
eigenvalue is searched by varying the band ﬁlling n.
We perform the calculation for U = 6t and U = 3t.
For U = 6t in the bilayer and for both values of
U in the ladder, λ is maximized when the bonding
band touches the Fermi level, i.e., when the bandis incipient. This is not the case for U = 3t in the

(a)
1.4

bonding band below EF

1.2
1
0.8
0.6

n=1.15

U=3

0.4
0.2
0

n=1.1511.5

n=1.072(b)bilayertunit cell

1.2

t
tr´

1

t

n=1.1

3

3.5

4

bonding band below EF

U=6

n=1.05bonding band below EF

U=3

λ

0.8

t
´

n=1.050.6
0.4

t

n=1.05

0.2
0
1

EF

t~t , t’~0

2.5

bonding band
below EF

1.4

2 leg laddert

U=6

n=1.05λWe have been studying spin-ﬂuctuationmediated superconductivity in two-band systems
with one of the bands intersecting the Fermi level
while the other band (“incipient band”) sits inthe vicinity of the Fermi level. In ref.[1, 2], we
studied the Hubbard model on a two-leg ladderlattice, which is characterized by the nearest
neighbor hoppings in the leg (t) and the rung(tr ) directions, and also the diagonal next nearest
neighbor hoppings t′ (Fig.1).
In 2019 ﬁscal year, we have extended the study
to two dimensional (2D) systems. A simplest extension of the two-leg ladder Hubbard model to twodimensions is the bilayer square lattice Hubbard
model, where two Hubbard models on a square lattice are coupled by vertical hoppings t⊥ along withdiagonal hoppings t′ (Fig.1). Here, t⊥ controls therelative energy between the two bands like tr in
the two-leg ladder. We adopted the ﬂuctuationexchange (FLEX) approximation, and solved thelinearized Eliashberg equation to obtain the eigenvalue at a ﬁxed temperature (T = 0.05t), which
gives a measure for the superconducting transition
temperature. We investigated a large parameter
space of (t⊥ , t′ , n, U ), where n is the band ﬁllingand U is the on-site Hubbard interaction.[3] Simultaneously, we also performed similar calculation for

t~t , t’ >0

1.2

1.4

1.6

tr

1.8

2

2.2

t<t , t’~0

FIG. 1. Upper panel : the bilayer lattice (left) and thetwo-leg ladder lattice (right). Lower panels : schematic
images of the bonding and antibonding bands of thebilayer lattice. Left : t ∼ t⊥ , t′ ∼ 0, middle : t ∼ t⊥ ,t′ > 0, right : t < t⊥ , t′ ∼ 0. In the middle and rightpanels, the bonding band is incipient.

204

FIG. 2. (a) Maximized λ at T = 0.05 of the bilayer
Hubbard model with U = 6t or 3t and t′ = 0 plottedagainst t⊥ . λ is maximized at each t⊥ by varying theband filling n. At some points, n that maximizes λis denoted by arrows. (b) Similar plot for the twoleg Hubbard ladder model, where t⊥ is replaced by tr .
From Ref.[3].

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a)comes small, the overall tendency does not changemuch in the ladder (except that larger tr is needed
for the bonding band to be incipient because theband width renormalization is weak), but for thebilayer model, superconductivity is strongly suppressed and it is no longer optimized in the incipient band situation.

(b)FIG. 3. mVMC calculation results of the pairing correlation for the two models with t′ = 0. (a) t⊥ /t dependence of the pairing correlation P s± (interlayer nearest
neighbor pairing)for the bilayer model with various values of U/t. The band filling is n = 1.06. (b) tr dependence of the pairing correlation P d (interchain nearest
neighbor pairing) for the two-leg ladder model with various values of U/t. The band filling is n = 1.03. From
Ref.[6].

bilayer, where λ is signiﬁcantly reduced.
We also performed multivariable variational
Monte Carlo calculation (mVMC) [4, 5] study forthe two models, and calculated the pairing correlation function against t⊥ (bilayer) or tr (two-leg
ladder)[6]. The results shown in Fig.3 resemble the
FLEX results of the eigenvalue of the Eliashberg
equation shown in Fig.2 (note that FLEX is performed only in the t⊥ ≥ t or tr ≥ t regime).
The above FLEX and mVMC results suggest
that, when U is suﬃciently large, superconductivity is strongly enhanced in both the bilayer andtwo-leg ladder models when the bonding band isincipient. As t⊥ or tr becomes small and the bonding band intersects the Fermi level, superconductivity is signiﬁcantly degraded for the bilayer model,
but not so strongly in the ladder. When U be-205

It is known that the spin ﬂuctuations within acertain moderate energy range work eﬀectively as
pairing glue, while those in the very low energy
range are pair breaking[7]. This, combined with thediﬀerence in the density of states (DOS) for the twomodels due to the diﬀerence in the dimensionality,
enables us to understand the obtained results[3, 6].
Namely, when the bonding band is incipient, thelow-energy spin ﬂuctuations is suppressed because
only the states around the bonding band edge cancontribute to their development, while there is signiﬁcant contribution from the bonding band to themoderate-energy spin-ﬂuctuations. This is the reason why superconductivity is strongly enhanced in
the incipient band situation. As t⊥ or tr is reduced
and the bonding band intersects the Fermi level,
the low energy spin ﬂuctuation rapidly develops in
the bilayer lattice because the DOS of the bonding
band at the Fermi level increases, while the development of the low energy spin ﬂuctuation in theladder is moderate because the DOS of the bonding band decreases as the Fermi level moves toward
the middle of the band. This explains the diﬀerence
between the two models. As for the eﬀect of U ,the band width is reduced by the renormalization,
so that the bonding band becomes incipient for asmaller t⊥ or tr for larger U . This eﬀect is essential for superconductivity to be strongly enhancedin the bilayer model because in this way the portionof the DOS that contributes to superconductivity
is squeezed into a narrower energy range. This effect is not so important in the ladder, where the
DOS at the band edge is diverging.

[1] K. Kuroki, T. Higashida, and R. Arita, Phys. Rev.
B 72, 212509 (2005).
[2] K. Matsumoto, D. Ogura, and K. Kuroki, Phys.
Rev. B 97, 014516 (2018).
[3] K. Matsumoto, D. Ogura, and K. Kuroki, J. Phys.
Soc. Jpn. 89, 044709 (2020).
[4] D. Tahara and M. Imada, J. Phys. Soc. Jpn. 77,
114701 (2008).
[5] T. Misawa et al., Comp. Phys. Comm. 235, 447(2019).
[6] D. Kato and K. Kuroki, Phys. Rev. Research, toappear (2020) (arXiv:1912.11983).
[7] A.J. Millis, S. Sachdev and C.M. Varma, Phys. Rev.
B 37, 4975 (1988).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study of magnetism and transport phenomena in strongly
correlated quantum systems using computational approaches
including non-equilibrium methods
Norio KAWAKAMI
Department of Physics,
Kyoto University, Kitashirakawa, Sakyo-ku, Kyoto 606-8502
We

have

studiedstrongly

correlated

Brillouin zone at which the effective non-quantum systems with a focus on magnetism

Hermitian Hamiltonian cannot be diagonalized,

and transport phenomena, using computational

occur at the Kondo temperature, at which theapproaches, including non-equilibrium methods.

magnetic moments are screened, and the wellknown

We have analyzed the effect of correlations
narrow-gap topological Kondo insulators bydynamical

localized

andFurthermore, we have studied the one-bandtheoryHubbard model on the honeycomb lattice by(DMFT) calculations. We have demonstrated

DMFT as well as by numerically exact

that the interplay between correlations andquantum Monte Carlo simulations. We havenonlocal hybridizations can lead to observableshown that the DMFT approximation is very

quantum oscillations even without a Fermi

accurate in the Dirac semi-metallic phase,surface and that quantum oscillations in a three-where local moment formation is present, anddimensional system can be understood from thethe spin correlation length small. Moreover, we

physics of the two-dimensional planes in thehave shown that although the quantum critical

momentum space for which the hybridization in

point can only be understood by lattice

the direction of the magnetic field vanishes.

Quantum Monte Carlo techniques, DMFT givesThisa reasonable estimate of the critical interaction

scenario

shouldmean-field

betweenitinerant f electrons takes place. [2]on the emergence of quantum oscillation in
performing

crossoverbe

relevantfor

understanding the observations in SmB6 andstrength. [3]

YbB12. [1]References[1] R. Peters, T. Yoshida, and N. Kawakami,

We have studied the impact of nonHermiticity due to strong correlations in f-

Phys. Rev. B 100, 085124 (2019).

electron materials, by analyzing the periodic-[2] Y. Michishita, T. Yoshida, and R. Peters,

Anderson model with local and nonlocal

Phys. Rev. B 101, 085122 (2020).

hybridization in the insulating and metallic
regimes by DMFT combined with numerical[3] M. Raczkowski, R. Peters, T. T. Phung, N.

renormalization group (NRG). We have shown

Takemori, F. F. Assaad, A. Honecker, and J.

that exceptional points, momenta in the

Vahedi, Phys. Rev. B 101, 125103 (2020).

206

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on metal-insulator transition in nickel oxides
Yusuke NOMURA
RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, 351-0198
Rare-earth nickelates LuNiO3 shows anenergy Hamiltonians for LuNiO3 eg manifold.

interesting phase diagram. Starting from theWe explicitly include the phonon degrees ofroom temperature, by cooling, it exhibits two-

freedom using newly-developed constrained

step transitions. The first one is the metal-

density functional perturbation theory (cDFPT)

insulator transition, and the second one is the[1]. We calculate the magnitude of phonon-

magnetic transition. At the first transition,

mediated electron-electron interaction as wellinterestingly, bond disproportionation occurs,

as the effective Coulomb interactions.

where one set of octahedra is compressed, andthe other is expanded. It means that thedisplacement of breathing phonon mode is
induced, and the Jahn-teller mode becomesinactive despite the (eg)1 configuration.

Fig. 2: Band structure of LuNiO3.
As a result, we find that coupling to the JahnTeller phonon mode indeed exists, which favors
Jahn-Teller distortion. However, at the sametime, non-local Coulomb interaction, whichfavors bond disproportionation, is substantial.

Fig. 1: Crystal structure of LuNiO3 at highTherefore, the coupling to Jahn-Teller modetemperature.

and the non-local Coulomb interaction competewith each other. In the real material, the latter
wins, and the bond disproportionation takes

In this study, we derive the effective low-207

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

place at the metal-insulator transition.

References[1] YN et al., Phys. Rev. Lett. 112, 027002(2014); YN and R. Arita, Phys. Rev. B 92,
245108 (2015)

208

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on frustrated magnetism using machine learning
Yusuke NOMURA
RIKEN Center for Emergent Matter Science, 2-1 Hirosawa, Wako, 351-0198
Quantum spin liquid (QSL) is an exotic

the benchmark to check the usefulness ofstate of the matter, in which long-range

machine learning, and interesting applications

magnetic order is suppressed even at zero

to explore many-body physics have not yet

temperature. The QSL has attracted much

performed.

attention not only because of its uniqueIn the study, by using a newly-developed

property such as the fractionalization of themachine learning method (RBM+PP), which

excitation

combines the restricted Boltzmann machine

but

also

becauseofpossibleand(RBM) and pair-product (PP) state [2], we

memory devices. However, to show theobtain strong support for the existence of theexistence of the QSL in the realistic quantum-

QSL phase in the thermodynamic limit of thespin Hamiltonians, except for rare cases such as

spin-1/2 Heisenberg spin system on the square

the Kitaev model where the exact ground statelattice with the nearest-neighbor and next-

can be constructed by hand, we need highly

nearest-neighboraccurate numerical methods.

respectively, called the J1-J2 Heisenberg model.

applications

toquantum

computingTo achieve high accuracy, we focus on

The

QSL

exchanges,

phase

shows

J1

and

J2,

unconventional

machine learning. Machine learning is good at

excitation spectrum, in which both the singlet

extracting essential patterns in the data. By

and triplet excitations become gapless at high-applying

body

symmetry momenta (0,0), (p,0), (0,p), (p,p), in

accurate

support of the nodal Dirac dispersion of the

problems,

it

to

the

quantum-many

we

can

obtainanrepresentation of the quantum many-body wave

fractionalized spinon at (±p/2,±p/2).

functions (vector with exponentially large
dimensions) with a finite number of parameters(data compression). Starting from the seminal

References

work by Carleo and Troyer [1], now, there is[1] G. Carleo and M. Troyer, Science 355, 602

growing evidence for the powerfulness of the(2017).

machine learning method to study many-body[2] Y. Nomura, A. S. Darmawan, Y. Yamaji, andproblems. However, studies so far are limited to

M. Imada, Phys. Rev. B 96, 205152 (2017).

209

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Variational Monte Carlo calculation of
two-dimensional Wigner crystal under latticecommensurability
Takeo KATO
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581
4

In this work, we studied the Wigner crystallization in spinless Fermion systems on asquare lattice at finite fillings by highly accurate simulation based on the many-variablevariational Monte Carlo (mVMC) method [5].
By performing the calculations up to the orderof 103 sites, we determine the transition points
for n = 2, 4, 8, 12, 16 and draw the phase diagram as functions of rs and 1/n as shown in
Fig. 1.
In contrast to the previous works by pathintegral renormalization group (PIRG) [4], wefound that the transition points at finite fillings
becomes significantly small. Nevertheless, thetransition points seem to continuously connect
to its continuum limits, which is consistent
with the previous works. We also examined thenature of the associated metal-insulator transition by calculation the momentum distribution

30

27

mVMC
HF
PIRG
DQMC

20
rs

Wigner crystallization, which breaks thetranslational symmetry due to the long-range
Coulomb interactions, is a fundamental problem in strongly correlated electron systems.
By the diﬀusive quantum Monte Carlo method(DQMC), the critical electron density for crystallization is obtained as rs = r0 /a∗B ≃ 150
for a three-dimensional electron gas (r0 =(πne )−1/2 , a∗B : the eﬀective Bohr radius) [1].
The critical value of rs is lowered down to rs ≃31 for a two-dimensional electron gas [2, 3].
In addition to the Coulomb interaction, thelattice commensurability reduces the critical
Coulomb interaction for crystallization [4].

28

1/8

10

1/4
0

0

0.1

0.2

0.3

0.4

0.5

n
Figure 5. Caption

Figure 1: Phase diagram in the plane of theelectron-density and rs . We also show the result of the Hartree-Fock (HF) approximation.
and the charge gap [6].

References[1] D. M. Ceperley and B. J. Alder, Phys. Rev.
Lett. 45, 566 (1980).
[2] M. Imada and M. Takahashi, J. Phys. Soc.
Jpn. 53, 3770 (1984).
[3] N. D. Drummond and R. J. Needs, Phys.
Rev. Lett. 102, 126402 (2009).
[4] Y. Noda and M. Imada, Phys. Rev. Lett.
89, 176803 (2002).
[5] T. Misawa, et al., Comput. Phys. Commun.
235, 447 (2019).
[6] M. K. Ritter, K. Ido, T. Misawa, and T.
Kato, in preparation.

210

put. Phys. Commun. 235, 447 (2019).
P. P. Ewald, Ann. Phys. 369, 253 (1921).
A. Grzybowski, E. Gwóźdź, and A. Bródka, Phys. Rev. B
61, 6706 (2000).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetic and transport properties indouble-exchange systems with quasiperiodicity
Akihisa Koga
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551

Quasicrystals (QCs) have no translational
symmetry but possess long-range order andspecial rotational symmetry. Since its first
discovery in 80’s, intensive efforts have been
made to search various type of QC materials
and to reveal characteristic features. In thisdecade, there have been several important experimental findings in QC materials, which include quantum critical behaviors in Au-Al-Yb
alloy and the emergence of superconductivity
in Al- Zn-Mg QC alloy. These experimentssuggest important roles of electronic correlations in these materials, and stimulate theoretical studies of the correlation and inducedordered phases in QC systems.
Motivated by this situation, we have studied possibility of the excitonic insulating (EI)
state in the two-band Hubbard model [1] andthe magnetism of the double exchange model[2] on the Penrose lattice. In the former
study [1], we considered the vertex model andthe center model on the Penrose lattice to determine their ground state phase diagram interms of the real-space mean-field theory. We
have revealed the existence of the stable EI
phase induced by small interband interactions[Fig. 1(a)]. We pointed out that this originates from the electron-hole paring for thecompletely or nearly degenerated states, which
is characteristic of the QC systems. In addition, we also discussed the spatial structure of
the order in terms of the so-called perpendicular space [Fig. 1(b)]. In the second study [2],we investigated the double exchange model on
the Penrose lattice in terms of a Monte Carlo
method. We showed the existence of the ferromagnetism and revealed that its general fea-

211

Figure 1: (a) EI order parameter of the twoband Hubbard model of the center model on
the Penrose lattice. Red dotted circles indicates the stable EI states with small interactions. (b) Analysis in the perpendicular space
for the stable EI phases.
tures such as temperature dependence resemble those of the system on the normal squarelattice. By means of the analysis in the parpendicular space, we discussed the characteristic
real-space structure of the magnetism in thisQC system.

References[1] K. Inayoshi, Y. Murakami, and A. Koga:
arXiv:2002.05870 (2020).
[2] Y. Takeuchi, Master thesis, Tokyo Institute of Technology (2020. Mar).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical analysis for nonequilibrium dynamics incorrelated electron systems with orbital degrees of
freedomAkihisa Koga
Department of Physics, Tokyo Institute of Technology, Meguro, Tokyo 152-8551
LETTERS

J. Phys. Soc. Jpn.

2

t/JK1

Strongly correlated systems with orbital de!"#(a)grees of freedom can lead to intriguing spin
⇥10 3 2(a)R
150
systems. One of the important examples is1
the Kitaev quantum spin model, which consists
100
L
B
R
0
of anisotropic exchange couplings on the honlocalized
50
1
h (t)
eycomb lattice and shows the quantum spinSz hi�nerant
02liquid (QSL) state at low temperatures. Al⇥10 3 2
12 13
16 17
20
(b)!$# (b)though the Kitaev model was originally proL
M
R
14 15
18 19
150
11
6 7
2 3
posed theoretically,itisconsidered
to
be
re1
10
FIG. 1. Kitaev model on a honeycomb lattice with zigzag edges.
4 5
8 9
100
1
Red, blue, and,green
linesotherrepresentstrongly
x, y, and z bonds,
respectively.
alized in α−RuClcorre3 and0
Solid (open) circles represent spin-1/2 in the A (B) sublattice. In
50(A along= Na,Li) arelated systems
such
A2 IrO
this figure,fourasz (green)bonds
the a directionin the R
3 exist1
region, namely, L = 4.
Fig. 3. (a) Schematic picture of the Kitaev system on the honeycomb
latticeSzalso candidates of theR Kitaev QSL. So far, thewith two0 edges. The lattice is composed of three regions. The static magnetic
2
region, where
field h is0applied in the
10right (R) 20
30the magnetization
40 appears.
static properties in the Kitaev QSL have been
In the bulk (B) region, no magnetic field is applied and the QSL state is reduces the phase transition to the spin-polarized state aroundx
alized without the magnetization. Time-dependent pulsed magnetic field isthe main focus
thischarac-we re0.042[30]field
within and
the MFmany
theory. Therefore,
hc /JK ⇠ofintroduced in the left (L) region. (b) 20-site cluster used in the exact diagoThe numbers
represent
the Kitaev
index ofspin
the latticesite.with L = 50
strict ourselves
the casehR < hc to discuss the spin
FIG.nalization.
2. Real-time
dynamicsof thesystemteristic features
suchto as
thewithfractionalizationatransport inherent in the Kitaev QSL.
and Lb = 300 after the magnetic-field pulse at t = 0. The contourzof specific heats
andthethermalHall
effectst) onSchematicthe plane of the timet and the space
x in theplot of 1:S (x,We study the time evolution of the system upon stimuli ofFigure(a)picturesof oursetup
system (a) without and (b) with the M (white) region where the QSL
magnetic pulsein the Laregion(see Fig.
1) [44, 45]. To
have been thereported.
Thus,
simplequestionprocess
involved
realizedwithnoisspinpolarization
betweenL (left gray) and spin
region,which
explicitly
given inas thetheanomalous
this end, we introduce the time-dependent Majorana MF the-andis the
R (right gray) regions (see the top of the
The dashed lines" panels).
#
naturally arises
characteristic
2 result of the spinory. Thewhat
details ofisthethe
formulations
are shown in dyRef. [46].transport.
(b)themean-fieldAtrepresent x = vt withvelocity v (seeexp, text).
(9)hL (t)the= Majoranap
The
Hamiltonian
Eq.
(1)
is
obtainedasafermionmodel
by2
namical properties of the Kitaev QSL.
2
2⇡ 2 model.
dynamics of the Kitaev
L

t/JK1

R

R

applying the Jordan-Wigner transformation to the spin opera-

where A andare magnitude and width of the Gaussian
tors [47–49].
Furthermore,
introducing thetwo kindsof MajoMotivatedby this,we bystudied
spin
z
z
B
2hSpulse.
2hS
i(x + xdwe
/2, fixt), ⇥= hi¯=rA 2/J.
In=thefollowing,
A 5=(x,1 t)
andr i, ⇥6 (x, t) =A i(x, t)Fig. 4. Real-time evolution of the change in the local magnetization in therana fermions, and ¯ , from a complex fermion at each site,
A B
¯
i,
where
x
is
the
horizontal
coordinateofr and= system with h /J = 0.01 after the introduction of the pulsed magnetic fieldIn
thiscalculation,
weexaminethe
20-sitecluster
withxdtwohitransport through
the
QSL
by
investigatingrrp
Eq. (1) is rewritten as
the1/(2
other
edge
under
the
staticwith A = 1 and = 2/J shown as the dashed line (o↵set for clarity). Dottededges,
periodic
condition3). where
This theMF
theory boundaryis exact
when magnetic
hL is=imposed
hR = for0.field,
the real-space dynamics
X Kithe direction
perpendicularto MF
the edge,as shown
in Fig.as3(b).
JK X ⇣ A of B theA S B ⌘= JK1/2
we believethat
ourresultsarereliable
far lines represent the results for the pulse with A = 1 and = 2/J.
A B A BtheTherefore,hybridization
betweenthelocal
Majorana
H(t) =ii r a+b r + i r+b r
r i¯ r ¯ rIn thecluster,theareR and
L regions
includesites.theThereexas thesmall
fieldsapplied.
In theMFfourtheory,many4 r r[2]taev system with4 ar zigzag
edge structure
fermions
yieldsfinitespin
momentum.
ist wave
twelvesites inthetheB region,where
no magnetic
fieldisoneap- We
bodyfunctionisexpressed
asadirectproductofXX⇣⌘
hL (t) afterhR
A[Fig.1(a)]. We followed
plied.
Althoughcluster we treat issmall, thebyspintransi A ¯ thei rBdynamics¯ rB +i B ¯ B , the (2)alsobody
states,whose
is toodescribed
theto
MFshowstudiedthethetime-evolutionS= 1 Kitaev
model
2 r2R r r
2 r2L r r
port characteristicof the Kitaev
systemexpected
be capHamiltonian.
Determining
the MFsat is
eachtime tofromthe polarization even in the S = 1 Kitaev model. Namely, we exmagnetic field pulse applied to one of the edges
pect that in the S = 1 Kitaev model without a static magnetic
tured since
thereofexist
fourweplaquettes
withthetime-evolution
local Z2 sym- spinthemany-bodyexistencethesimilaranomalous
wave
function,computethewhererindicates
theposition
of
the
z
bond
(the
centerofthemetry,
which iscrucialforthetheextended
peculiar spintransport,
in[50–
the field, the spin degree of freedom is fractionalized into two;with the time-dependentA Majorana
mean-fieldoftheone-body
stateswithEuler
methodA
B
B[3].
z bond; see Fig. 1). r and ¯ r ( r and ¯ r ) are the Majoranatransport
B region.
In fact, we have confirmed that, in the initial state itinerant and localized quasiparticles owing to the existence55]. The time-dependent
field is explicitly given as,
theory andfermion
theoperators
exactconnected
diagonalization.
i magnetic
with the z bond in theWesublattice(t ! A1), the hsite-dependent
magnetization mzi appears only of the local Z2 symmetry. The pulsed magnetic field in the L
t
p
h
(t)
=
exp
,
where
A
and
arez constantsfor the region creates the itinerant and localized quasiparticle exciz
z
z
L
=
h
(t)
=
0,
[H,
⌘
]
=
0
A
(B),
as
shown
in
Fig.
1.
When
h
2
R
L
in the R2⇡ region (m9 = m19 = 0.217 and m10 = m20 = 0.220).
showed that, although no spin
moments
are in-r
Gaussianfollowing,
weoffixthethe
systemsizespin
as tations, while only the formers propagate in the whole sysat each r, and ⌘r (= i¯ rA ¯ rB ) is the Z2 local conserved quanFigure pulse.
4 showsInthethe
timedependencechangein thezz
duced in the
QSL
region,the asspin
mo- References
La moment= 50 and m
Lbz [== m
300,
themstatic
field asthehR pulsed= 0.01J
tem. In the R region, the itinerant and localized quasiparticles
K , andtity. Kitaev
In the case,the model
is solvable
the Hamiltonian
magneticii (t)i ( 1)] after1
pulse
parameters
as A The= 1 magnetic
and = 2J
field
is introduced.
moments
at the sites 1 and are hybridized by the static magnetic field due to the lack ofbilinear ininterms, and its low-energy
dispersion isK .
ments are isexcitedtheofopposite
edge region
2 in thediscussing
L region areby thethroughpulsed magnetic
field. the local Z2 symmetry, leading to the finite spin oscillations.
given asp"k ' v|k kK | around the K point with the velocBefore
the induced
spin transport
the M region,[1]weA.
Kitaev:
Ann.
Phys.
321
(2006)[Fig.1(b)]. ityWethat this
On
the
other
nowithoutmagnetic
momentinthe
the static
B 2.
re- The scenario for the spin transport is schematically shown in
3JK /4. This indicatesthat anomalousand ¯ are regarded asv = revealed
examinethe hand,systemthisregion,appears
namely,gion, which
thesites
existence
local withcon- Fig. 3(a).
the itinerant
and localized
Majorana
respectively.
magnetic
field hisR consistentis appliedwith
to thein theofRthe
regionspin transport
originates
from
thefermions,fractionalserved
quantity.
Oncase,
theY.
other
hand,
after
some
delay,
thequanspin andThe spin fractionalization in the S = 1 Kitaev model has
Murakami,
A. Koga= LMinakawa,
1. In thisthere
are nolocal
conserved
Since the magnetic field hybridizes two kinds of the [2]LRT.
asuch as aoscillation
the sitesand 10 in the
R region.
ization of Majorana
the spinsin thetheHamiltonian
Kitaev isQSL
intotities,leading istoinduced
nonzeroat local
spin9 moments.
Figure2(a) been suggested in the thermodynamic properties
fermions,
no longer
exactlyJ.
Nasu:
arXiv:1912.10599(2019).
double-peak structure in the specific heat.21) We note that
This
means
that
the
wave-packet
triggeredbythemagnetic
shows the contour plot of the changes in the spin moments
solvable.
Here, we apply
the Hartree-Focktype decouthe itinerant
and localized
Majorana
fermions.
the L region
the t)iR regionthrough
re- the higher temperature peak is closely related to the nearest(x, t),inwhereO(x, t)reaches= hO(x,hO(x,1)i.theAsB exS zpulse
pling to the interaction on the z bond as i rA rB i¯ rA ¯ rB ⇠gion without spin oscillations. Since mix (t) = myi (t) = 0 for neighbor spin-spin correlations Ci j . It is known that the higher
A
B
A
B
A
A
Namely, after
excitation, only the itiner[3]pected,
A.
Koga,
T.
Minakawa,
Y.
Murakamii r r ⇥thewe find thatthewavepacket createdbythe magnetic- and
1 (x, t)+⇥2 (x, t)i¯ r ¯ r ⇥1 (x, t)⇥2 (x, t) i r ¯ r ⇥3 (x, t)
any sites, we can say that the spin moment plays no role in temperature peak in the S = 1/2 case corresponds to the mot)i rB ¯ rB +⇥3 (x,cant)⇥4 (x,propagatet) i rA ¯ rB ⇥5 (x, t)through⇥6 (x, t)i¯ rA rB +⇥4 (x, fermionsfield pulse flows to the right edge. Note that its velocity al- tion of the itinerant Majorana fermions. Therefore, one canant Majorana
the spintransportJ.
in theS = 1 Kitaev
model.
This remarkable
J.
Nasu:
Phys.
Soc.
Jpn.
89 (2020)⇥5 (x, t)⇥6 (x, t), where we have introduced the six kinds ofmost coincides with the Majorana velocity of the genuine Kiphenomenon is similar to that in the S = 1/2 Kitaev model,30) expect that the flow of Ci j is regarded as the motion of the itinA absent
B
the QSL, hencethemagnetization
is033701.
x- and t-dependent MFs as ⇥1 (x, t) = hi¯ r ¯ r i ⌘ h⌘i(x, t),taev
model,
whichis shown
as the dashedline in Fig.
2(a). erant quasiparticles in the S = 1 Kitaev model. Figures 5(a),wherethev,spintransport
is mediatedby the itinerant
Majorana
Thisfermions.
indicatesTherefore,that the propagation
is attributed
to the gapless= itinerant
hi rA rB i ⌘ h⇠i(x,t), ⇥3 (x, t) reaches= hi rB ¯ rB i =⇥2 (x, t)there. Whenthe
Majorana
ourresultssuggesttheexistenceof
the 5(b) and 5(c) show the real-time evolution of the change in the
z
z
A A
R

2

2

2hS B i(x, t) =2hS i(xxd /2, t), ⇥4 (x, t) = hi r ¯ r i =Majorana
in thewhichbulk withina small static
itinerantexcitation
quasiparticles,
is not associatedwithfield.
the spinnearest-neighbor spin correlations on the x-, y-, and z-bonds
except for the L region. Oscillations appear in the spin-spin

3

212

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Novel topological phenomena induced by strongly
correlated dynamics
Tsuneya YOSHIDA
Department of Physics, University of Tsukuba
Tsukuba, Ibaraki 305-8571

Focusing on non-Hermitian topological phenomena, we have analyzed correlated systems.
Speciﬁcally, we have analyzed exceptionalband touching for quasi-particle spectrum of
correlated systems in equilibrium [1, 2, 3].
Our works [1, 3] have discovered novel exceptional band touching which we dub symmetryprotected exceptional rings (surfaces) in two(three) dimensions, respectively. In addition,
we have also elucidated that for Kondo insulators, such non-Hermitian band touching
emerges around Kondo temperatures. Furthermore, focusing on dynamics of open quantum systems with two-body loss, we have discovered a non-Hermitian fractional quantum
Hall state (see Fig. 1), which extends thenon-Hermitian physics to long range entangledstates. The above set up is relevant to the cold
atoms with two-body loss.

ImE

(a)

0

(b) 0

-0.05

-0.05

-10.1

-10.05
ReE

-10

nθ=0
nθ=1
nθ=2
nθ=3
nθ=4
nθ=5

ticular, we have found that mirror symmetry
and non-Hermitian topology induces novel skineﬀect protected by mirror symmetry which
may be realized for an electric circuit composed of negative impedance converters. Besides that we have elucidated the other topological phases protected by crystalline symmetry [7, 8, 9]. For instance, we have extended
the notion of higher order topology to correlated systems, which discovered a new topological state, a higher-order topological Mott
insulating state [9]. We also have proposed aneﬃcient method to compute Z4 topological invariant for glide symmetric systems [7].

References[1] Kazuhiro Kimura, Tsuneya Yoshida, andNorio Kawakami: Phys. Rev. B 100,
115124 (2019).
[2] Yoshihiro Michishita, Tsuneya Yoshida,
and Robert Peters: Phys. Rev. B 101,
085122.

-0.85 -0.8 -0.75
100+10× ReE

Figure 1: (Color Online). Energy spectrum of
non-Hermitian Hamiltonian. Panel (b) is themagniﬁed version of the range in −10.085 <ReE < −10.075.
In addition to be above works on nonHermitian systems, we have addressed topology with crystalline eﬀects [5, 6]. In par-213

[3] Tsuneya Yoshida, Robert Peters, Norio Kawakami,
Yasuhiro Hatsugai:
arXiv:2002.11265.
[4] Tsuneya Yoshida, Koji Kudo, and Yasuhiro Hatsugai: Sci. Rep. 9, 16895(2019).
[5] Tsuneya Yoshida and Yasuhiro Hatsugai:
Phys. Rev. B 100, 054109 (2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[6] Tsuneya
Yoshida,Tomonari
Mizoguchi,
andYasuhiro
Hatsugai:
arXiv:1912.12022.
[7] Tsuneya Yoshida, Akito Daido, Norio
Kawakami, and Youichi Yanase: Phys.
Rev. B 99, 235105 (2019).
[8] Kazuhiro Kimura, Tsuneya Yoshida, andNorio Kawakami: JPS Conf. Proc. 30,
011012 (2020).
[9] Koji Kudo, Tsuneya Yoshida, and Yasuhiro Hatsugai: Phys. Rev. Lett. 123,
196402 (2019).

214

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Two-Channel Kondo Eﬀect Emerging in a
Multiorbital Anderson Model Hybridized with Γ7 andΓ8 Conduction Bands
Takashi HOTTA
Department of Physics, Tokyo Metropolitan University
1-1 Minami-Osawa, Hachioji, Tokyo 192-0397

To explore the emergence of a quantum critical point (QCP) between non-Fermi-liquid andFermi-liquid phases, we investigate the statesin the vicinity of two-channel Kondo phase.
For the purpose, we analyze a seven-orbital impurity Anderson model hybridized with three
conduction bands (one Γ7 and two Γ8 ) byemploying a numerical renormalization group(NRG) method.
First we consider one f -electron state, whichis the eigenstate of spin-orbit and crystalline
electric field (CEF) potential terms. Under
the cubic CEF potential, we obtain Γ7 doublet
and Γ8 quartet from j = 5/2 sextet, whereas
we find Γ6 doublet, Γ7 doublet, and Γ8 quartet from j = 7/2 octet. By using those oneelectron state as bases, we describe the local
f -electron Hamiltonian as
Hloc =∑†(λj + Bj,µ + Ef )fjµτ
fjµτ

j,µ,τ

+

∑ ∑ ∑

j1∼j4 µ1∼µ4 τ1∼τ4

Iµj11jτ21,jµ32jτ42 ,µ3 τ3 µ4 τ4 (1)× fj†1 µ1 τ1fj†2 µ2 τ2fj3 µ3 τ3fj4 µ4 τ4 ,where fjµτ denotes the annihilation operator ofa localized f electron in the bases of (j, µ, τ ),j is the total angular momentum, j = 5/2 and7/2 are denoted by “a” and “b”, respectively,µ distinguishes the cubic irreducible representation, Γ8 states are distinguished by µ = α
and β, while Γ7 and Γ6 states are labeled byµ = γ and δ, respectively, τ is the pseudo-spin
which distinguishes the degeneracy concerning

the time-reversal symmetry, and Ef is the f electron level to control the local f -electron
number at an impurity site.
As for the spin-orbit coupling term, we obtain λa = −2λ and λb = (3/2)λ, where λis the spin-orbit coupling of f electron. For
Pr ion, we set λ = 0.1eV in this research.
Concerning the CEF potential term for j =5/2, we obtain Ba,α = Ba,β = 1320B40 /7
and Ba,γ = −2640B40 /7, where B40 denotes
the fourth-order CEF parameter for the angular momentum ℓ = 3. Note that the sixthorder CEF potential term B60 does not appear
for j = 5/2, since the maximum size of thechange of the total angular momentum is lessthan six. On the other hand, for j = 7/2,
we obtain Bb,α = Bb,β = 360B40 /7 + 2880B60 ,Bb,γ = −3240B40 /7 − 2160B60 , and Bb,δ =360B40 − 3600B60 /7. Note also that B60 term
appears in this case. In the present calculations, we treat B40 and B60 as parameters.
The matrix element of the Coulomb interaction is expressed by I. Here we do notshow the list for the explicit forms of I, butthey are expressed with the use of four SlaterCondon parameters, F 0 , F 2 , F 4 , and F 6 . Although the Slater-Condon parameters of a material should be determined from experimental results, here we simply set the ratio as
F 0 /10 = F 2 /5 = F 4 /3 = F 6 = U , where U is
the Hund’s rule interaction among f orbitals.
it is reasonable to set U as 1 eV in this research.
In Fig. 1, we show the local CEF ground-215

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

0.01-0.005

G5

-0.01
-0.1

-0.05

B60 [meV]

0.0

U=1.0
l=0.1
W=0.001

G3

x=0.0

Entropy

0.005

x=1.0
G1

0.0
B40 [meV]

0.05

0.1

Figure 1: Local CEF ground-state phase diagram on the plane of (B40 , B60 ) for n = 2.
The line is given by B40 = W x/15 and B60 =W (1 − |x|)/180 with W = 10−3 .
state phase diagram for n = 2, obtained fromthe diagonalization of Hloc . For n = 2, theground-state multiplet for B40 = B60 = 0
is characterized by total angular momentum
J = 4. Under the cubic CEF potentials, thenonet of J = 4 is split into four groups as Γ1singlet, Γ3 doublet, Γ4 triplet, and Γ5 triplet.
Among them, Γ4 triplet does not appear as asolo ground state under the cubic CEF potential with Oh symmetry.
Now we include the Γ7 and Γ8 conduction
electron bands. Here we consider only the hybridization between conduction and j = 5/2
electrons. The Hamiltonian is given byH =∑εkc†kµτckµτ +k,µ,τ

+ Hloc ,∑Vµ(c†kµτ faγτ +h.c.)

k,µ,τ

(2)

where εk is the dispersion of conduction electron with wave vector k, ckγτ is an annihilation operator of conduction electrons, and Vµdenotes the hybridization between f electronin the µ orbital and conduction electron of theµ band. Here we set Vα = Vβ = Vγ = V .
In this research, we analyze this model by
employing the NRG method [1]. We introduce
a cut-oﬀ Λ for the logarithmic discretizationof the conduction band. Due to the limitationof computer resources, we keep M low-energy

2
x=0.0
U=1.0
1.8
x=0.18715
1.6
l=0.1
x=1.0
1.4
W=0.001
1.2
V=0.6
L=8.0
1
M=5000
0.8
0.6
log f
0.4
0.5log 2
0.2
0 -10 -9 -8 -7 -6 -5 -4 -3 -2 -1 0
10 10 10 10 10 10 10 10 10 10 10
Temperature T [eV]

Figure 2: Entropies vs. temperature for x = 0,0.18715, and 1 with W = 10−3 .
states. Here we use Λ = 8 and M = 5, 000.
Note that the temperature T is defined as T =DΛ−(N −1)/2 in the NRG calculation, where N
is the number of the renormalization step andD is a half of conduction band width. Here we
set D = 1 eV.
In Fig. 2, we show the calculation resultsfor entropies, when we change the local CEF
states from Γ3 doublet (x = 0) to Γ1 singlet(x = 1) on the line in Fig. 1. For x = 0,
we find an entropy of 0.5 log 2 at low temperatures, indicating the two-channel Kondo state(non-Fermi-liquid phase), while for x = 1,
we obtain the CEF singlet state (Fermi-liquid
phase). After repeating the NRG calculations,at x = 0.18715, we find an entropy plateau of√log ϕ with ϕ = ( 5 + 1)/2. This is the sameas the residual entropy for the three-channel
Kondo eﬀect. We consider that the entropy
log ϕ suggests the emergence of QCP between
non-Fermi-liquid and Fermi-liquid phases. Details will be discussed elsewhere in future [2].

References[1] H. R. Krishna-murthy, J. W. Wilkins, andK. G. Wilson, Phys. Rev. B 21, 1003
(1980).
[2] T. Hotta, in preparation.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Research of Two-Channel Kondo Eﬀect
in Transuranium Systems
Dai MATSUI and Takashi HOTTA
Department of Physics, Tokyo Metropolitan University
1-1 Minami-Osawa, Hachioji, Tokyo 192-0397

On the basis of the electron-hole relation
between f 2 and f 4 states in a j-j coupling
scheme, we hit upon an idea that two-channel
Kondo phenomena can be observed even in cubic transuranium compounds including Np and
Pu ions with local Γ3 non-Kramers doublet
ground state. To clarify this point, we analyze a seven-orbital impurity Anderson modelhybridized with degenerate Γ8 conduction electron bands by employing a numerical renormalization group (NRG) method [1].
The model Hamiltonian is given byH =∑εk c†kµτ ckµτ +

k,µ,τ

+

∑

∑

V (c†kµτ faµτ + h.c.)

k,µ,τ

†
fjµτ
(λj + Bj,µ + Ef )fjµτ

j,µ,τ

+

∑ ∑ ∑

j1∼j4 µ1∼µ4 τ1∼τ4

Iµj11jτ21,jµ32jτ42 ,µ3 τ3 µ4 τ4(1)

× fj†1 µ1 τ1fj†2 µ2 τ2fj3 µ3 τ3fj4 µ4 τ4 ,where εk denotes the energy of Γ8 conduction electron with wave vector k, ckµτ indicates the annihilation operator of Γ8 conduction electron, µ distinguishes the cubic irreducible representation, Γ8 states are distinguished by µ = α and β, while Γ7 and Γ6 states
are labeled by µ = γ and δ, respectively, τ isthe pseudo-spin which distinguishes the degeneracy concerning the time-reversal symmetry,
V is the hybridization between conduction andlocalized electrons, fjµτ indicates the annihilation operator of a localized f electron in thebases of (j, µ, τ ), j is the total angular momentum, j = 5/2 and 7/2 are denoted by “a”
and “b”, respectively, and Ef is the f -electronlevel to control the local f -electron number at
an impurity site. In the present case, we consider the hybridization between Γ8 conduction
electrons and the Γ8 quartet of j = 5/2.
As for the spin-orbit coupling term, we obtain λa = −2λ and λb = (3/2)λ, where λis the spin-orbit coupling of f electron. The
magnitude of λ depends on the kind of actinide atoms, but in this research, we set
λ = 0.3 eV, since we consider Np and Pu
ions. Concerning the CEF potential term for
j = 5/2, we obtain Ba,α = Ba,β = 1320B40 /7
and Ba,γ = −2640B40 /7, where B40 denotes
the fourth-order CEF parameter for the angular momentum ℓ = 3. Note that the sixthorder CEF potential term B60 does not appear
for j = 5/2, since the maximum size of thechange of the total angular momentum is lessthan six. On the other hand, for j = 7/2,
we obtain Bb,α = Bb,β = 360B40 /7 + 2880B60 ,Bb,γ = −3240B40 /7 − 2160B60 , and Bb,δ =360B40 − 3600B60 /7. Note also that B60 terms
appear in this case. In the present calculations,
we treat B40 and B60 as parameters.
The matrix element of the Coulomb interaction is expressed by I. To save space, we donot show the explicit forms of I here, but they
are expressed by four Slater-Condon parameters (F 0 , F 2 , F 4 , F 6 ) and Gaunt coeﬃcients.
As for the magnitudes of Slater-Condon parameters, first we set F 0 = 10 eV by hand.
Others are determined so as to reproduce excitation spectra of U4+ ion with two 5f electrons. The results are F 2 = 6.4 eV, F 4 = 5.6

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: Color contour map of the entropy
for n = 4 on the plane of (B40 , B60 ) for V =1.0
and T = 2.6 × 10−6 . White curves denote theboundaries among local CEF ground states.
eV, and F 6 = 4.1 eV [2].
In this research, we analyze the model by
employing the NRG method [3]. We introduce
a cut-oﬀ Λ for the logarithmic discretizationof the conduction band. Due to the limitationof computer resources, we keep M low-energy
states. Here we use Λ = 5 and M = 2, 500.
Note that the temperature T is defined as T =DΛ−(N −1)/2 in the NRG calculation, where N
is the number of the renormalization step andD is a half of conduction band width. We set
D = 1 eV in this research.
In Fig. 1, we show the contour color mapof the entropy on the plane of (B40 , B60 ) for
V = 1.0 and T = 2.6 × 10−6 . To visualize
precisely the behavior of entropy, we define
the color of the entropy between 0 and 1.5,
as shown in the right color bar. Note that thegreen and yellow regions indicate the entropyof log 2 and 0.5 log 2, respectively. We immediately notice that a region with an entropyof 0.5 log 2 (yellow region) almost corresponds
to that of the Γ3 CEF ground state. Notethat for large B60 , the color becomes green,
but when we decrease the temperature, wefind the entropy of 0.5 log 2 even for large B60 .
The results strongly suggest the emergence of
quadrupole two-channel Kondo eﬀect for thecase of n = 4. Note that in the present model,
we have observed the discontinuous change inentropy behavior between yellow (Γ3 ) and red(Γ1 or Γ5 ) regions. Quantum critical behavior which may occur between non-Fermi-liquid
and Fermi-liquid phases will be discussed elsewhere in future.
Here we remark that there exists a blue
region corresponding to log 3 in the local Γ5state. This is quite natural, since the local Γ5state is triply degenerate. The Γ5 moment isscreened by Γ8 conduction electrons and thus,
it is expected that the conventional Kondo effect occurs in the Γ5 region, although the magnitude of the Kondo temperature significantly
depends on the hybridization and excitationenergy.
Note also that in the region of B60 < 0,
we observe some blurry yellow spots along theboundary curve between Γ1 singlet and Γ5
triplet local ground states. The QCP is known
to appear between the CEF and Kondo singlet
states for n = 2 [4]. Thus, we deduce thatthose spots form a QCP curve, although we
could not obtain enough amounts of numericalresults to depict the smooth curve here.
Finally, we provide a brief comment on
actual materials to observe the two-channel
Kondo eﬀect for the case of n = 4. In rareearth ions, the case of n = 4 corresponds toPm3+ , but unfortunately, there exist no stable
isotopes for Pm. Thus, we turn our attention
to actinide ions such as Np3+ and Pu4+ with
5f 4 configurations. It may be diﬃcult to synthesize new Np and Pu compounds, but we
expect that Np 1-2-20 compound will be synthesized in future.

References[1] D. Matsui and T. Hotta, JPS Conf. Proc.
30, 011125 (2020).
[2] T. Hotta, Phys. Rev. B 80, 024408 (2009).
[3] H. R. Krishna-murthy, J. W. Wilkins, andK. G. Wilson, Phys. Rev. B 21, 1003
(1980).
[4] T. Hotta, Physica B 536, 203 (2018).

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles and quantum many-body calculations
for electronic states and superconductivity in themulti-band systems
Yoshiaki Ōno
Department of Physics, Niigata University
Ikarashi, Nishi-ku, Niigata, 950-2181

Tungsten bronzes Ax WO3 (A=Na, K, Rb,
Cs) are known to show the superconductivity for 0.15 < x < 0.35, where the superconducting transition temperature Tc is found toincrease rapidly with decreasing x up to 7K.
In addition, at further low doping x ∼ 0.05,
remarkable high-Tc superconductivities are reported at Tc =91K for A=Na and Tc =120K for
A=H. The systems also show rich structuralphases such as cubic for x > 0.4, tetragonal
for 0.1 < x < 0.4, orthorhombic for 0.03 <x < 0.1 and monoclinic for x < 0.03, which are
well accounted for by the first-principles calculations. However, the superconductivity inwhich the structural phases and those transitions are considered to play important roles fordetermining Tc was not discussed there. The
purpose of this work is to study the superconductivity in Ax WO3 on the basis of the firstprinciples calculation and to discuss the eﬀectof the ferro-orbital fluctuation which is foundto be largely enhanced around the structuralphase transition and is expected to induce thepairing interaction as previously discussed in
the iron-based superconductivity.
We calculate Tc on the basis of thefirst-principles calculation by using Quantum
ESPRESSO and find that the x dependenceof Tc is qualitatively consistent with the experiments. The significant x dependence of Tc
is mainly due to that of the electron-phonon
coupling constant λ which decreases with increasing x because of the screening eﬀect as

discussed by several authors. However, thecalculated value of Tc is considerably smaller
than the experimental values, and hence thepairing interaction mediated by the electronic
fluctuation such as the orbital fluctuation is expected to be responsible for the pairing mechanism in addition to the BCS phonon mechanism which is exclusively taken into account in
the present first-principles calculation. Then,
we also calculate the pairing interaction on thebasis of the eﬀective three band model consistsof W-t2g orbitals by taking into account of the
Jahn-Teller electron-phonon coupling within
the random phase approximation and find thatthe pairing interaction is largely enhanced dueto the ferro-orbital fluctuation which becomeslarge around the structural phase transition[1].
Recently, the Pr 1-2-20 systems PrT2 X20
have been intensively investigated concerning
their specific features including quadrupoleorders, superconductivity and non-Fermi liquid behaviors. The crystalline electric field
ground states of the Pr ions are the nonKramers doublets Γ23 which have the electric
quadrupole moments with no magnetic moment. In fact, PrTi2 Al20 and PrV2 Al20 exhibit
the ferro-quadrupole (FQ) and the antiferroquadrupole (AFQ) orders, respectively. They
also show remarkable superconductivities coexisting with the quadrupole orders. To discuss the quadrupole order and the superconductivity, the details of the energy bands andthe Fermi surfaces are important. In the Pr

219

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1-2-20 systems, the de Haas-van Alphen experiments revealed that the Fermi surfaces
are well accounted for by the first-principles
band calculations for the corresponding La 12-20 systems, indicating that the Pr 4f electrons are suﬃciently localized. Therefore, thequadrupole orders are considered due to the
Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between the quadrupole moments of
the localized Pr 4f electrons. The purpose ofthis study is to evaluate the RKKY interaction
on the basis of the realistic energy band structure extracted from the first-principles calculation and to discuss the quadrupole orders in
PrTi2 Al20 and PrV2 Al20 .
We perform the first-principles calculations
for LaT2 Al20 (T =Ti, V) by using WIEN2k
code where we also employ the GGA+U
method with U = 60eV to exclude the La4f components near the Fermi level. The obtained Fermi surfaces of LaTi2 Al20 are in good
agreement with those in the previous study.
Then, we construct the tight-binding modelfor the conduction electrons so as to reproduce the electronic structure near the Fermi
level by using the maximally localized Wannierfunctions which consist of 196 orbitals: La-d(5 orbitals × 2 sites), La-s (1 orbital times 2
sites), T-d (5 orbitals × 4 sites), T-s (1 orbital × 4 sites), Al-p (3 orbitals × 40 sites
and Al-s (1 orbital × 40 sites) in the conventional unit cell. Based on the eﬀective model,
we calculate the quadrupole susceptibility of
the conduction electrons and then evaluate the
RKKY interaction mediated by the conductions. The obtained results indicate that thewave vectors of the expected quadrupole orders are Q = (0, 0, 0) (FQ) for PrTi2 Al20 and
Q = (π/a, π/a, 0) (AFQ) for PrV2 Al20 , respectively, as consistent with the experiments[2].
Quasicrystals first discovered by Shechtman
et al. in Al-Mg alloy have been extensively
investigated as they show various anomalous properties due to their specific structures
which are not periodic but have kinds of trans-

lational orders with the 5-fold (8-, 10- and 12fold) rotational symmetry. Recently, the bulk
superconductivity at a transition temperature
Tc ∼ 0.05K has been discovered by Kamiya
et al. in the Al-Mg-Zn quasicrystal and its
approximant, where the basic cluster is considered to be the Bergman-type cluster, andhas attracted much attention for its symmetry
and pairing mechanism.
As for the theoretical study, the Al30 Mg40 Zn30 1/1 approximant was previously studied on the basis of
the first-principles calculation and the originof the pseudo gap near the Fermi level was discussed. However, the electronic state with thecomposition ratio corresponding to the superconducting compound was not discussed there.
Then, we perform the first-principles calculations (OpenMX code) for the Al-Mg-Zn 1/1
approximants with various composition ratios
including the superconducting one and findthat the over-all structure of the density ofstates seems to be almost independent of thecomposition ratio but the energy band dispersions near the Fermi level and the Fermi
surfaces are largely dependent on the composition ratio. On the basis of the obtained
electronic states, we also discuss the possiblesuperconductivity[3].

References[1] Takuya Sekikawa, Rai Watabe, Jun
Ishizuka, Yoshihiro Nitta, Kazuhiro Sanoand Yoshiaki Ōno, JPS Conf. Proc. 30,
011043 (2020).
[2] Yuto Iizuka, Takemi Yamada, Katsurou
Hanzawa and Yoshiaki Ōno, JPS Conf.
Proc. 30, 011152 (2020).
[3] Masaki Saito, Takuya Sekikawa andYoshiaki Ōno, 14th International Conference on the Structure of Non-Crystalline
Materials (NCM14).

220

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Search for new types of skyrmion crystals based on
point group symmetry
Satoru Hayami
Department of Applied Physics, The University of Tokyo, Tokyo 113-8656

Multiple-Q magnetic states, which are characterized as a superposition of diﬀerent wave
vectors, open a new path toward applications
to next-generation electronics and spintronics
device in condensed matter physics. Amongst
them, the superposition of spiral states gives
rise to unconventional noncollinear and noncoplanar magnetic textures, such as the magnetic vortex crystal and magnetic skyrmion
crystal, which become a source of unconventional topological excitations and transport
properties [1]. Especially, since the discoveryof the magnetic skyrmions in noncentrosymmetric magnets, their studies have been extensively done in both theory and experiments.
Meanwhile, recent theoretical studies pointout the emergence of the skyrmion crystals incentrosymmetric Mott insulators. They arestabilized by taking into account various factors, such as frustrated exchange interactions
and thermal fluctuations [2, 3, 4, 5]. Moreover,another interesting situation is brought by considering the interplay between itinerant electrons and localized spins. There, eﬀective longranged interactions mediated through itinerant electrons play an important role in stabilizing the skyrmion and vortex crystals [6, 7, 8],
which might provide a deep understanding of
the microscopic mechanism of the multiple-Q
skyrmion, vortex, and hedgehog crystals foundin d- and f -electron materials.
In this project, we investigate the skyrmion
physic in itinerant magnets by considering
an anisotropic magnetic interaction [9]. We
start from the Kondo lattice model with221

the anisotropic xxz-type spin-charge coupling.
The Hamiltonian is represented by
H = −

∑

tij c†iσ cjσ + Jz

i,j,σ

+ Jxy

∑

i,σ,σ ′∑
i,σ,σ ′zz †σσσ
′ Si ciσ ciσ ′

y
y †
x
x
(σσσ
′ Si + σ
σσ ′ Si )ciσ ciσ ′ , (1)where c†iσ and ciσ are creation and annihilation operators of an itinerant electron at sitei and spin σ, respectively. The first term represents the hopping of itinerant electrons andthe second and third terms denote the spincharge coupling where |Si | = 1 and σ is thePauli matrix. Jxy and Jz are the anisotropic
coupling constants for xy and z spin components, respectively.
We derive an eﬀective spin model in Eq. (1)by assuming (i) the weak-coupling regime for
Jxy , Jz ≪ W (W is the bandwidth) and (ii)the multiple peak structures of the bare magnetic susceptibility. Then, the spin model isobtained as
H = −2∑

˜ Q + K̃Γ2Q ),
(JΓ
ν
ν

(2)

ν=1−3

√
x Sx
where ΓQν=
1 − A2 (SQ
+
ν −Qν
y
y
z
z
SQν S−Qν ) + ASQν S−Qν .
We adopt a
triangular lattice with six peaks in thebare susceptibility:±Q1 = ±(π/3, 0),√±Q2 = ±(−π/6, 3π/6), and ±Q3 =√±(−π/6, − 3π/6). The first term represents
the bilinear interaction with J˜ = 1 andthe second term represents the biquadraticinteraction with the positive coupling constant K̃ = K/N > 0 (N is the numberof spins). The former originates from theActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
(a)

(b)

(c)

(d)

Figure 1: Snapshots of the spin configurations (see the text). The arrows represent the xy
component and the contour shows the z component of the spin moment.

second-order perturbation, while the latter
arises from the fourth-order perturbation.
The magnetic anisotropy is represented by√
A; 0 ≤ A < 1/ 2 for the easy-axis interac√tion and 1/ 2 < A ≤ 1 for the easy-planeinteraction.
The magnetic phase diagram of the eﬀective
spin model in Eq. (2) is investigated by performing simulated annealing from high temperature. We apply the Metropolis local updates under periodic boundary conditions inboth directions for the 962 spins. To find the
optimal spin configurations, we gradually reduce the temperature with the rate Tn+1 =αTn , where Tn is the temperature in the nth
step. We start from the initial temperature
T0 = 10−1 -100 . We typically set α ∼ 0.99999
and the final temperature T = 10−4 -10−3 .
As a result, we find several magnetic ordered states with a net scalar chirality including the skyrmion and vortex crystals by constructing the ground-state phase diagram ina wide range of model parameters. We showthat two types of the skyrmion crystal phaseswith the topological number of two are realized for large K: one is identified as the superposition of the magnetic vortex structuresin the xy spin component and the sinusoidal
wave in the z spin component [Fig. 1(a)] andthe other is denoted as the bubble-type magnetic configurations satisfying the sixfold rotational symmetry in both xy and z spin components [Fig. 1(b)]. We also find a triple-Q

222

state with a finite net scalar chirality, which
is diﬀerent from the skyrmion crystal by increasing the easy-plane anisotropic interaction[Fig. 1(c)]. Moreover, we find that the strong
easy-axis anisotropic interaction gives rise to
the triple-Q magnetic bubble crystal with thecollinear z spin component [Fig. 1(d)].

References[1] N. Nagaosa, Y. Tokura, Nat. Nanotech.
8 (12) (2013) 899–911.
[2] T. Okubo, S. Chung, H. Kawamura, Phys.
Rev. Lett. 108 (2012) 017206.
[3] A. O. Leonov, M. Mostovoy, Nat. Commun. 6 (2015) 8275.
[4] S.-Z. Lin, S. Hayami, Phys. Rev. B 93
(2016) 064430.
[5] S. Hayami, S.-Z. Lin, C. D. Batista, Phys.
Rev. B 93 (2016) 184413.
[6] Y. Akagi, M. Udagawa, Y. Motome, Phys.
Rev. Lett. 108 (2012) 096401.
[7] R. Ozawa, S. Hayami, K. Barros, G.W. Chern, Y. Motome, C. D. Batista, J.
Phys. Soc. Jpn. 85 (10) (2016) 103703.
[8] S. Hayami, R. Ozawa, Y. Motome, Phys.
Rev. B 95 (2017) 224424.
[9] S. Hayami, submitted.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Multipole and anisotropic superconductivity fromfirst-principles
Jun Ishizuka
Department of Physics, Graduate School of Science, Kyoto University,
Kyoto 606-8502, Japan

Recently discovered heavy fermion superconductor UTe2 [1], as a member of the ferromagnetic

and three two-dimensional Z2 numbers by Fermi
surface formulas [9, 10, 11]:superconductors [2, 3], provides a new platform toω=study the spin-triplet superconductivity. The spin-

1X
n(Ki )
2(mod 2).

(1)

Ki

triplet state in UTe2 is supported by various exper-

The GGA+U Fermi surfaces indicate topologicalimental results: large upper critical field Hc2 alongsuperconductivity for the reasonable values of U ,the three principal axes [1, 4], reentrant supercon-

and accompanied surface states are provided. We

ductivity under magnetic field along b axis [5], andalso predict the superconducting gap node at zero

the temperature dependence of the Knight shift inmagnetic field and under magnetic field along b

superconducting state [6].

axis. Based on these results, we proposed multiple
study

superconducting phases under the magnetic field.

[7].

Our another aim of this project is to study the

Theoretically, a band structure has been investi-

exotic phenomena due to the spatial inversion sym-

gated for UTe2 from first-principles [4]. However,metry breaking. Recently, it was found that thepreviously obtained result shows insulating state

noncentrosymmetric Nb/V/Ta superlattice showswith an extremely small gap, incompatible withsuperconducting transition at 4.4 K [12] and ex-

superconducting instability.

To overcome thishibits nonreciprocal charge transport in supercon-

program, we perform a GGA+U calculation using

ducting state. To identify the Rashba spin-orbit

WIEN 2k package [8] and find the insulator-metalinteraction in the artificial superlattice [Nb/V/Ta]ntransition by Coulomb interaction. The insulator-

without a center of inversion, we carried out den-metal transition is characterized by multi-orbitalsity functional theory calculations using WIEN2k

effect in Kondo lattice system.

The insulator-

package [8]. We created a slab [Nb/V/Ta]5 con-metal transition is a peculiar property of UTe2 ,taining 30 atoms, which corresponds to the fivewhich was not observed in other uranium-based

times stacking of two layers Nb, V, and Ta of asuperconductors nor in Kondo insulators. We canbcc structure. We obtained the Rashba splitting at

identify the three-dimensional winding number ω

the Fermi level, and the magnitude of the Rashba

In

this

anisotropic

project,

wetheoreticallysuperconductivity

in

UTe2

223

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

splitting is around 10 meV, which originate from

[8] P. Blaha, K. Schwarz, G. K. H. Mad-V atoms and is the origin of the nonreciprocity.

sen, D. Kvasnicka, J. Luitz, R. Laskowski,
F. Tran, and L. D. Marks, WIEN2k, An Augmented Plane Wave+Local Orbitals Program

References

for Calculating Crystal Properties (Karl[1] S. Ran, C. Eckberg, Q.-P. Ding, Y. Furukawa,heinz Schwarz, Techn. Universität, Wien,

T. Metz, S. R. Saha, I.-L. Liu, M. Zic,
H. Kim, J. Paglione, and N. P. Butch, Science
365, 684 (2019).

Austria, 2018).
[9] M. Sato, Phys. Rev. B 79, 214526 (2009).
[10] M. Sato, Phys. Rev. B 81, 220504(R) (2010).

[2] D. Aoki and J. Flouquet, J. Phys. Soc. Jpn.
83, 061011 (2014).

[11] L. Fu and E. Berg, Phys. Rev. Lett. 105,
097001 (2010).

[3] D. Aoki, K. Ishida, and J. Flouquet, J. Phys.
Soc. Jpn. 88, 022001 (2019).

[12] F. Ando, D. Kan, Y. Shiota, T. Moriyama,
Y. Shimakawa, T. Ono J. Magn. Soc. Japan[4] D. Aoki, A. Nakamura, F. Honda, D. Li,

43, 17-20 (2019).

Y. Homma, Y. Shimizu, Y. J. Sato, G. Knebel,
J.-P. Brison, A. Pourret, D. Braithwaite,
G. Lapertot, Q. Niu, M. Vališka, H. Harima,
and J. Flouquet, J. Phys. Soc. Jpn. 88, 043702(2019).
[5] G. Knebel, W. Knafo, A. Pourret, Q. Niu,
M. Vališka, D. Braithwaite, G. Lapertot, M. Nardone, A. Zitouni, S. Mishra,
I. Sheikin, G. Seyfarth, J.-P. Brison, D. Aoki,
and J. Flouquet, J. Phys. Soc. Jpn. 88, 063707(2019).
[6] G. Nakamine, S. Kitagawa, K. Ishida,
Y. Tokunaga, H. Sakai, S. Kambe, A. Nakamura, Y. Shimizu, Y. Homma, D. Li,
F. Honda, and D. Aoki, J. Phys. Soc. Jpn. 88,
113703 (2019).
[7] J. Ishizuka, S. Sumita, A. Daido, andY. Yanase: Phys. Rev. Lett. 123, 217001(2019).

224

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development and applications of continuous-timequantum Monte Carlo method in the thermodynamic limit
Takahiro OHGOE
Research Institute for Science and Engineering,
Waseda University, Okubo, Shinjuku-ku, Tokyo 169-8555
Quantum Monte Carlo methods are power

reach the 11th order in shorter CPU time bytools for investigating quantum many-bodyusing the CDet code. Furthermore, we alsosystems. However, they often offer from theobtained some results of density and Tan’snotorious negative-sign problem for fermioniccontact for imbalanced cases where thesystems and frustrated spin systems when theconventional quantum Monte Carlo method

system-size is increased. Recently, a novel

suffers from the negative-sign problem. The

determinant quantum Monte Carlo method wasdeveloped code will be useful for revealing

proposed,thefascinating physics such as FFLO or p-wave

thermodynamic limit [1]. The method is calledsuperconducting instability which are expectedconnected determinant Monte Carlo method

in imbalanced populations. This work was done

(CDet), and its applications to the Hubbard

in collaboration with Riccardo Rossi (Flatiron

model revealed non-trivial analytic structure of

institute), Felix Werner and Kris Van Houcke

the self-energy in strongly-correlated regime [2].

(ENS, Paris).

which

is

formulatedin

Therefore, it is a promising method for tacklingchallenging problems of quantum many-bodyReferences

systems.

[1] R. Rossi: Phys. Rev. Lett. 119 (2017) 045701

Here, we developed the original CDet code[2] F. Simkovic IV. and E. Kozik, Phys. Rev. B

which is applicable to the two-component

100 (2019) 121102

unitary Fermi gas. To show its advantage, the[3] R. Rossi, T. Ohgoe, K. Van Houcke, and F.

method was compared with the diagrammatic

Werner: Phys. Rev. Lett. 121 (2018) 130405

Monte Carlo method in the case of balanced[4] R. Rossi, T. Ohgoe, E. Kozik, N. Prokof’ev

population [3,4]. In the diagrammatic Monteand B. Svistunov, K. Van Houcke, and F.

Carlo method, the maximum expansion order

Werner: Phys. Rev. Lett. 121 (2018) 130406

which we could reach was 9, whereas we could

225

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Kitaev spin liquid under time-dependent magnetic
field
Joji NASU
Department of Physics, Yokohama National University
Hodogaya, Yokohama 240-8501

Nonequilibrium phenomena in insulating
magnets such as real-time dynamics of magnetization and transport of spin excitations haveattracted considerable attention in condensed
matter physics. In the insulating magnets,
spin excitations are carried by magnons in thepresence of a magnetic order. On the other
hand, it was suggested that the spin transport
can be also governed by spinons, which are elementary excitations fractionalized from spins
in one-dimensional Heisenberg systems. Thiswas confirmed in the cuprate Sr2 CuO3 by thespin Seebeck experiments under the magnetic
field.
The Kitaev quantum spin model is anothercandidate of the magnetic systems associatedwith fractional quasiparticles. In this model,
the ground state is exactly shown to be a quantum spin liquid and the elementary excitations
are described by two kinds of quasiparticles:
itinerant and localized Majorana fermions. In
this work, we study spin dynamics under thetime dependent magnetic field to clarify therole of the fractional quasiparticles for thenonequilibrium phenomena.
Here, we examine the the real-time dynamics of the spin moments in the Kitaev model
under the time-dependent magnetic field. In
particular, we investigate the following twocases by using the Majorana mean-field theory.
First, 1) we study the eﬀect of the field quenchof the uniform magnetic field to understandfundamental properties of nonequilibrium dynamics of the fractional quasiparticles in the

Kitaev model. Next, 2) we consider the eﬀectof the time-dependent magnetic field pulse at
the edge of the cluster to mimic the spin injection into the Kitaev magnet.
With respect to 1), we find that two kindsof Majorana fermions are observed separately
in distinct time-scales in the time evolutionof the magnetization; the low-energy localized
Majorana fermions survive as long-lived excitations whereas the high-energy itinerant ones
are damped in the early stage [3].
With respect to 2), we find that the propagation of the spin excitations occurs even in
the absence of the magnetic field in the bulk
without spin polarization. We clarified that
this is attributed to the itinerant Majorana
fermions [2]. We also discuss the eﬀect of the
Heisenberg interaction and extension to theS = 1 Kitaev model [3] on this phenomenon.

References[1] J. Nasu, and Y. Motome: Phys. Rev. Research 1, 033007-1-16 (2019).
[2] T. Minakawa, Y. Murakami, A. Koga, and
J. Nasu: arXiv:1912.10599.
[3] A. Koga, T. Minakawa, Y. Murakami, and
J. Nasu: J. Phys. Soc. Jpn. 89, 033701-1-4(2020).

226

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetocaloric eﬀect on the Shastry–Sutherland
lattice antiferromagnet SrCu2(BO3)2
Subaru AKIMOTO and Yasuhiro H. MATSUDA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

We have studied the magnetocaloric eﬀect(MCE) of the Shastry–Sutherland (SS) lattice
antiferromagnet SrCu2 (BO3 )2 [1] with numerical simulations using the thermal pure quantum (TPQ) state. We used the HΦ as a numerical solver. The magnetic field dependence ofthe entropy (SM ) and specific heat (CM ) havebeen computed and compared with those experimentally obtained from the magnetic field
variation of the MCE at diﬀerent initial temperatures. Figures 1 (a) and (b) show the calculated SM and CM . The five trial curves andthe averaged result are shown for the SM and
CM , respectively.

SS lattice such as 1/4 and 1/3 plateaux [2].
The computed B–T (magnetic field – temperature) phase diagram shown in Fig. 2 is found tosemiquantitatively reproduce the experimental
results.

Figure 2: The calculated SM are plotted ina B–T plane with color graduation. Several
isentropic curves are also plotted.

Figure 1: The five trial curves and the averaged result of the calculation with TPQ state
are shown. The magnetic field is set to be 57 T
corresponding to the 1/3 plateau. (a) Calculated SM . (b) Calculated CM .

References

The distinct peak is shown in the temperature dependence of the CM at a magnetic field
and the peak positions at diﬀerent temperatures and magnetic fields would give the phaseboundaries of the quantum spin states of the[2] Y. H. Matsuda, N. Abe, S. Takeyama, H.
Kageyama, P. Corboz, A. Honecker, S. R.
Manmana, G. R. Foltin, K. P. Schmidt,
and F. Mila: Phys. Rev. Lett. 111 (2013)
137204.

[1] H. Kageyama, K. Yoshimura, R. Stern, N.
V. Mushnikov, K. Onizuka, M. Kato, K.
Kosuge, C. P. Slichter, T. Goto, and Y.
Ueda: Phys. Rev. Lett. 82 (1999) 3168.

227

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Spin-Charge Separation in Charge Order Phase of
Organic Dirac Electron System α-(BEDT-TTF)2I3
Akito KOBAYASHI
Department of Physics, Nagoya University
Nagoya 464-8602

The organic Dirac electron system α(BEDT-TTF)2 I3 ehibits a phase transition between a massless Dirac electron phase and acharge-ordered phase under pressure as shownin Fig. 1. In the charge-ordered phase, thespin gap measured by NMR, the optical gap
in the optical conductivity, and the resistancegap determined by the DC resistance showcompletely diﬀerent values and pressure dependences. The mechanism of this novel spincharge separation has not been elucidated yet.
We have theoretically studied the mechanismof the spin-charge separation in α-(BEDTTTF)2 I3 .

tions by H. Kino and T. Tsumuraya. This factstrongly suggests that the type-I Dirac electronic state observed under hydrostatic pressure cannot be explained without the strong
correlation eﬀect. We will study the type-I
Dirac electronic state under hydrostatic pressure using the variational Monte Carlo method
in cooperation with Dr. Yoshimi of ISSP, andthen elucidate the mechanism of spin charge
separation of charge-ordered phase.

First, we have investigated the Dirac electron system with charge order in α-(BEDTTTF)2 I3 using the real-space-dependent meanfield approximation, and have shown that
there is a domain wall of the charge order thatspontaneously appears due to ferroelectricity.
We have shown that the wall-bound Dirac electrons form a one-dimensional conduction channel. Furthermore, we have shown that the linear response theory can explain the large difference between the optical gap and the resistivity gap[1].
Next, we have performed the first principles
calculation for α-(BEDT-TTF)2 I3 under hydrostatic pressure using Quantum ESPRESSO
in the Supercomputer Center, the ISSP. However, the result exhibits a type-II Diracsemimetal, which is diﬀerent from the experimental results. Similar results have been independently shown by the first-principles calcula-

Figure 1:
TTF)2 I3 .

Phase diagram of α-(BEDT-

References[1] D. Ohki, Y. Omori, and A. Kobayashi,
Phys. Rev. B 100, 075206 (2019).

228

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum Monte Carlo simulation and electronic
state calculations in correlated electron systems
Takashi YANAGISAWA
Electronics and Photonics Research InstituteNational Institute of Advanced Industrial Science and Technology (AIST)
AIST Central 2, 1-1-1 Umezono, Tsukuba 305-8568'!

!"#$%&

!"&

%"#

∆E/N

Our calculations are based on the optimized
variational Monte Carlo method[1, 2, 3, 4]. We
have investigated the ground-state phase diagram of the two-dimensional Hubbard modeland the two-dimensional d-p model. We performed parallel computation in Monte Carlocalculations. In order to reduce statistical errors, we carried out 100 ∼ 200 parallel calculations. Parallel computing is very importantto reduce Monte Carlo statistical errors.

%"&

AFI

&"#

SC
AF
SC

We used the wave function of anexp(−λK) − PG -type wave function. This
wave function is a very good many-body wave
function because the ground-state energy islowered greatly and the ground-state energy
is lower than that evaluated by any otherwave functions[2]. We can improve the wave
function systematically by multiplying by
operators PG and e−λK many times.

We show the phase diagram as a function of
the hole doping rate x in Fig. 1. The calculations were performed on a 10 × 10 lattice with
U/t = 18 and t′ = 0. There are three phases:
the antiferromagnetic insulator state (AFI),
the coexistent state of antiferromagnetism andsuperconductivity (AF+SC) and the d-wave
superonducting state (SC). Near half-filling for
approximatedly 0 ≤ x < 0.06, the ground stateis an AF insulator. The coexistent state exists
for 0.06 < x < 0.09. When the doping rate is
as large as x > 0.09, the ground state is d-wave
superconducting state. High-temperature superconductivity will occur in the SC phase inthis figure.

229

&"&
&"&&

&"&#

&"%&

x

&"%#

&"!&

&"!#

Figure 1:
Phase diagram for the twodimensional Hubbard model. The condensation energy per site as a function of the hole
doping rate x = 1 − ne on a 10 × 10 lattice.
We set t′ = 0 and U/t = 18. AFI indicatesthe antiferromagnetic insulating state and SC
denotes the d-wave SC phase. There is the coexistent state indicated as AF-S between thesestates.

References[1] T. Yanagisawa et al., J. Phys. Soc. Jpn.
67, 3867 (1998).
[2] T. Yanagisawa, J. Phys. Soc. Jpn. 85,
114707 (2016).
[3] T. Yanagisawa, J. Phys. Soc. Jpn. 88,
054702 (2019).
[4] T. Yanagisawa, Condensed Matter 4, 57(2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Dynamical mean-field theory + quantum Monte
Carlo approach to strongly correlated electron
systems with multi-orbitals
Shintaro HOSHINO
Department of Physics, Saitama University, Saitama 338-8570, Japan

We have also mapped out the phase diagramof the doped fulleride, which is also exprimentally realized [1]. To do this, we have analyzed the three-orbital Hubbard model with
antiferromagnetic Hund’s coupling by using
the dynamical mean-field theory. In this theory, the many-body problem in the lattice
is mapped onto the effective impurity problem without spatial periodicity, for which thecontinuous-time quantum Monte Carlo solver[5] has been used. Using the facilities of ISSP
supercomputer, we have calculated the susceptibilities which signal the instability of the normal state toward ordering state with spontaneously broken symmetries. The exemplary

230

0.14

orb. freez.
FO
SC
AFO

D=1, J/U=-0.25, n=1.5

0.12
0.1
T

The electrons with multiple orbital degrees
of freedom show a variety of intruguing phenomena as realized in heavy-electron materials
and also in d-electron systems such as ruthenate and iron-based superconductors. In addition, the fulleride superconductors are another example of the multiorbital electron systems [1], where the three-degenerate t1u molecular orbitals are occupied by electrons originating from alkaline doping. Due to the effectively sign-inverted Hund coupling by JahnTeller phonons, the electrons favor the low-spinstate and show superconductivity at low temperatures. Recently the experimental study
has revealed the existence of anomalous metallic state near the Mott insulator [2], and thepossibility of active orbital degrees of freedom
is pointed out theoretically [3]. The characteristic dynamical structure in the self-energy isidentified and can be a source of the anisotrpic
response function [4].

0.08
0.06
0.04
0.02
0

0

1

2

3

4
U

5

6

7

8

Figure 1: Temperature-interaction phase diagram.
The pahse boundaries for orbital ordering (FO) andsuperconductivity (SC) are shown, together withorbital freezing line.

results at the electron number n = 1.5 permolecule are shown in the figure. Here thephase diagram in the plane of temperature andCoulomb interaction is mapped out, where thehorizontal axis indicates the pressure or lattice constant dependence when one compare
the results with the experiments. We havedemonstrated that the superconductivity appears with dome-shaped transition temperatures, while the orbital ordering dominates atlarge Coulomb repulsive interaction.
References[1] For a review, see O. Gunnarsson, Rev. Mod.
Phys. 69, 575 (1997). [2] R.H. Zadik et al., Sci.
Adv. 1, e1500059 (2015). [3] S. Hoshino and P.
Werner, Phys. Rev. Lett. 118, 177002 (2017). [4]S. Hoshino, P. Werner, and R. Arita, Phys. Rev.
B 99, 235133 (2019). [5] E. Gull et al., Rev. Mod.
Phys. 83, 349 (2011).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Superconductivity and magnetic properties of the
Hubbard model
Atsushi Yamada
Department of Physics, Chiba University
Chiba 263-8522, Japana, Chiba 277-8581

Frustrated magnetic systems yield a rich variety of phenomena. For example, a spin liquidstate, which is a purely non-magnetic Mott insulator without spontaneously broken spatial
or spin symmetry, has attracted a lot of interest. This state is realized in geometrically frustrated systems like the charge organic transfer
salts κ-(BEDT-TTF)2 X[1] and Cs2 CuCl4 .[2] A
simple theoretical model of these compounds isthe Hubbard model on the an-isotropic triangular lattice, and spin liquid state is in fact
found in this model.[3] A spin liquid could
arise also in the intermediate coupling regionof strongly correlated systems between a semimetal and ordered state, because in this casea correlation-driven insulating gap might open
before the system becomes ordered. This possibility might be realized in the half-ﬁlled Hubbard model on the honeycomb lattice.

We have studied the magnetic and metalto-insulator transitions in the half-ﬁlled Hubbard model on the honeycomb lattice by variational cluster approximation using 10-site and16-site clusters as a reference system.[5] Thisapproach uses an exact diagonalization of the
Hubbard model deﬁned on these clusters andparts of numerical calculations were done using the computer facilities of the ISSP.Our results agree with recent large scale Quantum
Monte Carlo simulations.[4] We are currently
studying the eﬀect of the frustration on various
physically measurable quantities in the Hubbard model on the 51 -depleted square lattice.

References[1] Y. Shimizu, K. Miyagawa, K. Kanoda,
M. Maesato, and G. Saito, Phys. Rev.
Lett. 91, 107001 (2003); Y. Kurosaki, Y.
Shimizu, K. Miyagawa, K. Kanoda, and
G. Saito, Phys. Rev. Lett. 95, 177001(2005).
[2] R. Coldea, D.A. Tennant, A.M. Tsvelik,
and Z. Tylczynski, Phys. Rev. Lett. 86,
1335 (2001); R. Coldea, D.A. Tennant,and Z. Tylczynski, Phys. Rev. Lett. 68,
134424 (2003).
[3] T. Yoshioka, A. Koga, and N. Kawakami,
Phys. Rev. Lett. 103, 036401 (2009); P.
Sahebsara and D. Sénéchal, Phys. Rev.
Lett. 100, 136402 (2008); L.F. Tocchio,
H. Feldner, F. Becca, R. Valenti, and C.
Gros, Phys. Rev. B 87, 035143 (2013); A.
Yamada, Phys. Rev. B 89, 195108 (2014);
L.F. Tocchio, C. Gros, R. Valentı́, F.
Becca, Phys. Rev. B 89, 235107 (2014); A.
Yamada, Phys. Rev. B 90, 235138 (2014).
[4] S. Sorella, Y. Otsuka, and S. Yunoki, Sci.
Rep. 2, 992 (2012); F. F. Assaad andI. F. Herbut, Phys. Rev. X 3, 031010(2013); F. Parisen Toldin, M. Hohenadler,
F. F. Assaad, and I. F. Herbut, Phys. Rev.
B 91, 165108 (2015).
[5] A. Yamada, Int. J. Mod. Phys. B 30,
1650158 (2016).

231

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Exploring low-rank tensor representation of
Matsubara Green’s functions
Hiroshi SHINAOKA
Department of Physics, Saitama University,
Saitama 338-8570

We have studied a low-rank representationof two-particle Green’s functions [1]. Twoparticle Green’s functions and the vertex functions play a critical role in theoretical frameworks for describing strongly correlated electron systems. However, numerical calculations at the two-particle level often suffer fromlarge computation time and massive memory
consumption. Example includes parquet approximation and diagrammatic non-local extensions of dynamical mean-field theory. For
example, a simulation for the single-band twodimensional Hubbard model based on the parquet approximation requires more than a TB
of memory even at a high temperature.
Thus, a compact representation of two-particle
Green’s functions is highly desired.
In Ref. [1], we introduced a sparse sampling
scheme in the Matsubara frequency domain as
well as a tensor network representation for twoparticle Green’s functions. The sparse sampling is based on the intermediate representation basis [2, 3, 4] and allows an accurate extraction of the generalized susceptibility froma reduced set of Matsubara frequencies. The
tensor network representation provides a system independent way to compress the information carried by two-particle Green’s functions.
We used System B at the ISSP supercomputer center to demonstrate efficiency of thepresent scheme for calculations of static anddynamic susceptibilities in single- and twoband Hubbard models in the framework of dynamical mean-field theory.

Figure 1 shows the dynamical lattice susceptibility computed by Bethe-Salpeter equation (BSE) based on dynamical mean-field theory for a two-band Hubbard model. In solving BSE, we compressed the local two-particle
Green’s function using the tensor-network representation. The uncompressed data takes up
700 MB even on the sparse grid, while thetensor network representation takes up only
330 kB for D = 60. Here, D is a bond dimension in the tensor network.
In future studies, we will use the new techniques to study real compounds by means of
the non-local extension of the dynamical meanfield theory and the parquet approximation.
This report is based on the collaboration
with D. Geffroy, M. Wallerberger, J. Otsuki,
K. Yoshimi, E. Gull, J. Kuneš.
Sz

1.0

y

y

0.8
0.6
0.4
0.2
0.0

X

M

X

M

X

M

Figure 1: Dynamical lattice susceptibility computed for a two-band Hubbard model. Reproduced from Ref. [1] under the CC BY 4.0 license.

References[1] H. Shinaoka, D. Geffroy, M. Wallerberger,
J. Otsuki, K. Yoshimi, E. Gull, J. Kuneš,232

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

SciPost Phys. 8, 012 (2020)[2] H. Shinaoka, J. Otsuki, M. Ohzeki and K.
Yoshimi, Phys. Rev. B 96, 035147 (2017)[3] H. Shinaoka, J. Otsuki, K. Haule, M.
Wallerberger, E. Gull, K. Yoshimi and M.
Ohzeki, Phys. Rev. B 97, 205111 (2018)[4] J. Otsuki, M. Ohzeki, H. Shinaoka andK. Yoshimi, Sparse modeling in quantum
many- body problems, J. Phys. Soc. Jpn.
89, 012001 (2020)

233

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Photoinduced dynamics and high harmonic
generation in magnetism
Sumio Ishihara
Department of Physics, Tohoku University
Sendai 980-8578

Nonequilibrium susceptibility in Floquet
statesRecent great progress in laser light technology significantly promotes scientific researchin strongly coupled light-matter systems. Oneof the fascinating phenomena induced by thestrong light-matter coupling is the appearance of the Floquet states, in which a timeperiodic electromagnetic field behaves as photons and hybridizes with electrons. We examine the spin/charge susceptibility in photoinduced Floquet states [1]. We consider a freeelectron system coupled to a fermionic heatbath. We adopt the Hamiltonian given byH∑ ††ks εk cks cks +ν bν bν()∑+ ksν Vn u c†ks bν + b†ν cks ,=2) On the other hand, in the case of smallΩ comparable to the bandwidth, the multiple
Floquet bands cross the Fermi level of the bathand the additional peaks emerge at momenta
corresponding to nesting vectors between
the Floquet-band Fermi surfaces (Fig. 2).

∑(1)

where c†ks is a creation operator of an electronwith momentum k and spin s(=↑, ↓), and b†νis that of a fermion in a bath with a quantum
number ν.
The susceptibility is formulated on the basisof the Floquet Green s function method, andits perturbative expression is derived from aseries expansion. Through the numerical calculations, we have the following results.
1) In the case of the large electric-field frequency Ω in comparison with the electron
bandwidth, we demonstrate that the bandwidth reduction due to the dynamical localization eﬀect enhances the susceptibility anda deformation of the Fermi surface which depends on light polarization shifts the peak positions of the susceptibility (Fig. 1).

234

Figure 1: The susceptibility at q = (0, 0)
and (π, π) as a function of the light amplitude
A0 [1].
Optical response in the excitonic insulating state
The excitonic insulating (EI) state was proposed more than a half century ago in semiconductors and semimetals and has been studied
intensively on both the experimental and theoretical sides. We study the optical responses in
EI states [2]. We adopt the two-orbital Hubbard model with finite energy diﬀerence between the orbitals defined by
H = ∆

∑

(niaσ − nibσ ) +

iσ

+

∑

∑

i

α

(U

∑

tα c†iασ cjασ

⟨ij⟩ασniα↑ niα↓ + U ′ nia nib )Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 2: The susceptibility, the momentum
distribution function; and the spectral functionat ω = 0, under the linearly polarized light of
A0 = 0.4 and 1.6 [1].
+ J

∑
iσσ ′

+ I

c†iaσ c†ibσ′ ciaσ′ cibσ∑ †ciα↑ c†iα↓ ciᾱ↓ ciᾱ↑ ,

(2)

iα

where ciασ is an annihilation operator of anelectron with spin σ(=↑, ↓) and the orbitalα(= a, b) at site i, and niασ = c†iασ ciασ is theparticle number operator.
The variational cluster approach method
was applied to the two-orbital Hubbard modelwith a finite energy diﬀerence between the orbitals. In the analyses of the ground state, we
considered possibilities of the low-spin state,
the high-spin antiferromagnetic state, the EI
state. The optical conductivity spectra were
formulated by the Green’s function method,where the vertex correction is taken into account. Figure 3 shows the optical conductivity
spectra. In the EI phase, a new peak aroundω/t ∼ 10 and a continuum around 3 < ω/t < 8appear. The intensity of the EI component increases with increasing J/t in the EI phase. It
is shown that the intensity of this structure at
low temperatures almost follows the EI orderparameter.
These researches have been performed withcollaboration with A. Ono, H. Li, M. Naka
and J. Ohtsuki. The numerical calculations in

235

Figure 3: Optical conductivity spectra for several values of the Hund coupling J. The
red solid lines show results including the vertex corrections, while the black dashed results show results without the vertex corrections. [2].
these works have been done using the facilitiesof the Supercomputer Center, the Institute for
Solid State Physics, the University of Tokyo.

References[1] A. Ono and S. Ishihara: Phys. Rev. B
100, 075127 (2019).
[2] H. Li, J. Otsuki, M. Naka and S. Ishihara
Phys. Rev. B 101 125117 (2020).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Mechanism of superconductivity and electron-holeasymmetry in molecular conductors
κ-(BEDT-TTF)2X
Hiroshi WATANABE
Cluster for Pioneering Research (CPR), RIKEN
2-1 Hirosawa, Wako-shi, Saitama 351-0198

The family of quasi two-dimensional molecular conductors κ-(BEDT-TTF)2 X has been
extensively studied as a typical example ofstrongly correlated electron system. Depending on the monovalent anion X, they show
various quantum phases such as antiferromagnetic (AF) and spin-liquid dimer-Mott insulators, and superconductivity (SC) [1]. Owing
to the similarities in the experimental phase
diagrams, κ-(BEDT-TTF)2 X system is often
compared with high-Tc cuprates, which exhibit
Mott metal-insulator transition and SC [2].
Recently, carrier doping in κ-(BEDT-TTF)2 X
has been realized using electric-double-layertransistor [3], and the direct comparison withcuprates becomes possible. The experimental
result shows the electron-hole doping asymmetry, reminiscent of the high-Tc cuprates.

electron-hole doping asymmetry in the phase
diagram where AF spin order, diﬀerent patterns of charge order, and SC compete witheach other. Hole-doping stabilizes the dimertype AF phase and promotes SC with dxy -wave
symmetry, which has similarities with high-Tc
cuprates. In contrast, in the electron-dopedside, geometrical frustration destabilizes the
AF phase and the enhanced charge correlationinduces another SC with extended-s+dx2 −y2 wave symmetry. Our results disclose the mechanism of each phase appearing in filling-control
molecular Mott systems, and elucidate how
physics of diﬀerent strongly-correlated electrons are connected, namely, molecular conductors and high-Tc cuprates.

Here, we theoretically study the doping effect in κ-(BEDT-TTF)2 X. We consider a fourband extended Hubbard model including onsite (U ) and intersite Coulomb interactions(Vij ) with κ-type geometry with the largest
hopping integral tb1 as an energy unit. The
ground state properties are studied with thevariational Monte Carlo (VMC) method. The
Gutzwiller-Jastrow type wave function is used
for the VMC trial wave function. The systemsizes for calculation are from 288 (2×12×12)
to 1152 (2×24×24).
Figure 1 shows the ground-state phase diagram of the extended Hubbard model for
κ-(BEDT-TTF)2 X [4]. We find significant

236

Figure 1: Ground-state phase diagram ofthe extended Hubbard model for κ-(BEDTTTF)2 X [4].

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] K. Kanoda: J. Phys. Soc. Jpn. 75 (2006)
051007.
[2] R. H. McKenzie: Science 278 (1997) 820.
[3] Y. Kawasugi et al., Sci. Adv. 5 (2019)eaav7282.
[4] H. Watanabe, H. Seo, and S. Yunoki: Nat.
Commun. 10 (2019) 3167.

237

3.4

Cooperative Phenomena

in Complex Macroscopic Systems

238

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Tensor-network-based methods and their application todiscrete lattice models
Naoki KAWASHIMA
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Tensor network (TN) is a useful concept in

the local-minima-trapping due to the formation

various fields, not only in the condensed matteroftheory, but also in data science and machine

benchmark showed that the new method

learning. Even in the condensed matter theory

efficiently removes such loops when the target

alone, the application of the TN concept is

tensor has, at least approximately, the structure

multi-fold. In variational principles calculation,of the corner double line tensor, which is

the TN is used as a new type of variational

typical in TN-based RG calculations.

wave

function.

Inthereal-space

redundantIn[2,3],

entanglement

wedeveloped

loops.

theOur

tensorrenormalization group (RG) theory, it serves asrenormalization group (TRG) algorithm fora natural representation of a renormalized

statistical systems with open boundaries. Thissystem. In the pure mathematical physics, it isallows us to investigate properties of boundary

used as a new language for discussing theoperators. We applied the method to several

topological nature of the quantum states. In

two-dimensional classical spin models with

SY2019, we developed new algorithms foropen boundaries. The boundary conformal

generalthespectrumwasobtainedboundary conformal-field theory [2,3], theconsistent

with

the

classical

conformal field theories (BCFTs) for the Ising,TN-based
dynamics

computation
[4],

and

[1],

variational

optimization of topological quantum states.

andturnedunderlyingoutboundary

tricritical Ising, and three-state Potts models.

[5,6]

In [4], we developed a method for tracing

In [1], we proposed a new method forthetime-evolution

of

the

probability

obtaining an efficient representation of a many-

distribution function of a given dynamicalranked tensor in terms of a ring network ofsystems, which is otherwise difficult. We

smaller-ranked tensors. This kind of operations

studied (1+1)-dimensional directed percolation,is vital both in TN application to the real spacea canonical model of a nonequilibrium

renormalization group and in data science. The

continuous transition. We find a universal

central technical problem here is, how to avoid

relaxation of Rényi entropy at the absorbing

239

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

transition point. We also detected a singularity

phase appears between the low field zig-zag

in the "entanglement entropy" in the active (i.e.,magnetic order and the high field polarized

non-absorbing) phase. Although the absorbing

state. We found that the chiral Kitaev spinstates is exponentially rare in this phase, its rareliquid occupies an area in the phase diagram,appearance causes this singularity.

smaller than predicted by other groups.

In [5], we studied the Kitaev model by the
TN representation. We proposed a new wave

References

function that is extremely simple in the TN[1] Hyun-Yong Lee and Naoki Kawashima: J.

representation but still shares many essential

Phys. Soc. Jpn. 89, 054003 (2020)

properties with the ground state of the Kitaev[2] Shumpei Iino, Satoshi Morita, and Naoki

model, such as the quasi-long-range correlation,

Kawashima: Phys. Rev. B 101, 155418 (2020)

the short-range magnetic correlation, the flux-[3] Shumpei Iino, Satoshi Morita, and Naoki

free property, the Z2 gauge structure, and the

Kawashima: Phys. Rev. B 100, 035449 (2019)2D Ising universality. We call this state the[4] Kenji Harada and Naoki Kawashima: Phys.

"loop gas state" because of its mathematical

Rev. Lett. 123, 090601 (2019)equivalence to the loop gas model, one of the[5] Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi

standard and solvable statistical physicalOkubo, and Naoki Kawashima: Phys. Rev. Lett.

models. We showed that the loop gas state is123, 087203 (2019)adiabatically connected to the ground state of[6] Hyun-Yong Lee, Naoki Kawashima, andthe Kitaev model, indicating a similar role to

Yong Baek Kim:arXiv:1911.07714

the AKLT state for the S=1 AFH chain.

[7] Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi
Okubo, Naoki Kawashima: Phys. Rev. B 101,

Later we extended our method to several
other models: S=1 Kitaev model [6], and035140 (2020)

Kitaev-Gamma model [7,8]. In particular, in[8] Hyun-Yong Lee, Ryui Kaneko, Li Ern[8], we studied field-induced quantum phases

Chern, Tsuyoshi Okubo, Youhei Yamaji, Naoki

in theoretical models of the Kitaev magnets,

Kawashima and Yong Baek Kim: Naturesuch as α-RuCl3 for which the half quantizedCommunications 11, 1639 (2020)

thermal Hall conductivity was discovered. Our
TN calculation suggested that a field-induced240

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Kármán-Vortex Cavitation Around Circular-Cylinder Arrays
Yuta ASANO1, Hiroshi WATANABE1, 2, and Hiroshi NOGUCHI1
1

Institute for Solid State Physics, University of Tokyo,
Kashiwa-no-ha, Kashiwa, Chiba 277-8581, Japan2

Department of Applied Physics and Physico-Informatics, Keio University,
Yokohama, Kanagawa 223-8522, Japan

Cavitation

is

a

flow

phenomenon

bubbles and their effects on the surrounding

accompanied by the formation, growth, andflow are investigated by MD calculations [2].

collapse of bubbles caused by local pressure

3-dimensional MD simulation is carried out tochanges in a liquid with the high flow velocity.

analyze the flow around the periodicallySince cavitation has adverse effects on fluidaligned cylinders. The Lennard-Jones (LJ)machinery such as performance degradation,interaction is used for the interaction between

vibration and noise, and erosion, the elucidation

the fluid particles. The cylinder is modeled byof its mechanism is of great engineering

fixing LJ particles on its surface. Periodic

importance. The cavitation inception is thoughtboundary conditions are used for all directions

to be caused by the growth of small bubble

in the system, and two cylinders are arranged

nuclei in a low-pressure region for enough time

perpendicular to the flow to represent an

to grow [1]. However, since it is extremely

infinite row of cylinders. In this way,difficult to discuss the dynamics of microscopic

interference of the vortices behind the upper

bubble nuclei in a macroscopic flow field, theand lower cylinders can be taken into account.

mechanism of cavitation generation is not well

The temperature and velocity are controlled byunderstood. In addition, because the phase

the Langevin heat bath at the downstream sidetransition has to be directly discussed in theof the cylinder. Fluids in the supercriticalflow field, it is extremely difficult to analyze

region are inflowed. Cavitation is generated by

the cavitation inception of the liquid in whicha decrease in the local temperature of the

no bubble nuclei are contained as in the case of

inflow fluid.

flow in hydraulic machines.

Figure 1 shows a snapshot of the density (left

In the present study, molecular dynamics

panels) and vorticity (right panels) fields. At(MD) calculations are performed to analyze

high temperature (temperature T=2), there arecavitation around periodically aligned cylinders,no bubbles and therefore non-cavitating flow isand the formation and growth processes ofobtained. An anti-phase synchronized Kármán

241

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

vortex is generated behind the cylinder. It ischanges occur due to temperature changes.

also found that this synchronization amplifies

The change in the vortex structure should

the vibrations acting on the cylinder. At thechange the characteristics of the vibrations

lower

are

excited by the vortex. It is found that thegenerated in conjunction with the shedding

bubbles generated near the cylinder inhibit thecycle of the Kármán vortex. The Kármán

propagation of the vibration associated with thevortex remains synchronized in the anti-phase

ejection of the vortex, and the vibration

as in the non-cavitating flow. At T=1.25, a gas-

amplitude decreases and eventually disappears.

phase region is formed behind the cylinder andIn summary, the analysis from the molecular

the distance to the formation of the Kármán

scale reveals that bubbles generated near thevortices increases. The phase of the Kármán

cylinder significantly change the properties ofvorticesthe lift and flow fields.

temperature,isslightly

T=1.3,

bubbles

disturbed.

As

the

temperature is further reduced to T=1.2, thegas-phase region behind the cylinder is further

References

expanded and the upper and lower Kármán

[1] C. E. Brennen, Cavitation and Bubble

vortices become asymmetric. It is also found

Dynamics (Oxford University Press, 1995).

that this asymmetric structure is switched by a[2] Y. Asano, H. Watanabe, and H. Noguchi: J.

long period of time. In Newtonian fluids in

Chem. Phys. 152 (2020) 034501.

which no phase transitions occur, no such

Figure 1: Snapshots of density (left panels) and vorticity (right panels)
fields of LJ fluid. The black circles in the figure represent cylinders.

242

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Detachment of fluid membrane from substrate byprotein adhesion
Hiroshi NOGUCHI
Institute for Solid State Physics, University of Tokyo, Kashiwa, Chiba 277-8581

Lipid membranes supported on a solid substrate are considered as a model system for biological membranes and are extensively used to
study protein functions and membrane properties. Recently, the membrane detachmentfrom the substrate was reported by the adhesion of Ca2+ -dependent membrane-binding
proteins annexin. The membrane rolling andblebbing have been observed. To understandthe mechanism to form these membrane structures, we have perfromed meshless membrane
simulations with the isotropic spontaneous
curvatures. We focus on the generation of the
spontaneous curvature by the protein adhesion
here.
Before considering the detachment from thesubstrate, we investigated the closing transition from a membrane patch to a vesicle at a
finite spontaneous curvature [1]. We have determined the theoretical condition of the closure and proposed the estimation method of
the membrane Gaussian modulus from the curvature of the membrane patch.
Next, we added the attraction to a solid substrate by the Lennard-Jones potential. When ahigh curvature C0 is imposed, a membrane disk
is detached from the substrate, and vesicles areformed [see Fig. 1] [2]. The membrane edge
is rolled up, and the edge undulation expands
leading to the vesicle formation. The averagevesicle size is several times larger than the minimum vesicle size formed by the membrane closure of a cup-shaped membrane patch.
With strong adhesion, the competition between the bending and adhesion energies determines the minimum value of the spontaneous curvature for the detachment. In contrast, with weak adhesion, a detachment occurs at smaller spontaneous curvatures due

243

Figure 1: Sequential snapshots of the detachment and vesiculation of the disk-shaped membrane from a solid substrate.
to the membrane thermal undulation. Whenparts of the membrane are pinned on the substrate, the detachment becomes slower, and aremained membrane patch forms straight orconcave membrane edges. The edge undulation induces vesiculation of long strips anddisk-shaped patches. Therefore, membrane
rolling is obtained only for membrane strips
shorter than the wavelength for deformation
into unduloid. This suggests that the rollingobserved for the annexins A3, A4, A5, andA13, results from by the anisotropic spontaneous curvature induced by the proteins.

References[1] H. Noguchi: J. Chem. Phys. 51, 094903(2019).
[2] H. Noguchi: Soft Matter 15, 8741 (2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Brittle structure of semicrystalline polymers bylarge-scale coarse-grained molecular dynamics
simulation
Yuji HIGUCHI
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

We have studied mechanical properties ofsemicrystalline polymers [1, 2, 3] and doublenetwork gels [4] via coarse-grained molecular dynamics simulations. Understanding thefracture process of the semicrystalline polymers at the molecular level is essential to increase its toughness against the stretching.
This year, void formation and growth processes in the fracture process of semicrystalline
polymers were studied on System B.
Figure 1 shows the fracture process of
the lamellar structure consisting of 1.5 × 107
monomers. The lamellar structure consists ofamorphous and crystalline layers. Voids are
generated in amorphous layers, and then theygrow parallel to the stretching direction cylindrically. This process is diﬀerent from thosein elastomers and glassy polymers. The void
structures during their growth process at themolecular level are still debatable in experiments. The maximum length of voids along
x, y, and z-directions are monitored during
the stretching. At ﬁrst, the maximum lengthof voids in x and y-directions, which are perpendicular to the stretching direction, is larger
than that in z-direction, which is parallel tothe stretching direction. Then, the length inz-direction becomes larger than those in x andy-directions. This result is consistent withthat observed in the experiment [5]. Thus,
the void generation and growth processes in
the lamellar structure of crystalline polymers
at the molecular level are successfully revealed.

Snapshot
Amorphous
CrystalStrain = 0.00
Strain = 0.75

Void growth

Strain = 1.00

Strain = 1.50

Void

Strain = 0.00
Strain = 0.75

Strain = 1.00 Strain = 1.50

Figure 1: The deformation and fracture process of the lamellar structure. (a) Snapshotand (b) void generation and growth processes.

References[1] Y. Higuchi and M. Kubo: Macromolecules
50 (2017) 3690.
[2] Y. Higuchi: Polym. J. 50 (2018) 579.
[3] Y. Higuchi: Macromolecules 52 (2019)6201.
[4] Y. Higuchi, K. Saito, T. Sakai, J. P. Gong,
and M. Kubo: Macromolecules 51 (2018)3075.
[5] S. Humbert, O. Lame, J. M. Chenal, C.
Rochas, and G. Vigier: Macromolecules
43 (2010) 7212.

244

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Topological Magnetization Plateau of Quantum
Antiferromagnetic Spin Chain with Anisotropies
Tôru SAKAI1,2 , Hiroki NAKANO1,2 , and Tokuro SHIMOKAWA3 ,1
Graduate School of Material Science, University of Hyogo,
Kouto, Kamigori, Hyogo 678-1297, Japan
2
Synchrotron Radiation Research Center, Kansai Photon Science Institute,
Quantum Beam Science Research Directorate,
National Institute for Quantum and Radiological Science and Technology (QST)
SPring-8, Kouto, Sayo, Hyogo 679-5148, Japan
3
Okinawa Institute of Science and Technology Graduate University, Onna,
Okinawa 904-0945, JapanThe symmetry protected topologicalphase[1, 2] is one of interesting topics inthe strongly correlated electron systems.
The recent study[3, 4] using the numerical
diagolaization of finite-size clusters and thelevel spectroscopy analysis revealed that thesymmetry protected topological phase appears
in the S = 2 antiferromagnetic chain withthe single-ion anisotropy D and the coupling
anisotropy ∆. However, the region of thisphase is quite small in the ground state phase
diagram. Thus it would be diﬃcult to discoverin some real experiments. In the present
study we focused on the symmetry protected topological phase in the magnetization
plateau of the S = 2 antiferromagnetic chain,using the same numerical diagonalizationand level spectroscopy analysis. As a result,
it is successfuly found that the symmetry
protected topological phase appears in muchlarger region of the phase diagram of the
1/2 magnetization plateau. In addition thebiquadratic interaction is revealed to enhanse
this phase[5].
The 1/3 magnetization plateau of the distorted diamond spin chain was also investigated using the nimerical diagonalization andthe finite-size scaling analysis. As a result it

245

is found that the magnetization plateau vanishes for suﬃciently large XY -like coupling
anisotropy. The phase diagram of the 1/3 magnetization plateau was also obtained[6, 7].
As related topics to the magnetization
plateau, we invesitgated the spin gap of
the kagome-lattice antiferromagnet. We performed the large-scale numerical diagonalization of the spin gap and the magnetization
curve of the system and tried to compare themwith the recent experimental results[8, 9]References[1] F. Pollmann, A. M. Turner, E. Berg and
M. Oshikawa, Phys. Rev. B 81, 064439(2010).
[2] F. Pollmann, E. Berg, A. M. Turner and
M. Oshikawa, Phys. Rev. B 85, 075125(2012).
[3] T. Tonegawa, K. Okamoto, H. Nakano, T.
Sakai, K. Nomura and M. Kaburagi, J.
Phys. Soc. Jpn. 80, 043001 (2011).
[4] K. Okamoto, T. Tonegawa and T. Sakai,
J. Phys. Soc. Jpn. 85, 063704 (2016).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[5] T. Sakai, K. Okamoto and T. Tonegawa,Phys. Rev. B 100, 054407 (2019).
[6] Y. Ueno, T. Zenda, Y. Tachibana, K.
Okamoto and T. Sakai, JPS Conference
Proceedings 30, 011085 (2020).
[7] T. Zenda, Y. Tachibana, Y. Ueno, K.
Okamoto and T. Sakai, JPS Conference
Proceedings 30, 011084 (2020).
[8] H. O. Jeschke, H. Nakano and T. Sakai,Phys. Rev. B 99, 140410(R) (2019).
[9] R. Shirakami, H. Ueda, H. O. Jeschke,
H. Nakano, S. Kobayashi, A. Matsuo, T.
Sakai, N. Katayama, H. Sawa, K. Kindo,
C. Michioka and K. Yoshimura, Phys.
Rev. B 100, 8722674 (2019).

246

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Diagonalization Study on Spin Nematic
Phase of Low-Dimensional SystemTôru SAKAI1,2 , Hiroki NAKANO1,2 , and Tokuro SHIMOKAWA3 ,1
Graduate School of Material Science, University of Hyogo,
Kouto, Kamigori, Hyogo 678-1297, Japan
2
Synchrotron Radiation Research Center, Kansai Photon Science Institute,
Quantum Beam Science Research Directorate,
National Institute for Quantum and Radiological Science and Technology (QST)
SPring-8, Kouto, Sayo, Hyogo 679-5148, Japan
3
Okinawa Institute of Science and Technology Graduate University, Onna,
Okinawa 904-0945, JapanThe spin nematic phase has attracted a lotof interests in the field of the quantum spin systems. It was theoretically predicted to appear
around the saturation magnetization in themagnetization process of the frustrated spin
chain[1]. Our present study using the numerical diagonalization and the finite-size scaling
analysis revaled that the spin nematic liquid
phase apears in the S = 1 spin ladder systemwith the easy-axis single-ion anisotropy D evenfor a small magnetic field H. The phase diagram in the DH plane and the DH plane wereobtained[2, 3].
The research of the three-leg spin tube withthe ring-exchange interaction J4 using the unmerical diagonalization and the finite-size scaling analysis[4] indicated that the spin nematic
liquid pahse appears for suﬃciently large J4 .
In addition the spin nematic liquid phase wasalso revealed to appear in the spin ladder system with the antiferromagnetic leg and the ferromagnetic rung exchange interaction in thepresent of the XXZ anisotropy[5].

References[1] T. Hikihara, L. Kecke, T. Momoi and A.
Furusaki, Phys. Rev. B 78, 144404 (2008).

247[2] R. Yamanokuchi, K. Okamoto and T.
Sakai, Proceedings of 2018 16th International Conference on Megagauss Magnetic Field Generation and Related Topics (MEGAGAUSS) (2019) 8722674.
[3] T. Sakai and K. Okamoto, JPS Conference Proceedings 30, 011083 (2020).
[4] T. Sakai, JPS Conference Proceedings 29,
014004 (2020).
[5] K. Okamoto, T. Tonegawa, M. Kaburagi
and T. Sakai, JPS Conference Proceedings 30, 011024 (2020).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Aggregation process of full-length amyloid-beta peptides
studied by molecular dynamics simulations
Hisashi Okumura
Exploratory Research Center on Life and Living Systems,
Institute for Molecular Science, Okazaki, Aichi 444-8585
Alzheimer's disease is thought to be caused

number of combinations between replicas andby aggregates of amyloid-beta peptides, such asparameters without the loss of sampling

oligomers and amyloid fibrils. Amyloid-beta

efficiency. For comparison, we applied the

peptide is a peptide consisting of 39-43 amino

replica sub-permutation, replica-permutation,acid residues. The oligomer structure of theand replica-exchange methods to a β-hairpin

amyloid-betaWemini protein, chignolin, in explicit water. We

investigated the aggregation process of full-calculated the transition ratio and number oflength amyloid-beta peptides by moleculartunneling events in the parameter space, thedynamics simulations. Several amyloid-beta

number of folding–unfolding events, and the

peptides were placed in explicit water, and theirautocorrelation function to compare sampling

dynamics and structural changes were observed.

efficiency. The results indicate that among the

As a result, aggregates with intermolecular

three methods, the RSPM is the most efficientbeta-sheet structure was generated. During thisin both parameter and conformational spaces.

peptidesis

notclear.

oligomerization process, Aβ peptides are first
aggregated by electrostatic force. Then, they

References

are aggregated by hydrophobic interaction.

[1] K. Hukushima, K. Nemoto, J. Phys. Soc.
Jpn. 65 (1996) 1604.

We also developed an improvement of thereplica-exchange [1, 2] and replica-permutation[2] Y. Sugita, Y. Okamoto, Chem. Phys. Lett.

methods [3], which we call the replica sub-314 (1999) 141.

permutation method (RSPM) [4]. Instead of[3] S. G. Itoh, H. Okumura, J. Chem. Theor.

considering all permutations, this method uses

Comput. 9 (2013) 570.

a new algorithm referred to as sub-permutation[4] M. Yamauchi and H. Okumura: J. Comput.

that contains transitions only to the adjacentChem. B 40 (2019) 2694.

temperatures. The RSPM can reduce the248Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Monte Carlo study of the critical properties of noncollinear
Heisenberg magnets: O(3)×O(2) universality class
Yoshihiro Nagano, Kazuki Uematsu and Hikaru Kawamura
Graduate School of Science, Osaka University, Toyonaka 560-0043
The

criticalthetype, characterized by the complex-valued

antiferromagnetic Heisenberg model on thecorrection-to-scaling exponent, ω=0.1+0.4-0.05 +three-dimensional stacked-triangular lattice [1]i 0.7+0.1-0.4. The focus-like nature of the chiral

are studied by means of a large-scale Montefixed point accompanied by the spiral-like

Carlo simulation in order to get insight into therenormalization-group (RG) flow [5] is likely tocontroversial issue of the criticality of thebe the origin of the apparently complicatednoncollinear magnets with the O(3)×O(2)critical behavior. The results are compared andsymmetry [2]. The maximum size studied is

discussed in conjunction with the results of other3843, considerably larger than the sizes studied

numerical simulations, several distinct types ofby the previous numerical works on the model.

RG calculations including the higher-order

Availability of such large-size data enables us toperturbative

examineproperties

calculations and the nonperturbative functional

including the effect of corrections to the leading

RG calculation, and the conformal-bootstrap

scaling. Strong numerical evidence of the

program.

theproperties

detailed

criticalof

massiveandmassless

RG

continuous nature of the transition is obtained.
Our data indicates the existence of significant

References

corrections to the leading scaling. Careful[1] H. Kawamura, J. Phys. Condens. Matter 10,

analysis by taking account of the possible

4707 (1998).

corrections yield critical exponents estimates, α[2] Y. Nagano, K. Uematsu and H. Kawamura,=0.44(3),β=0.26(2),γ=1.03(5),ν=Phys. Rev. B 83, 103704 (2019).

0.52(1),

η=0.02(5), and the chirality exponents βk =[3] H. Kawamura, Phys. Rev. B 8, 4916 (1988).

0.40(3)

the[4] A. Pelissetto, P. Rossi and E, Vicari, Phys.

existence of the O(3) chiral (or O(3)×O(2))

Rev. B 63, 140414(R) (2001); B 65, 020403(R)universality class governed by a new `chiral'(2001).hi

fixed point [3,4]. We also obtain an indication[5] P. Calabrese, P. Parruccini and A.I. Sokolov,

that the underlying fixed point is of the focus-

Phys. Rev. B 66, 180403(R) (2002).

andγk=0.77(6),supporting249

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Multiscale analysis of polymeric fluids and solids
Takahiro MURASHIMA
Department of Physics, Graduate School of Science,
Tohoku University, Aramaki-Aza-Aoba, Aoba-Ward, Sendai, Miyagi 980-8578
100 tetrahedral elements and the deformationof each element is calculated using the finite
element method. Each element has a molecularsimulation system and molecular simulation iscarried out according to the deformation. The
stresses are then obtained from the molecularsimulation system and passed on to themacroscopic system. On the macro-scale side,
the deformation occurs according to thedetermined stress field. The entire system isdeveloped in time by alternating these macroand micro-scale calculations. Multiscale
simulations are now possible to include
molecular features that are difficult to handle inconventional macro-scale simulations, and to
calculate large deformations that are difficult tohandle in conventional micro-scale simulations.

Polymeric materials are used in many
products and are now an integral part of ourlives. In recent years, however, the use of
microplastics has tended to be discouraged due
to concerns about the damage they can cause to
ecosystems. The development of new materials
with less impact on ecosystems, such as
biodegradable plastics, is expected.
In order to develop more functional
materials, it is essential to control the physicalproperties on the molecular scale and to control
the formability on the macro scale. The
micro-scale properties of polymer materials andmacro-scale mechanical properties are strongly
correlated and cannot be treated independently,
making their understanding difficult. Therefore,
we have been developing multi-scale
simulations that simultaneously combine
micro-scale
molecular simulations andmacro-scale continuum simulations. In thisproject, we have developed a multi-scale
simulation that combines molecular dynamics
simulation and finite element simulation, andthe results have been published in several
papers[1-3].
The method of multi-scale simulation is asfollows. The macro-scale cube is divided into

References[1] T. Murashima, S. Urata, S. Li: Euro. Phys.
J. B ​92​(2019) 221.
[2] T. Murashima: CICSJ Bulletin ​37 (2019)
87.
[3] S. Li, S. Urata, T. Murashima: IACM
Express. 4​6​(2020) 10.

250

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Dynamical simulation of spin-orbit insulators
Hidemaro Suwa
Department of Physics, University of Tokyo
7-3-1 Hongo Bunkyo, Tokyo 113-0033

Dynamics of correlated quantum materials
is a long-standing problem in condensed matter physics. The recent development of experimental techniques such as inelastic neutronand x-ray scattering has revealed dynamical
properties and excitations with unprecedented
precision. In particular, resonant inelastic Xray scattering has revealed a lot of hiddenfeatures of high-Tc superconductors and spinorbit insulators. It is of great interest to ﬁnd
novel quasi-particles and understand complex
excitations in correlated materials.
Spin-orbit insulators emerge from 5d electron systems with strong spin-orbit coupling.
Coulomb repulsion between electrons in 5d
atomic orbitals is not strong enough to suppress charge degrees of freedom completely.
As a result, the charge gap can be comparable to the magnon-band width, as experimentally measured in strontium iridates. Suchelectron systems can be described by the Hubbard model with an intermediate Coulomb repulsion, which is parameterized by U .
Strontium iridates, which can be approximated by a half-ﬁlled J = 1/2 singleband Hubbard model, provide an excellent
play ground of charge-spin-orbital entanglement. The dimensionality drastically changes
the electronic property: the single layer material Sr2 IrO4 is a Mott insulator with 400
meV charge gap, the bilayer material Sr3 Ir2 O7
is an insulator in the intermediate coupling
regime with 130 meV charge gap, and thethree-dimensional material SrIrO3 is a correlated metal. These systems provide one of thebest opportunities to study the metal-insulatortransition. Particularly, the bilayer system is
expected to show a characteristic excitation
emerging in the crossover regime. Moreover,in the view of engineering, the magnetic energy
scale enhanced in the crossover regime would
be crucial to realistic devices.
To understand the dynamics of spin-orbit
insulators, we have developed an eﬃcient numerical approach that enables large-scale calculation of dynamical quantities at ﬁnite temperatures in a broad-U region of the Hubbard
model. In our approach, sampling of the auxiliary vector ﬁelds from the Boltzmann distribution is combined with real time evolution of
the self-consistent density matrix.
We used ISSP System B through class
C projects (ID: H31-Ca-0057, H31-Cb-0047).
Our code is implemented with MPI parallelization using GPUs. In particular, GPU programming is crucial to fast matrix-vector multiplication and diagonalization. Applying our approach to the bilayer iridate Sr3 Ir2 O7 , we haveclariﬁed excitonic excitations of the longitudinal or Higgs mode appearing in the dynamical
spin structure factor. Interestingly, excitons
exhibit a signiﬁcant softening as the temperature approaches the magnetic transition temperature, while transverse magnons do not.
Our approach is applicable to a broad rangeof the Hubbard model without restrictions of
the lattice, hopping parameters, and electron
ﬁlling. The developed method is expected topush the boundary of dynamical simulation ofcorrelated electron systems and lead to theidentiﬁcation of hidden excitations emerging
from charge-spin-orbital entanglement.

251

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Computational design of enzymes and ligand-binding
proteins
Kazuhisa OHARA1, Mio SANO1, Shunji SUETAKA1, Nao SATO1, Yoshiki OKA1,
Koji OOKA2, Yuuki HAYASHI1, and Munehito ARAI1,2
Department of Life Sciences, Graduate School of Arts and Sciences, and1

Department of Physics, Graduate School of Science,

2

The University of Tokyo, Komaba, Meguro, Tokyo 153-8902
Proteins have various functions, including

top mutants, created the mutant proteinsbinding and catalysis. Thus. proteins areexperimentally, and measured their activities.

potentially useful for industry and medicine if

We found that 20 out of 34 mutants had thetheir functions are sufficiently improved or

activity higher than the wild-type protein.

modified. However, because the protein folding

Moreover, for the top 2 mutants, we succeeded

problem remains unsolved, development ofin improving the activity ~4-fold compared

computational protein design strategies haswith the wild type. Thus, our strategies forbeen a great challenge. To solve this issue, here

rationally improving activity of an enzyme will

we attempted to use the Rosetta software suite

be applicable to industrial use.

to computationally design various proteins,(2) Second, to develop a protein that can be

including enzymes and ligand-binding proteins.

used as an anti-allergy drug, we designed two

The static version of the Rosetta 3.8 suite wastypes of proteins that inhibit the interaction ofused in the following calculations [1,2]. In

interleukin-33 (IL-33) with the ST2 receptor of

addition, to solve the protein folding problem,

type 2 innate lymphoid cells [4]. One template

we developed a statistical mechanical model offor the inhibitor design was a fragment of theprotein folding that can explain the folding

ST2 protein. Rosetta calculation was used topathways of multi-domain proteins.

reduce the number of disulfide bonds in the(1) First, we aimed to rationally improve afragment, to make it easier to purify the protein

catalytic activity of an enzyme. By optimizingthat was expressed in Escherichia coli. As

theenzyme,expected, we could obtain the mutant of thedihydrofolate reductase [3], and its ligands, we

ST2 fragment having a reduced number ofcomputationally designed many mutants of thedisulfide bonds as well as the ability to bind IL-

enzyme that were expected to improve its

33. Another strategy to design the IL-33–ST2

catalytic activity. Subsequently, we selected 34

inhibitors was to make mutants of IL-33 thatinteractions

betweenan252

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyobinds tightly to one of the two IL-33 binding(5) Finally, to solve the protein folding

sites on ST2 but does not bind to another site.

problem, we developed a statistical mechanicalThe calculations were already done, and themodel of protein folding. The WSME modelexperimental verification is now under way.

has been known to be able to explain the(3) Third, we rationally designed inhibitors

folding pathways of small proteins and isfor the interactions between the KIX domain of

considered to be a promising model to solve theaandprotein folding problem [6]. However, thetranscriptional activators [5]. We designed andmodel could not be applicable to large, multi-

createddomain proteins, and this problem has beentranscriptionalthecoactivatormutantCBP

fragmentsofthetranscription activator MLL, which bind moreunsolvedtightly than the wild type. We also designed theintroducing a new Hamiltonian in the WSME

KIX mutant that can bind more tightly to themodel and computationally calculating thetranscription activator c-Myb than the wild-

closed form of the partition function, we

type KIX. Since the protein-protein interaction

succeeded in predicting the folding pathways of

between KIX and c-Myb is responsible for themulti-domain proteins. Thus, our model isblood cancer, leukemia, our results may bepromisinguseful for developing anti-cancer drugs.

description of protein folding mechanisms.

for

more

for

a

than

20

unifiedyears.

By

theoretical(4) Fourth, we attempted to modify asubstrate specificity of a ligand-binding proteinusing the Rosetta software. Here, an ATP-

Referencesbinding protein was designed to bind GTP[1] B.J. Bender, et al.: Biochemistry, 55 (2016)

instead of ATP. For experimental verification,

4748-4763.

we selected more than 20 mutants that were

[2] R. F. Alford, et al.: J Chem Theory Comput.

predicted by Rosetta to bind GTP more tightly

13 (2017) 3031-3048.

than ATP. However, the experimental results[3] M. Arai, et al.: J Mol Biol. 410 (2011) 329-

showed that none of the mutants acquired a342.

new function to bind a different ligand. It might[4] X. Liu, et al.: Proc Natl Acad Sci USA. 110

be possible that dynamics of both the protein(2013) 14918-14923.

and ligand should be taken into account more

[5] R. N. De Guzman, et al.: J Mol Biol. 355

extensively to accommodate the difference in(2006) 1005-1013.

the size and shape of ligands, although it[6] M. Sasai, et al.: Biophys Physicobiol. 13

requires much more calculations.

(2016) 281-293.

253

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Event-chain Monte Carlo method applied to
non-equilibrium relaxation analysis
Y. Ozeki and Y. Osada
Graduate School of Informatics and Engineering, The University of Electro-Communications

The event-chain algorithm is investigated for
its applicability to the nonequilibrium relaxation(NER) method and the estimation of the dynamical exponent z, which indicates an eﬃciency to perform Monte Carlo (MC) simulations. The eventchain method has introduced for the MC simulation with a multi-spin-ﬂip algorithm [1,2]. It shows
an eﬃcient performance for the relaxation even in
frustrated systems and gives estimation of the dynamical critical exponent z ∼ 1 [1], which indicatesa faster dynamics as compared with those with asingle-spin-ﬂip algorithm such as the the Metropolis one.
The NER method is an eﬃcient numerical technique for analyzing equilibrium phase transition [3].
It provides the critical temperature and critical exponents accurately for second-order transition systems, and has been used successfully to study various problems, including frustrated and/or random
systems. In the NER analysis, the equilibration
step is not necessary. Simulation is made only up
to steps when the asymptotic behavior indicatesthe equilibrium state. Thus, one can analyze large
systems as compared with equilibrium simulations.
This advantage becomes more eﬀective for slowrelaxation systems.
We analyze the classical XY model in three dimensions;∑
Si · Sj ,(1)
H = −J

as those in the thermodynamic limit. In otherwords, the ﬁnite size eﬀect must be avoided in
the observed regime of relaxations. Thus, ﬁrst,
we check the size-dependence for the relaxation of|m(t)|. Calculations are carried out at around the
expected transition temperature T / = 2.202 on 43
to 350 − 3 simple cubic lattices up to the observation time of 200 MCSs. Note that the temperatureis measured in the unit of J/kB hereafter. About
840 samples are taken for statistical averaging. The
result is plotted in Fig. 1. It is conﬁrmed that thesize dependence disappears for L ≥ 300 up to 200
MCSs. It is remarked that the relaxation simulated by the event-chain algorithm is much fasterthan that by the Metropolis one, which is an advantage. Furthermore, the appearance of the size
dependence also becomes faster. In the Metropoliscase, it does not appear at least in 104 MCSs for
L = 200 lattice, while it does at 100 MCSs in theevent-chain case. The latter property is an disadvantage, since we must simulate on larger lattices.
Anyway, in the present study, we will use L = 300
lattice for the analysis of phase transition.

⟨ij⟩

where summation for ⟨ij⟩ is taken over all nearestneighboring sites on a simple cubic lattice. The initial state of relaxation is prepared as the all-aligned
state (1, 0). Since the relaxation is much fast in thesimulation with the event chain analysis, we cannot
use the magnetization ⟨Six ⟩ as the dynamical orderparameter, which is used in the NER analysis with
the Metropolis algorithm. Thus, we estimate therelaxation of the absolute value of the magnetization,|m(t)| = (⟨Six ⟩2 + ⟨Siy ⟩2 )1/2 .
(2)In the standard NER analysis, the asymptotic
behaviors of relaxations are used to analyze thephase transition, and are necessary to be regarded

254

Figure 1: Size dependence for the relaxation of|m(t) at T = 2.202 for the 3D XY model.
The relaxation of the order parameter |m(t|) arecalculated for 2.182 ≤ T ≤ 2.222 on the 3003 simple cubic lattice up to an observation time of 200

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoY = τλm(t,J)

10

1

0.1
0.1

1

X = t/τ

Figure 3: Scaling plot for the data in2.204 ≤ T ≤2.222 in Fig. 2
10

MCSs. About 864 samples are taken for statistical
averaging. The estimations are plotted in Fig. 2.
Using the improved dynamical scaling analysis for
the NER data [4], we analyze the dynamical scalingform,|m(t, T )| = τ −λ Y [t/τ ],(3)

Y = τλm(t,J)

Figure 2: Relaxation of |m(t) for the 3D XY modelin 2.182 ≤ T ≤ 2.222 with the interval ∆T = 0.002.

1

0.1
0.1

1

X = t/τ

where τ (T ) is the relaxation time and λ is a dynamical critical exponent. In Fig. 2, the relaxation
curves show downward trend in 2.204 ≤ T ≤ 2.222,
which indicates the paramagnetic phase. Thus, applying the scaling form (3), the data for these temperatures collapse as in Fig. 3 with Tc = 2.20216
and z = 1.461. Furthermore in Fig. 2, the relaxation curves show upward trend in 2.182 ≤ T ≤2.200, which indicates the ferromagnetic phase.
Thus, applying the scaling form (3), the data forthese temperatures collapse as in Fig. 4 with
Tc = 2.20183 and z = 1.478.
The estimated transition temperature Tc = 2.202
is consistent with Tc = 2016 obtained previously[5]. The estimated dynamical exponent z ∼ 1.47
is greater than z ∼ 1 estimated previously forthe event-chain algorithm [1], while it keeps stilla smaller value than z ∼ 2 which is expected forthe short-range algorithm such as the Metropolis
one. Consequently, the event-chain algorithm canbe used in the NER analysis with an eﬃcient relaxation performance, and would be applicable tovarious slowly relaxing problems such as frustrated
and/or random systems.

255

Figure 4: Scaling plot for the data 2.182 ≤ T ≤2.200 in Fig. 2

References[1] Y. Nishikawa et. al., Phys. Rev. E92 063306(2015)[2] M. Michel et. al., Europhys. Lett. 112
20003 (2015)[3] Y. Ozeki and N. Ito, J. Phys.: Math.
Theor. 40 R149 (2007).
[4] Y. Echinaka and Y. Ozeki, Phys. Rev. E94
043312 (2016).
[5] A. P. Aloysius and M. Harsenbusch,
Physica A201 593 (1993)

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Entanglement, Quantum Phase Transition, andQuantum Dynamics in Quantum Many-body Systems
Synge Todo
Department of Physics, University of Tokyo, Tokyo 113-0033, Japan
Institute for Solid State Physics, University of Tokyo, Kashiwa, 277-8581, Japan

We have developed various novel numerical methods for quantum/classical many-bodysystems with strong correlations. An eﬃcientquantum Monte Carlo method has been developed to calculate the entanglement entropyof quantum spin systems. The entanglement
entropy is an essential index that characterizes quantum correlations and the topologicalorder in quantum many-body systems. Our
method works directly at absolutely zero temperature, and thus it is entirely free from systematic errors coming from extrapolation to
the zero-temperature limit, unlike the previous
methods.
We also have developed a nonlocal-update
quantum Monte Carlo method for quantum
dimer models on general lattices. By implementing the technique recently suggested forquantum Monte Carlo simulation on quantum
dimer model with the help of priority queue,
which can help ﬁnd the next operator for updating eﬃciently, we can simulate on the ﬁnite temperature region of the quantum dimer
model. By the ﬁnite-size scaling, the phaseboundary between low-temperature columnar
phase with the maximum number of parallel
neighboring dimers, and disordered phase athigh temperatures can be decided in a broad
region of dimer-dimer interaction potential,
and the value of which is both consistent of theclassical limit, where a KT phase transition is
known, and also tends to a constant slope near
the RK-point.

The tensor renormalization group method
can eﬃciently calculate physical quantities oflarge-scale classical/quantum systems. However, the existing methods, such as the tensor
renormalization group (TRG) and the higherorder tensor renormalization group (HOTRG),
suﬀer from the huge computational cost in
higher dimensions. To solve this problem, we
have developed the anisotropic tensor renormalization group (ATRG) that can dramatically reduce the computational complexity
in high-dimensional systems such as threedimensional quantum systems. In addition,
we further improve the accuracy of ATRG by
combining with techniques such as the tensor
renormalization group method that incorporates bond weights, etc.
Spins coupled with photon degrees of freedom in the cavity exhibit a non-equilibriumphase transition with bistability in the number of photons. We have performed simulation
based on the quantum master equations. Fromthe eigenvalues and eigenstates of the time evolution operator, we discussed the correspondence to the ﬁrst-order phase transition in theequilibrium system. We have calculated thehysteresis loop under the periodic modulationof laser intensity, from the viewpoint of the
Floquet operator, and clariﬁed that a dynamical phase transition phenomenon appears withrespect to the period of laser intensity.

In the meantime, the real-space renormalization group methods based on the tensor networks have been widely used in recent years.

256

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Superconducting dome in electron doped FeSeintercalates
Harald JESCHKE
Research Institute for Interdisciplinary Science, Okayama University
3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530

The van-der-Waals gap of iron chalcogenide
superconductors can be intercalated with a variety of inorganic and organic compounds thatmodify the electron doping level of the ironlayers. In Lix (C3 N2 H10 )0.37 FeSe, a dome inthe superconducting transition temperature Tc
has been reported to occur in the doping rangeof x = 0.06 to x = 0.68 [1]. We used massive parallel computer simulations to address
magnetic and superconducting properties ofLix (C3 N2 H10 )0.37 FeSe [2]. With a combinationof density functional theory and spin fluctuation theory, we capture the evolution of superconducting transition temperatures theoretically. We clearly demonstrate how the changing electronic structure supports an increasing
superconducting Tc (Figure 1). The suppression of Tc at high doping levels can, however,
only be understood by analyzing the magnetic
tendencies. We determine the Heisenberg exchange couplings between the iron moments;
superconductivity is realized out of these underlying interactions. We can show that withdoping, they evolve from stripe-type at low
doping to bicollinear at high doping. With increasing carrier density, magnetic interactions
mutate from FeSe-like to FeTe-like, explaining
a Tc suppression at high doping.

Figure 1: Structure, band structure andleading eigenvalues of the gap equation forLix (C3 N2 H10 )0.37 FeSe.
[2] M. Shimizu, N. Takemori, D. Guterdingand H. O. Jeschke, Importance of Fermi
surface and magnetic interactions for thesuperconducting dome in electron doped
FeSe intercalates, under review (2020).

References[1] R. J. Sun et al., Phys. Rev. B 98, 214508(2018).

257

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Properties of electron doped iron based
superconductor LaFe2As2
Harald JESCHKE
Research Institute for Interdisciplinary Science, Okayama University
3-1-1 Tsushima-naka, Kita-ku, Okayama 700-8530

For more than a decade after the discovery of Fe-based superconducting pnictides it
seemed that superconductivity existed in a relatively narrow range of dopings away from thenominal Fe2+ valency. One of the few examples of strongly overdoped (up to Fe2.5+
valency) pnictides was provided by the 1111
material LaFeOAs, with up to 50% of O2−
replaced by H− .
Recently, another compound with formally Fe2.5+ has been synthesized [1], LaFe2 As2 . It was found experimentally that the material can exist in two
distinctly different crystallographic phases,“collapsed-tetragonal” (CT) and “uncollapsedtetragonal” (UT). We used massive parallel computer simulations to address structural, magnetic, and electronic properties of
LaFe2 As2 [2]. We show that the UT phase, as
opposed to the CT one, bears a strong shortrange magnetism of the stripe type driven
by the next-nearest-neighbor exchange. The
structural changes are triggered by magnetic
collapse, as in CaFe2 As2 . Even though the orbitals relevant for the low-energy physics are
not the usual dxz and dyz , the electron pockets do not exclude the usual spin-fluctuation
driven mechanism with an overall s symmetry (Figure 1). Importantly, La in this compound assumes a non-integer valence closer to
2.7+ than to 3+, corresponding to doping of∼ 0.35e, rather than 0.5e. It is thus overdoped,
but not dramatically.

Figure 1: Susceptibility and Fermi surface of
LaFe2 As2 .

References[1] A. Iyo et al., J. Phys. Chem. Lett. 10,1018 (2019).
[2] I. I. Mazin, M. Shimizu, N. Takemori, and
H. O. Jeschke, Novel Fe-Based Superconductor LaFe2 As2 in Comparison with Traditional Pnictides, Phys. Rev. Lett. 123,
267001 (2019).

258

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Novel phases and dynamics in frustrated spin systems
Tsuyoshi OKUBO
Department of Physics, The University of Tokyo
7-3-1 Hongo, Bunkyo-ku, Tokyo 133-0033

Frustrated interactions in spin systems often
induce novel phenomena, e.g., non-magnetic
ground states including spin liquid and topological orders. Conventionally, geometricallyfrustrated spin systems, such as the kagomélattice and the pyrochlore lattice Heisenberg
antiferromagnets have been investigated actively. Recently, a diﬀerent kind of frustrated
interaction introduced by the strong spin-orbit
coupling has attracted much interest. For example, in Na2 IrO3 and α-RuCl3 , the dominantmagnetic interaction induced by the strong
spin-orbit coupling is considered to be the Kitaev interaction: it is an Ising like anisotropicinteraction with diﬀerent spin component depending on the bonds. When we consider theS = 1/2 quantum spin model on the honeycomb lattice with only the Kitaev interaction (Kitaev model), its ground state is a spin
liquid state without any spontaneous symmetry breakings [1]. This fact indicate real compounds might have a spin liquid ground states.
However, real compounds contain other interactions such as the Heisenberg interaction, further neighbor interactions, or the oﬀ-diagonalinteractions, and they can induce magnetic
long range orders at low temperature.
In this year, in order to clarify eﬀects of additional interactions in the Kitaev materials,
we numerically investigated the ground stateand ﬁnite temperature properties of the models with the Kitaev interaction and the Γ interactions (the Kitaev-Γ model) by means of
tensor network methods. The Γ term is anoﬀ-diagonal interaction and the Hamiltonianof the model is given by
∑
H=
Hγ ,

(1)

γ∈x,y,zwhere for γ = z,∑
Hz =[KSiz Sjz + Γ(Six Sjy + Siy Sjx )].

(2)⟨i,j⟩zFor γ = x, y, we consider similar interaction
with cyclic rotation of x, y, z components. We
consider the honeycomb lattice and γ = x, y, z
corresponds to three directions of the bonds.
This model is considered to be an eﬀectivemodel for α-RuCl3 [2, 3].
Firstly, we investigated the phase diagram of
the Kitaev-Γ model by using a two-dimensional
inﬁnite tensor network approach. We represented the ground state wave function as products of small tensors, and optimize each tensor element so that the energy expectation
value becomes smaller. By assuming severaltransnational symmetries of the ground state,
we can represent inﬁnitely large system by using ﬁnite numbers of tensors. As a networkof tensors, we used the inﬁnite tensor productstates (iTPS), which is also called as the inﬁnite projected entangled-pair states (iPEPS).
As the optimization algorithm, previously, we
have used the imaginary time evolution. However, it have become clear that the imaginary
time evolution often trapped at local minima
and it was very hard to obtain novel spin liquid state from random initial states. Thus, thisyear, we used a diﬀerent type of optimization,so called variational optimization [4]. We conﬁrmed that by using the variational optimiza-

259

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyotion, we correctly obtained the Kitaev spin liquid state at the pure Kitaev model (Γ = 0)even from the random initial states. Then weapplied the variational optimization to ﬁnite
Γ and draw the phase diagram. Although theobtained variational energies were largely improved from those obtained by the imaginary
time evolution, the phase diagram was almost
unchanged; except for the vicinity of the pure
Kitaev model, the ground states were magnetically ordered states. This observation was contrasted with the phase diagrams obtained by
the exact diagonalization (ED) [2] or by theinﬁnite density matrix renormalization group(iDMRG) [3]; they concluded much wider spin
liquid phases. In order to clarify nature of thephase diagram further, we might need larger
scale calculation with iTPS.

[3] M. Gohlke, G. Wachtel, Y. Yamaji,
F. Pollmann, and Y. B. Kim: Phys. Rev.
B 97 (2018) 075126.
[4] P. Corboz:
035133.

Phys. Rev. B 94 (2016)[5] P. Czarnik, J. Dziamaga, and P. Corboz:
Phys. Rev. B 99 (2019) 035115.
[6] A. Kshetrimayum, M. Rizzi, J. Eisert, and
R. Orús: Phys. Rev. Lett. 122 (2019)070502.
[7] J. Nasu, M. Udagawa, and Y. Motome:
Phys. Rev. B 92 (2015) 115122.

Secondly, we investigated ﬁnite temperature
properties of the model. In order to calculate
physical quantities at a ﬁnite temperature, we
represented the density matrix of the system intensor network representations. We employed
two types of the tensor network representations: the local puriﬁcation, e.g., Ref. [5], andthe direct tensor product operator (TPO) [6].
By applying them to the pure Kitaev model,
we found that the former representation failed
to reproduce the expected lower temperature
speciﬁc heat peak [7], while the latter TPO
representation reproduced it, at least qualitatively. This observation indicated that thedirect TPO representation was more eﬃcientthan the local puriﬁcation. The applicationsof the developped technique to the model withﬁnite Γ is on going.

References[1] A. Kitaev: Ann. Phys. 321 (2006) 2.
[2] A. Catuneanu, Y. Yamaji, G. Wachtel,
H.-Y. Kee, and Y. B. Kim: npj Quantum
Materials 3 (2018) 23.

260

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Thermal effects on quantum frustrated magnetisms
Tokuro Shimokawa
Okinawa Institute of Science and Technology Graduate University,
Tancha, Onna-son, Kunigami-gun, Okinawa 904-0495
moderate

We know well that quantum frustrated

temperatures

exhibitingamagnetisms often exhibit rich many-bodycharacteristic ring-like structure in the equal-

physics, but we also know difficulties totime spin structure factor. These obtained

investigatetheresults

fluctuations

numerically,effects

of

the

hence

thermalfreedom in the intermediate plaquette groundstate, we found the signature of the finite-

investigating the finite-temperature properties

temperature phase transition associated with theof S=1/2 bilayer-breathing-kagome (BBK)

breaking of the mirror symmetry at moderate

Heisenberg model for Ca10Cr7O28 and S=1/2

temperatures via specific heat and correlation

Shastry-Surtherland (SS) Heisenberg model for

functions calculations. We also investigate the

SrCu2(BO3)2.

joinedrelationship the transition and the existence ofrecently the family of quantum spin liquid

the degenerated excited states by the exact

candidates [3] in spite of the complexity of its

diagonalization method. [6]former

[1-2]

explaining

for

The

methodfor

The SS model: Owing to the Ising degrees of

We use a state of art numerical method,
typicality

reasonable

qualitatively the nature of the Ca10Cr7O28. [5]thermally

induced novel phases still remain unexplored.
quantum

aremagnetHamiltonian. The latter magnet has been known
well, but recent experiments under highReferences

pressures [4] could reveal successfully the[1] A. Hams and H. De Raedt, Phys. Rev. E

existence of the intermediate plaquette state, so

62, 4365 (2000).

the theoretical studies at finite temperatures are[2] S. Sugiura and A. Shimizu, Phys. Rev.

required.

Lett. 111, 010401 (2013).

The BBK model: We computed the several[3] C. Balz, et al, Nat. Phys. 12, 942 (2016).

physical quantities such as specific heat,[4] M. E. Zayed et al, Nat. Phys. 13, 962 (2017).

magnetization curve, and equal-time spin

[5] T. Shimokawa, R. Pohle, N. Shannon, in

structure factor at finite-temperature with the

preparation.

quantum typicality method and found the[6] T. Shimokawa, in preparation.

possible existence of a spiral spin liquid state at261

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical studies on magnetization process of theKitaev spin liquid
Kota IDO
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

The Kitaev model is one of the prominent examples of quantum many-body systems
where quantum spin liquids emerge[1]. In the
Kitaev model, the nearest-neighbor spins interact with each other via bond-dependent Isingtype interactions. Although the Kitaev modelseems to be an artiﬁcial model, it has been proposed that the Kitaev model can be realized inreal materials[2]. Inspired by the proposal, it
is now one of the hot topics in the condensed
matter physics how to synthesize and characterize the Kitaev-like materials.
The Kitaev model under a magnetic ﬁeld has
been intensively studied, because the magnetization processes oﬀer useful information forcharacterizing the nature of the quantum spin
liquid in the Kitaev model. Recently, it wasreported that an intermediate gapless state
appears in the antiferromagnetic coupling Kitaev honeycomb model under a magnetic ﬁeld.
For example, exact diagonalization (ED) calculations showed that the magnetization curve
has two abruptly changes by increasing theﬁeld[3, 4]. This feature was observed by othernumerical methods such as the density matrix
renormalization group (DMRG)[5] and Majorana mean-ﬁeld (MF) theory[6]. However, ED
and DMRG studies were done in small system size and quasi-one-dimensional system on
cylindrical boundary condition, respectively.
It is desired to perform accurate analysis basedon a numerical calculation method applicableto the large two-dimensional system.
In this study[7], by using the variational

Monte Carlo (VMC) method, we investigate
whether the intermediate state exists as theground state of the Kitaev model in two dimensions in a [001] magnetic ﬁeld. We used a generalized Bardeen-Cooper-Schrieﬀer trial wavefunction with Jastrow factor, which can exactly represent the ground state of the pure Kitaev model fermionized by the Jordan-Wignertransformation[8, 9]. Our benchmark for asmall system show that this trial wavefunction well reproduces the exact magnetization
process. In applications to the antiferromagnetic Kitaev model with large system sizes, adouble-peaked structure is found in the magnetic susceptibility, which signals the existenceof the intermediate phase. In the intermediate strength of the magnetic ﬁeld, we ﬁnd thatthe local Z2 gauge ﬁeld takes non-integer values, which is consistent with the spin liquid
phase with ﬂuctuating ﬂux for [111] case. Our
results also show that the momentum distribution of the complex fermions changes topologically at the ﬁrst transition point, suggesting that this is a topological phase transition
resembling the Lifshitz transition. We cannot ﬁnd these properties in the ferromagnetic
Kiteav model. Our results show that in theantiferromagnetic Kitaev model, the intermediate state is stable against many-body correlations beyond the MF approximation.
Our VMC results also suggest that it is a
useful and accurate way to analyze the Kitaev
model in a magnetic ﬁeld by using fermionization of the localized spin diﬀerent from the262

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

spinon representation. Using other types of thefermionizations, it would be possible to accurately analyze the magnetization process of theKitaev model with additional interactions suchas the Heisenberg term and the Γ term within
the framework of VMC. Our study oﬀers a ﬁrm
basis for such extended treatments.
In addition, we have proposed how to calculate the charge (density) dynamical structure
factors for the ground states of correlated electron systems based on the VMC method[10].
It is a future issue to study complex fermion
dynamics of quantum spin liquids by using our
proposed method.

References[1] A. Kitaev: Ann. Phys. 321 (2006) 2.
[2] G. Jackeli and G. Khaliullin: Phys. Rev.
Lett. 102 (2009) 017205.
[3] Z. Zhu, I. Kimchi, D. N. Sheng, and L.
Fu: Phys. Rev. B 97 (2018) 241110(R).
[4] C. Hickey and S. Trebst: Nat. Commun.
10 (2019) 530.
[5] M. Gohlke, R. Moessner, and F. Pollmann: Phys. Rev. B 98 (2018) 014418.
[6] J. Nasu, Y. Kato, Y. Kamiya, and Y. Motome: Phys. Rev. B 98 (2018) 060416(R).
[7] K. Ido, and T. Misawa: Phys. Rev. B 101(2020) 045121.
[8] H.-D. Chen and Z. Nussinov: J. Phys. A
41 (2008) 075001.
[9] X.-Y. Feng, G.-M. Zhang, and T. Xiang:
Phys. Rev. Lett. 98 (2007) 087204.
[10] K. Ido, M. Imada, and T. Misawa: Phys.
Rev. B 101 (2020) 075124.

263

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

A new block-spin transformation in Potts models
Yusuke TOMITA
College of Engineering, Shibaura Institute of Technology
Saitama, Saitama 337-8570

Magnetic susceptibilities for 2D Potts models through the new block-spin transformation are shown in Fig. 1. The original system size is 8192. Slopes of lines in Fig. 1 are
drawn by using exact critical exponents, γ/ν’s.
The result indicates the new transformation
rule works well for each q-state Potts model.
While the newly proposed transformation utilizes the fractal property of Kasteleyn-Fortuin
cluster on critical points, I also examined
the renormalization properties at oﬀ-criticalpoints. Figure 2 shows numbers of clusters forthe 2D Ising model for T = 0.95 × Tc , Tc , and1.05 × Tc . At the critical point, the number ofclusters is well ﬁtted by a power function withexponent 4/(2 − β/ν). On the other hand, thenumbers of clusters at oﬀ-critical points suddenly drop at some block-spin transformation
steps. A renormalized cluster expands almost
whole the system at a some ﬁnite renormalized
step when the temperature is lower than thecritical temperature, while all of the clusters
disappear at a some ﬁnite renormalized stepwhen the temperature is higher than the critical temperature. Therefore, we can estimate
critical points by the linearity of the numberof clusters.
107

q⟨1

106

q⟨2

q⟨4

q⟨3

⟨χ⟩

105
104
103
102
101
100

213211 29 27 25 23 21213211 29 27 25 23 21213211 29 27 25 23 21213211 29 27 25 23 21

L

Figure 1: Plot of the susceptibilities for the
2D Potts models. Slopes of lines are drawn by
using exact critical exponents, γ/ν

107

T ⟩ TcT ⟩ 0⟨95 × Tc
T ⟩ 1⟨05 × Tc

106
105
104

⟨nc ⟩

In usual block-spin transformation, the majority rule is mainly used as a renormalization
scheme. Many studies using the block-spintransformation have shown that spin conﬁgurations are well renormalized well by the majority rule. But the legitimacy of the majority
rule has not been understood. In this study,
I propose a block-spin transformation rule,
which utilizes the fractality of the KasteleynFortuin cluster on the critical point. The
new block-spin transformation is constructedto conform Kasteleyn-Fortuin clusters to theusual ﬁnite-size scaling form, L−β/ν .

103
102
101
100
10−1

213

211

29

27

L

25

23

21

Figure 2: Plot of the numbers of clusters forthe 2D Ising (q = 2) models. A slope of line isdrawn by using exact critical exponents, 4/(2−
β/ν)

264

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Screening for Thermal Functional Materials using Materials
Informatics
Junichiro SHIOMI
7-3-1, Hongo, Bunkyo-kun, The University of Tokyo, Tokyo 113-8656
Controllingthethermalconduction, the overlap results in the higher

boundary

conductance (TBC) between copper and carbon

value

in

TBC

compared

crystals is important since it can bottleneck thecopper/diamond interface.

with

the

thermal conductivity when reinforcing copper

To improve the TBC at the copper/diamondwith carbon-crystals fillers, namely diamond orinterface, the covalently bonded SAMs withgraphite, to develop heat sinks and spreadersdifferent chain lengths are installed at theneeded for the thermal management. In the work

interface. The resultant values of TBC withof this year [1], we demonstrate the spectral

SAMs of various chain lengths are plotted in Fig.

control of TBC between cooper and carbon

2. The data at n=0 refers to the TBC at

crystal by self-assembled monolayers (SAMs)

copper/diamond and copper/graphite interfaces

using the non-equilibrium molecular dynamics

without SAMs. For the chain length studied insimulation.

this work, the value of TBC increases
formonotonically with the chain length for chaincopper/diamond and copper/graphite interfaces

length shorter than C15 and reaches a plateau

are 9.06 ± 0.16 MW/m2K and 81.76 ± 14.85

afterward. The highest value of TBC approaches

MW/m2K, respectively. The result indicates theto that of bare copper/graphite interface.

The

resultantvaluesofTBC

TBC at copper/graphite interfaces is almost anorder of magnitude greater than that at
copper/diamond interface. In order to interpretthe behavior, the vibrational density of states(VDOS) of copper/diamond and copper/graphite
interfaces are calculated, as shown in Fig. 1. The
result indicates the out-of-plane VDOS ofgraphite surface provides the overlap in phonon

Fig. 1: Vibrational density of states of various

vibrational modes with that of copper surface. In

components of (a) copper/diamond and (b)view of elastic energy transport, which is usuallycopper/graphite interfaces.

the main contribution to interfacial heat265

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

useful to improve the thermal conductivity ofmetal/carbon-crystal composite materials in theindustry applications.
In summary, we have demonstrated (1) thepoor TBC at cooper/diamond interface is mainly
due to the mismatch of VDOS between cooper
Fig. 2: Thermal boundary conductance as aand diamond (2) the installation of SAMs atfunction of chain length of SAMs. n=0 refer tocooper/diamond interface can improve the TBC

the interfaces without SAMs.

significantly.

The TBCshowsastrongdependence on chain length that the TBC
increases with the increasing chain length for

Both the spectral and structural analysis arethechain length shorter than C15 and reaches aunderlying mechanism. The analysis identifies

plateau afterward. The materials informatics

that this is because the SAMs becomes softer

technique will be helpful for the design of SAMs

with increasing chain length due to disordering

toof the collective SAMs structure, enhancing themetal/carbon-crystal composite materials.

implemented

tofurtherunderstandenhancethethermalconductivityofspectral overlap with copper at low frequency
vibrational modes. In the future, the materials

References

informatics techniques can be conducted to find[1] S.-W. Hung, S. Hu, and J. Shiomi, ACS Appl.

out the optimum design of SAMs to enhance theElectron. Mater. 1 (2019) 2594.

interfacial heat transfer. The obtained results are

266

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Wave function analyses in disordered electron
systems
TOMI OHTSUKI1
TOHRU KAWARABAYASHI2
KEITH SLEVIN3
KOJI KOBAYASHI4
TOMOHIRO MANO1
1) Dept. Phys., Sophia University, Chiyoda-ku, Tokyo 102-8554, Japan
2) Dept. Phys., Toho University, Miyama 2-2-1, Funabashi 274-8510, Japan
3) Dept. Phys., Osaka University, Toyonaka, Osaka 560-0043, Japan
4) IMR, Tohoku University, Sendai 980-8577, Japan

Recent discoveries of Weyl semimetal(WSM) have inspired extensive research ofthese novel topological materials, especiallyfrom the point of the new universality classes,
which has discrete symmetries such as particlehole symmetry. Here we have studied the Anderson transition in chiral orthogonal class aswell as class BDI, the latter showing the nodalline Weyl semimetal phase[1]. We have alsostudied the various quantum phase transitions
by analyzing the wave functions via convolutional neural network (CNN) [2]. The typicalwave functions in disordered quantum systems
are shown in Fig. 1. The method is especially powerful when analyzing the quantum
percolation, where the transfer matrix method
breaks down due to the irregular lattice structure. We have trained CNN to capture the features of wave functions in topological as well
as nontopological phases, and let CNN draw
the phase diagram (Fig.2) [3]. In addition, we
have calculated the distribution of Kondo temperature at the Anderson transition from thelocal density of states obtained by kernel polynomial method[4].
References
1. X. Luo, B. Xu, T. Ohtsuki, R. Shindou: Physical Review B 101, 020202(R), (2020).
2. T. Ohtsuki, T. Mano: Journal of the PhysicalSociety of Japan 89, 022001 (2020).
3. T. Mano, T. Ohtsuki: Journal of the PhysicalSociety of Japan 88, 123704 (2019).

4. K. Slevin, S. Kettemann, T. Ohtsuki: The European Physical Journal B 92, 281 (2019).

Figure 1: Typical 3D wave functions in real
space in various phases. Taken from [2].

Figure 2: Phase diagram of quantum percolation in 3D topological insulator. OI (ordinary insulator), WTI (weak topological insulator), STI (strong topological insulator), andDM (diﬀusive metal).(ijk) indicates the weakindices.

267

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical study on low-energy statesof quantum spin systems
Hiroki NAKANO
Graduate School of Material Science, University of Hyogo
3-2-1 Kouto, Kamigori-cho, Ako-gun, Hyogo 678-1297, Japan

It is diﬃcult to precisely estimate physicalquantities for many-body problems. Particularly, we often have to tackle such manybody problems in condensed matter physics.
Quantum spin systems are typical many-bodyproblems. Under circumstances, numerical approaches have widely and eﬀectively been employed to examine the systems. Many computational investigations have been carried out
and provided us with useful information anddeeper understanding of the target systems.
It is well known that within the field of
quantum spin systems, three methods are effectively used; the numerical diagonalizations,the quantum Monte Carlo (QMC) simulations,and the density matrix renormalization group(DMRG) calculations. Each of them has advantages and disadvantages at the same time.
In the QMC simulations, large systems canbe treated irrespective of their spatial dimensions although it is diﬃcult to obtain precise
evaluations due to the negative sign problem
when the systems include frustrations. On theother hand, the DMRG method is very useful when spatial dimension of a target system
is one irrespective of whether frustrations ispresent or absent in the system. However,this method is still under development for thecases when the spatial dimension is larger thanone. The numerical diagonalization method
can be applied irrespective of the spatial dimension and the presence of frustrations. Unfortunately, this method has a serious weak
point that it can treat only very small systemsizes. As one way to overcome this disadvantage, we successfully developed a hybrid-typeparallelized code of Lanczos diagonalization[1].
If we use this Lanczos-diagonalization code, it268

is possible to treat various large systems thathave not been previously treated yet within
this method. Therefore, we investigate various quantum spin systems by this method asa primary approach.
In the project in 2019, we tackled two systems. The first one is the S = 1/2 Heisenberg antiferromagnet on the kagome latticewith a specific distortion[2, 3]. We investigated a family of materials with Ti3+ S = 1/2
ions forming distorted kagome lattices. Employing all electron density functional theory
technique, the Heisenberg Hamiltonian was established for each material; finite-size clusters
for the Hamiltonians were numerically diagonalized. Our calculations successfully provided
us with the magnetization processes, which enable us to analyze experimental measurements.
The comparisons were quite good; our theoretical calculations succeeded in predicting the
behavior in fields higher than the maximum
field which the present experiments can reachpresently.
The second one is the large-S Heisenberg
antiferromagnet in one dimension[4]. Particularly, we focused our attention on the cases of
S = 5 and S = 6. The case of S = 5 had beenstudied before in Ref. [1] where systems up to
10 sites were treated. We successfully carriedout our huge-scale parallel calculation in the K
computer using approximately 97% of the total computational nodes without any troubles
and obtained novel results up to 14 sites of
the target system. Note also that the Hilbert
space dimension of 14-site cluster for the S = 5
chain is larger than the case of 20-site cluster
for the S = 2 chain[5]. From the new results,
our analysis gave a more precise estimation of

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

the S = 5 Haldane gap. In this study, we also
attempted to estimate the Haldane gap for thecase of S = 6, which had not been examined
before. From our new estimates of the Haldane gaps for large S, the asymptotic formulaof the Haldane gap was examined; we successfully determined the coeﬃcient in the formulamore precisely.
Our studies contribute to our deeper understandings of the various antiferromagnets andthe nontrivial eﬀect of quantum nature andfrustration in magnetic materials.

References[1] H. Nakano and A. Terai: J. Phys. Soc.
Jpn. 78 (2009) 014003.
[2] H. O. Jeschke, H. Nakano, and T. Sakai:Phys. Rev. B 99 (2019) 140410(R)(1-6)[3] R. Shirakami, H. Ueda, H. O. Jeschke,
H. Nakano, S. Kobayashi, A. Matsuo, T.
Sakai, N. Katayama, H. Sawa, K. Kindo,
C. Michioka, and K. Yoshimura: Phys.
Rev. B 100 (2019) 174401(1-7)[4] H. Nakano, N. Todoroki, and T. Sakai: J.
Phys. Soc. Jpn. 88 (2019) 114702(1-4)[5] H. Nakano and T. Sakai: J. Phys. Soc.
Jpn. 87 (2018) 105002(1-2)

269

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Efficient Sampling Simulation of
the Soft Modes Significantly Contribute to Protein Properties
Kazuhiro TAKEMURA, Duy TRAN, Hiroaki HATA, Kenichiro TAKABA,
Mohamed Marzouk SOBEH, and Akio KITAOSchool of Life Science and Technology, Tokyo Institute of Technology
Ookayama, Meguro, Tokyo 152-8550
We have developed a method to evaluate

for efficiently selecting near-native decoys

binding free energy differences of complex

using Best Arm Identification (BAI), called

models generated by docking prediction

evERDock BAI[3].

using the all-atom molecular dynamics
simulation and solution theory in the energy
representation (ER), termed evERdock(evaluation with ER method of docking
generateddecoys)[1].

Byevaluating

binding free energy difference with themethod, we previously showed that “nearnative” models similar to crystal structure
are successfully selected as the lowest
energystructuresinseveralcomplexsystems. The method requires relatively
short MD simulations (2 ns) and cancalculate binding free energy difference
among several hundreds of complex models.
We also reported that refinements ofdocking generated decoys by relatively long
MD simulation and averaging the binding
free

energies

obtainedfrommultiplesnapshots further improved the evaluationof evERdock[2]. However, such treatments
required additional computational costs. To

Fig. 1 Flows of (A) uniform sampling and (B)address this problem, we propose a method

BAI (UCBE) based evaluation.

270

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Let the number of evERdock runs decoys

successfully reduced computational cost by a

are N be M, respectively. If we conduct

factor of 2.20, 1.22, and 4.05 (values in

evERdock runs for all decoys equally

parentheses in Table 1) for 1AY7, 1PPE, and(uniform sampling, US), all decoys are

3SIC, respectively.

evaluated M/N times (Fig.1A). Fig. 1B shows

As shown above, we successfully improved

the flow chart of evERdock-BAI using UCBE

the computational efficiency of the evERdock

as a BAI algorithm. After all decoys areevaluation of protein-protein complex models

evaluated once, the algorithm repeatedly

by combining with BAI algorithm.

calculates UCBE scores, selects the decoy
with

the

highestscore,

andconducts

evERdock run for the selected decoy.
Promisingdecoysfor

exploitationareevaluated by the first term of the score(binding free energy, −∆𝐺 ). The second termof the score contains the number of evERdock
runs for the decoy i (ni) in its denominator.
Fig. 2 Structures of target complexesThus, the score decreases as the number of
evERdock runs for a decoy i increases. As a

Table 1 Summary of results

result, unpromising decoys are sometimes

Complex
NdecoysNnear-native
N95% (US)
N95% (UCBE)

selected, and exploration is realized. Such abalance between exploitation and exploration
is essential to achieve an efficient and

1AY7
11
2
33
15 (2.20)

1PPE
11
4
33
27 (1.22)

3SIC
21
1
336
83 (4.05)

accurate prediction of the correct decoy.
WeappliedevERdock-BAI

to

three

References

protein-protein complex systems (Fig. 2).

[1] K. Takemura, N. Matubayasi, and A.

Decoys are generated by rigid-body dockings.

Kitao, J. Chem. Phys. 148, 105101 (2018).

The number of decoys (Ndecoys), the number of[2] A. Shinobu, K. Takemura, N. Matubayasi,

near-nativeand A. Kitao, J. Chem. Phys. 149,

decoys(Nnear-native),

and

the

number of total evERdock runs to achieve a

195101 (2018).

prediction accuracy 95 % (N95%) using US[3] K. Terayama, A. Shinobu, K. Tsuda, K.

and UCBE are shown in Table 1. For all three

Takemura, and A. Kitao. J. Chem. Phys. 151,

cases, N95% using UCBE were smaller than

215104 (2019).

those using US. The UCBE algorithm271

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Pseudo-fermion functional renormalization group
approach for frustrated qunatum spin systems
Kiyu FUKUI, Yukitoshi MOTOME, and Yusuke KATO
Department of Physics, The University of Tokyo, Bunkyo, Tokyo 113-0033
Department of Applied Physics, The University of Tokyo, Bunkyo, Tokyo 113-8656
Department of Basic Science, The University of Tokyo, Meguro, Tokyo 153-8902

Frustrated quantum spin systems have beenstudied intensively for very long time [1, 2].
It is impossible to solve them exactly mathematically in general. Therefore, numericalapproaches to investigate frustrated quantum
spin systems are indispensable. Numerical approaches used widely to study them are, forexample, exact diagonalization (ED), quantum
Monte Carlo (QMC), density matrix renormalization group (DMRG). Each method has pros
and cons, of course. Since 2010s, a new method
called pseudo-fermion functional renormalization group (PFFRG or pf-FRG) has been usedgradually [3]. Although PFFRG overestimatesordering tendencies to magnetic orders [4],it can treat large-size systems and stronglyfrustrated systems and detect quantum paramagnetism due to strong frustration.

nian (1 = Heisenberg Hamiltonian with timereversal symmetry), respectively. Typically,
NL = 10-20, Nω = 50-100, and NΛ = 200500. Therefore, it is necessary to exploit parallelization. We submitted jobs parallelized by
openMP+MPI to F144cpu queue using 64-144
nodes and O(1000) MPI processes. One PFFRG calculation with spin susceptibility calculation with vertices obtained by PFFRG takes
one to several days. In addition, we tried to use
GPU nodes by openACC directives in order toaccelerate our PFFRG calculation.

In order to study quantum paramagnetism,
particularly quantum spin liquid, we made up
a PFFRG numerical code and tested it by reproducing previous studies. At first, we madePFFRG codes for SU(2) symmetrical systems(i.e. systems with Heisenberg-type interactions) [3] and benchmarked it. Then we extended our codes to systems with XXZ-type [4]and Kitaev-type [5] interactions.

[2] H. T. Diep, Frustrated Spin Systems(World Scientific, Singapore, 2013) 2nded.

Computational complexity of PFFRG calculation is scaled by O(NL2 · Nω4 · NΛ · Nσ ). NL ,Nω , NΛ , and Nσ are symmetry-reduced systemsize, the number of frequency mesh points, thenumber of energy cut-oﬀ grid points, and relative complexity due to symmetry of Hamilto-

272

References[1] C. Lacroix, P. Mendels, and F. Mila,
Introduction to Frustrated Magnetism(Springer, New York, 2011).

[3] J. Reuther and P. Wölfle, Phys. Rev. B
81, 144410 (2010).
[4] S. Göttel, S. Andergassen, C. Honerkamp,
D. Schuricht, and S. Wessel, Phys. Rev. B
85, 214406 (2012).
[5] J. Reuther, R. Thomale, and S. Trebst,
Phys. Rev. B 84, 100406(R) (2011).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Precise measurement of crystal nucleation rate in a
hard-sphere colloidal system
Michio Tateno and Hajime Tanaka
Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo
4-6-1 Komaba, Meguro-ku, Tokyo 153-8505

Hard-sphere colloids have been intensively
studied as one of the most fundamental systems that show a liquid-crystal transition [1].
In 2001, Auer and Frenkel pointed out [2]a huge mismatch in the crystal nucleation
rate between results of light scattering experiments and numerical prediction based onMonte Calro simulations using the Umbrella
Sampling method. Revealing the physical origin behind this huge discrepancy is one of
the central issues in this field [1]. Hydrodynamic interactions (HI) among colloids are
viewed as one of the possible factors to cause
the discrepancy since simulation results used
for the comparison completely neglect HI. So
far, two simulation studies based on different
models incorporating HI have been performed
to address this problem. However, these studies reported conflicting results: one concluded
that HI might speed up crystal nucleation [3],whereas the other claimed that HI slows down
it [4].
In this project, we study the crystallization
kinetics of hard-sphere colloids by two simulation methods with HI (Fluid Particle Dynamics method: FPD [5]) and without (Brownian
Dynamics method: BD). By comparing two
results, we can investigate the impact of HI
on the crystal nucleation process. By combining the FPD method with fluctuating hydrodynamics, we have shown that FPD simulations can almost perfectly reproduce the motion of colloids under thermal noise at low volume fractions while retaining statistical mechanical consistency between colloids and asolvent. Furthermore, we have confirmed that
this simulation approach can precisely reproduce the phase separation process of colloidal
suspensions observed by confocal microscopy
measurements without any adjustable parameters [6]. However, crystal nucleation is a rare
event, and thus, the resulting computational
cost is quite high. We have overcome this problem by speeding up our code, utilizing ISSP’s
GPGPU implementation services [7].
According to Ref. [2], the theoretical valuesof I change mainly by a small change in the volume fraction φ: for example, I at φ = 52.8 %differs from that at 53.4% by at least 4 ordersof magnitude. Thus, in order to study the nucleation rate accurately, we need to estimate
the volume fraction φ precisely. To realize this,
we first check the volume fraction dependenceof the virial pressure. In Fig. 1a, we show theresults obtained by BD and FPD together withtheoretical predictions (the Carnahan-Starling
equation of a state in the liquid phase and the
Speedy equation of a state in the solid phase).
Here we can see almost perfect agreement between them, supporting the validity of our numerical simulation methods from the thermodynamic point of view.
Now we turn our attention to a dynamic aspect. Here we examine the volume-fraction dependence of the long-time self-diffusion constant, DL as one of the most fundamental
quantities to characterize colloidal dynamics.
Figure 1b shows the results for FPD and BD,
where we can see that DL deviates from thediffusion coefficient for a free isolated particle

273

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoab

Figure 1: (a) Virial pressure in equilibrium
states. Cross and square symbols represent theresults obtained by BD and FPD simulations,
respectively. Gary curve is the theoretical prediction for a hard-sphere system. (b) Volume
fraction dependence of the long-time diffusion
constant DL scaled by that in the dilute limit
D0 . Cross and circle symbols represent the results obtained by BD and FPD simulation, respectively. The light blue square symbols areexperimental data obtained by dynamic lightscattering measurements for hard-sphere-likecolloids with 5 % polydispersity [8].
D0 for large φ, but the deviation is more significant for FPD than for BD, which depends
on the presence or absence of hydrodynamic
interactions. For example, we can see that
DL in BD is approximately four times larger
than that in FPD at φ = 0.54. In the figure, we also compare the simulation resultswith experimental data obtained by dynamic
light scattering measurements for hard-spherelike colloids with 5 % polydispersity [8]. Here
we can see that there is a mismatch between
FPD and BD, but there is a good agreement
between FPD and the experimental results atleast at intermediate volume fractions. To determine the nucleation rate I, we used an approach to monitor the temporal change of acluster with the largest size. We compare I at
0.54 ≤ φ ≤ 0.545 between BD and FPD, by
using DL and the diameter of colloids as spatiotemporal units, and find that all nucleation
rates collapse onto a single curve.

time diffusive dynamics of the colloids is more
rapidly slowed down by HI with increasing volume fraction. We find that this long-time diffusion controls the nucleation rate and that it
is possible to account for most of the effectsof HI by rescaling with this time scale. The
research results are summarized in Ref. [9].

References[1] T. Palberg: J. Phys. Cond. Matt. 33(2014) 333101[2] S. Auer and D. Frenkel:(2001) 1020

Nature 409[3] M. Radu and T. Schilling:(2014) 26001

EPL 105[4] D. Roehm, S. Kesselheim and A. Arnold:
Soft matter 10 (2014) 30[5] H. Tanaka and T. Araki: Phys. Rev. Lett.
85, (1999) 1338; A. Furukawa and H.
Tanaka: Phys. Rev. Lett. 104, (2010)
245702; A. Furukawa, M. Tateno and H.
Tanaka: Soft Matter 14 (2018) 3738
[6] M. Tateno and H. Tanaka: npj Comput.
Mater. 5 (2019) 40[7] M. Tateno, K. Takae and H. Tanaka,“GPGPU implementation of Fluid Particle Dynamics method”, Activity Reportin 2017[8] P. N. Segre and S. P. Meeker, P.N. Pusey
and W. C. K. Poon: Phys. Rev. Lett. 75(1995) 958[9] M. Tateno, T. Yanagishima, J. Russo, and
H. Tanaka: Phys. Rev. Lett. 123, (2019)258002In summary, to examine the influence of HI
on crystallization kinetics of hard-sphere colloids, we precisely compare simulation resultswith and without HI. We show that the long-274

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Impact of hydrodynamic interactions on colloidal
dynamics near a critical point
Michio Tateno and Hajime Tanaka
Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo
4-6-1 Komaba, Meguro-ku, Tokyo 153-8505

The behaviors of simple liquids near a critical point are well-understood both from a theoretical and experimental point of view. The
density fluctuation decays exponentially withsingle relaxation time. Contrary to this knowledge, several studies on colloidal suspensions
using light scattering experiments report thattime correlation function of concentration fluctuations in the vicinity of the critical pointshow nonexponential decay [1].
The central aim of this project is to reveal
the physical mechanism underlying the nonexponential decay. As a possible candidate tobring about this unconventional dynamical behavior in colloidal suspensions, we focus on hydrodynamic interactions (HI), which is an essential difference between simple liquids andcolloidal suspensions. We use two different
simulation methods; the Brownian dynamics(BD) method neglecting HI and Fluid particle
dynamics (FPD) method incorporating HI [2].
We compare the results from two simulation
methods and aim to examine the effect of HI
on dynamical critical phenomena.
In order to capture dynamical critical phenomena numerically, a long time simulation isrequired, since the relaxation time for density
fluctuation grows dramatically as approaching
to a critical point. However, FPD method isnumerically costly because it is based on the direct computation of Navier-Stokes equations.
To overcome this, we implemented GPU on
our FPD codes utilizing a service provided by
ISSP. To further suppress numerical cost, weFigure 1: Temperature-volume fraction phase
diagram. The cross symbols show the gas andliquid phases. The black line represents thetieline, which is obtained from asymptotic behavior of median between two phases (square)
towards the vertex of binodal line. We fit aparabolic function to the cross symbols withvolume fraction and tieline as two axis, anddetermine the critical point (circle).

adopt a rather short-range interaction. Morespecifically, we use the modified Lennard-Jones
potential with cutoff length rc = 1.7σ: U (r) =4((σ/r)24 − (σ/r)12 + c2 (r/σ)2 + c0 ) for r < rc
and U (r) = 0 for otherwise. Here c2 and c0 are
constants to satisfy U (rc ) = 0 and U 0 (rc ) = 0.
This short-range nature of intercolloid potential suppresses the correlation length of density fluctuations and allows us to perform simulations with a rather small system size (L =17.3σ).

275

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyoab

Figure 2: The correlation length ξ (a) and susceptibility χ (b) as a function of critical parameter  := Tc /(T −Tc ). The red line represents a
power-law function with critical exponent (approximately 0.62 and 1.24 for ξ and χ, respectively)

correlation function decays exponentially witha single time τξ scale, and τξ is proportional
to the cube of ξ, which coincides with the caseof dynamical critical phenomena for simple liquids.
In summary, we performed numerical simulations for colloidal suspensions with and without HI and examined the effect of HI on the dynamical critical phenomena. We obtained theresults that HI does not influence both staticand dynamical behaviors. However, due to theconstraint by numerical cost, the critical parameter that we accessed is limited (0.05 < ),and the anomaly in the time correlation function of concentration fluctuations is reported
in a smaller . To make a definitive conclusion
for this phenomenon, we realize a much larger
simulation.

References[1] J. Rouch, et al.: Phys. Rev. Lett. 71,(1993) 1947; B. M. Fine, et al.: Phys. Rev.
Lett. 74, (1995) 198; B. M. Fine, et al.:J. Chem. Phys., 104, (1996) 326[2] H. Tanaka and T. Araki: Phys. Rev. Lett.
85, (1999) 1338

We study the static behavior of colloidal suspensions near a critical point. We perform
simulations for states on tieline (see the blackline in Fig. 1) approaching to a critical point(red circle point). Figure 2 shows the correlation length ξ and susceptibility χ, which is determined by fitting the static structure factor
with the Ornstein-Zernike form. Here we cansee that the two results obtained from BD and
FPD show an excellent agreement with eachother, and both follow to power-law function
with the critical exponent. These trends are
consistent with a well-known fact that HI does
not influence the thermodynamic behaviors of
colloidal suspensions. Next, we compute theauto-correlation function of density fluctuationand evaluate the dependence of lifetime on thecritical parameter . We find that the auto-

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Coarsening mechanism of network-forming phaseseparation in colloidal suspensions
Michio Tateno and Hajime Tanaka
Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo
4-6-1 Komaba, Meguro-ku, Tokyo 153-8505

Phase separation is one of the most fundamental physical phenomena in nature to form aspatially inhomogeneous structure, whose basic coarsening laws were well-established in
the 20th century. However, the conventional
mechanisms are valid only near the criticalpoint, and the coarsening behavior under deep
quench remains elusive. We noticed that for
network-forming deeply-quenched phase separation, unusual coarsening behavior of network
structures had been reported in experimentsfor various soft matter such as colloidal suspensions [1], protein solutions [2] and lyotropic
liquid crystal [3]: their characteristic network
size ` commonly grows as ` ∼ t1/2 while retaining their connectivity. The goal of this projectis to reveal the physical principle behind thegrowth exponent 1/2.
To address this problem, we used a hydrodynamic simulation model for colloidal
suspensions, Fluid Particle Dynamics (FPD)
method [5], which is based on the direct computation of the Navier-Stokes equation, andstudied network-forming process during gasliquid phase demixing. To capture the coarsening of network structure without suffering froma finite-size effect, we developed GPU-MPI hybrid codes utilizing a service provided by ISSP
and realized a large scale simulation. Since ourinterest is in phase separation dynamics undera deep quench, we neglect thermal noise.
We show in Fig. 1 the time evolution ofphase-separation structures in the colloidal
suspension. Here we can clearly see that aspace-spanning network structure is spontaneously formed in the early stage, and its characteristic length scale grows afterward. By
computing the temporal change of the first moment of the structure factor, we confirmed thatthe characteristic length of network structure `follows a power-law growth with exponent 1/2
while retaining self-similarity.
In the absence of thermal noise at zero temperature, the coarsening cannot be due to thermal activation but should be of purely mechanical nature. Then, we focus on the slow elastic
dynamics of dense colloidal aggregates and analyze the strain field  by coarse-graining thedisplacements of colloidal particles. Here inparticular, we consider the time evolution of
the distribution function, P (), from a reference time t0 to an arbitrary time t0 + t0 . We
find that the distribution functions are collapsed onto a master curve after scaling theargument  by t0 /t0 (see Fig. 2), indicating thatthe elastic relaxation of network structure controls the speed to the coarsening process.
Here we note that the exponent 1/2 is observed only in the presence of solvent component: for example, the Brownian dynamics
method completely neglecting the motion of asolvent does not reproduce the exponent 1/2(see, e.g., Ref. [4]). This fact implies that dynamic coupling between densely-packed colloid
and a solvent saturated in the colloid-rich domain plays a crucial role. Biot’s poroelastic
theory is known as a model to describe themotion of fluid saturated elastic materials. By

277

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: Coarsening behavior of network-forming phase separation of colloidal suspensions.
Particles are colored to distinguish front particles from back ones.
and the domain grows with the growth exponent of 1/2. We revealed that the exponent is
a consequence of slow elastic relaxation of the
network-forming dense phase, whose limiting
process is permeation flow of the solvent.

References[1] H. Tanaka, et al., J. Phys.: Condens.
Matter, 17, (2005) L143: A. Bailey, etal.: Phys. Rev. Lett. 99, (2007) 205701:
M. Tateno and H. Tanaka, npj Comput.
Mater., 5, (2019) 40

Figure 2: P () after scaling  by t0 /t0 . The
data are sampled from the data whose reference time is t0 = 31.0 (blue), 46.5 (green),
62.0 (brown).
Then, cross, triangle andsquare symbols represent the data at t0 /t0 =0.001, 0.01, 0.02, respectively.

performing a scaling analysis on this theory, we
obtain a coarsening law, ` ∼ (Dp t)1/2 , where
Dp is a poroelastic diffusibility. See Ref. [6] forfurther discussion on the validity of the coarsening law.

[2] H. Tanaka and Y. Nishikawa: Phys. Rev.
Lett., 95, (2005) 078103[3] Y. Iwashita and H. Tanaka: Nat. Phys.,
5, (2006) 147[4] A. Furukawa and H. Tanaka: Phys. Rev.
Lett. 104, (2010) 245702.
[5] H. Tanaka and T. Araki: Phys. Rev. Lett.
85, (1999) 1338
[6] M. Tateno and H. Tanaka: Nat. Commun., under review.

In summary, we performed a large-scale hydrodynamic simulation for colloidal suspensions and studied the dynamic process of
network-forming phase demixing. We foundthat the coarsening process has self-similarity,

278

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Structural origin of glassy slow dynamics
Hua Tong and Hajime Tanaka
Department of Fundamental Engineering, Institute of Industrial Science, University of Tokyo
4-6-1 Komaba, Meguro-ku, Tokyo 153-8505

Despite the use of glasses for thousandsof years, the nature of glass and the glasstransition remains probably “the deepest andmost interesting unsolved problem” in condensed matter physics and materials science.
In contrast to crystallization where the solidity emerges as a result of the formation of
long-range periodic order, the drastic dynamical slowing down toward the glass transition isaccompanied by little change in the geometricstructure, as measured by two-point correlators accessible through diffraction and scattering experiments [1, 2]. Therefore, glasses arewidely thought as the epitome of completely
disordered state of materials and the glasstransition is described as a purely dynamical
phenomenon in kinetically constrained models.
The physical scenarios which posit a growing
static order and hence a thermodynamic origin behind the slowing down of glassy dynamics have regained popularity since the discovery of the so-called dynamic heterogeneity in
1990s. The spatially correlated domains whichmove significantly faster or slower than the average are proposed to be the long sought-after
cooperatively relaxing regions (CRRs), whichis the core concept of Adam-Gibbs theory ofglass transitionand its modern version, i.e., therandom first-order transition (RFOT) theory.
Meanwhile, a growing correlation length characterizing the extent of heterogeneous dynamics is also suggestive of a similarity between
glass transition and the critical phenomena [3–5]. However, since the dynamic heterogeneity
is only accessible through dynamic variables[6, 7], the crucial physical mechanism is still
not established, namely a quantitative characterization of the glassy structural order andits link to dynamics, which precludes a decisive279

underpinning to the (thermodynamic) natureof the glass transition.
To look for key structural features responsible for glassy dynamics, one typical approach is
to consider specific physical aspects of the local
atomic environment, e.g., free volume, potential energy, and symmetry. The free volume
approach [8, 9] and the inherent potential energy based on the potential energy landscape(PEL) formalism enjoyed early success showing a clear macroscopic correlation (that is,for globally averaged quantities) with dynamics, but not microscopically at a particle level[10–12]. Therefore, more efforts have been devoted to the identification of locally favored
structures (LFSs) based on symmetry considerations. For instance, icosahedral [13, 14],
crystal-like orders [3, 4, 15], or more complicated topological clusters [16] are identified
and suggested as the origin of slow dynamics
in different glass-forming liquids. However, thegeneral relevance of LFSs in glassy slow dynamics remains controversial due to its strong
and sensitive system dependence. This may
arise from the system-dependent nature of locally low free-energy configurations [4]. Another approach developed by Cubuk et al. recently is to define some structural quantity,“softness”, based on machine-learning methods [17, 18]. The strong correlation observed
between softness and structure relaxation suggests that important structural features arecaptured. However, softness is defined in ahigh-dimensional space with more than 100
structure functions, prohibiting a clear identification of glassy structural order. It is desirable to unveil the structural characteristics ofglass-forming liquids from a physically inspired
perspective.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Recently in ref. [12], we constructed a setof structural order parameters, namely Θ in
2D and Ω in 3D , to capture sterically favored structures with high local packing capability in hard-sphere-like glass formers. In
the absence of obvious density fluctuations beyond the particle scale, such sterically favored
structures provide more room for particle motions through better arrangement, and hence
higher correlational (or, vibrational) entropy
and lower free energy [4]. This is analogous tothe crystallization process of hard spheres. We
showed at a picture level that the mobility develops systematically following the structuralorder parameter field and confirmed a common
structural origin for both fast β and slow α dynamics.
In this study, we move a crucial step forward to study quantitatively the formation of

structural order and its relation to slow glassy
dynamics. We find that the degree of glassy
structural order follows a linear scaling law
with temperature, which initiates around theonset temperature Ton of the super-Arrhenius
dynamics and is ceased by the dynamical glasstransition Tg . This provides us with a direct
quantitative relation between structural orderand structure relaxation time τα , and therefore represents a key thermodynamic characteristic of the glass transition. More interestingly, based on a nonlocal excitation scenario,
we confirm that such an intimate structuredynamics correlation is valid even microscopically at a particle level. Therefore, our results may provide an essential piece in the microscopic theoretical description of the longstanding glass transition problem from a structural perspective.

[1] J. C. Dyre, Rev. Mod. Phys. 78, 953 (2006).
[2] K. Binder and W. Kob, Glassy materials anddisordered solids: An introduction to their statistical mechanics (World Scientific, 2011).
[3] H. Tanaka, T. Kawasaki, H. Shintani, andK. Watanabe, Nature Mater. 9, 324 (2010).
[4] H. Tanaka, Eur. Phys. J. E 35, 113 (2012).
[5] J. S. Langer, Phys. Rev. E 88, 012122 (2013).
[6] M. D. Ediger, Annu. Rev. Phys. Chem. 51, 99(2000).
[7] L. Berthier and G. Biroli, Rev. Mod. Phys.
83, 587 (2011).
[8] M. H. Cohen and G. S. Grest, Phys. Rev. B
20, 1077 (1979).
[9] F. W. Starr, S. Sastry, J. F. Douglas, and S. C.
Glotzer, Phys. Rev. Lett. 89, 125501 (2002).
[10] A. Widmer-Cooper and P. Harrowell, Phys.
Rev. Lett. 96, 185701 (2006).
[11] A. Widmer-Cooper and P. Harrowell, J. Non-

Cryst. Solids 352, 5098 (2006).
[12] H. Tong and H. Tanaka, Phys. Rev. X 8,011041 (2018).
[13] F. C. Frank, Proc. R. Soc. Lond. A 215, 43(1952).
[14] P. J. Steinhardt, D. R. Nelson, and
M. Ronchetti, Phys. Rev. B 28, 784 (1983).
[15] M. Leocmach, J. Russo, and H. Tanaka, J.
Chem. Phys. 138, 12A536 (2013).
[16] C. P. Royall and S. R. Williams, Phys. Rep.
560, 1 (2015).
[17] E. D. Cubuk, S. S. Schoenholz, J. M. Rieser,
B. D. Malone, J. Rottler, D. J. Durian,E. Kaxiras, and A. J. Liu, Phys. Rev. Lett.
114, 108001 (2015).
[18] S. S. Schoenholz, E. D. Cubuk, D. M. Sussman, E. Kaxiras, and A. J. Liu, Nature Phys.
12, 469 (2016).

280

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Universality of bulk-edge correspondence bynumerical methods
Y. Hatsugai
Department of Physics, University of Tsukuba
1-1-1 Tennodai, Tsukuba 305-8571, Ibaraki, JapanOne of the key concepts of the topological phases is the bulk-edge correspondence, that relates
non-trivial topology of the bulk to the low energy physics near boundaries or impurities[1]. Nontrivial bulk topology is hidden for low energy physics of the bulk and most of the characteristic
and experimental features appear as generalized edge states living near the boundaries. Although
its historical example is a quantum phenomenon (quantum Hall eﬀect), its validity is much
more universal and the concept is applicable even for non-quantum phenomena such as photonic
crystals of classical electromagnetic ﬁeld and even classical mechanics of periodic systems. Usinga formal analogy among the various systems, one can deﬁne a Berry connection for the bulk
(even for the classical systems). Although there is no physical, at least, direct meaning forthe topological quantities based on the Berry connection, the edges states predicted by thebulk-edge correspondence are physical observables. Such a hidden Berry connection of thebulk and topological numbers support the edge states of various physical phenomena. This is
the universality of the bulk-edge correspondence, which we numerically try to establish in the
project.
The corner states of the higher order topological phases are such generalized edge states whichcharacterize the speciﬁc bulk topology reversely. We have shown such examples supported by
the quantized ZN (n ∈ Z) Berry phases as a bulk topological invariants for a quantum three
dimensional model [2] and classical mechanics on a Kagome lattice[3]. We have further proposeda higher order topological Mott insulator that hosts spin-charge separated corner states anddemonstrated its validity numerically[4].
We also performed a topological characterization of the J1 − J2 spin ladder for higher integer
spins using a quantized Berry phases[5]. It justiﬁes a generalized valence bond solid state as
the adiabatic limit of the ground state obtained numerically. Then sequential topological phasetransitions associated with the valence bond reconstruction are clearly demonstrated.
We further discussed several other topics related such as non hermitian topological phenomena[6,7, 8, 9] and obtained new insight for the adiabatic heuristic argument[10] that is a conceptual/historical background of topological characterization.

References[1] Yasuhiro Hatsugai, Phys. Rev. Lett. 71, 3697 (1993).
[2] Hiromu Araki, Tomonari Mizoguchi and Yasuhiro Hatsugai: Phys. Rev. Research 2,
012009(R) (2020).
[3] Hiromasa Wakao, Tsuneya Yoshida, Hiromu Araki, Tomonari Mizoguchi, and Yasuhiro
Hatsugai: Phys. Rev. 101, 094107 (2020).
[4] Koji Kudo, Tsuneya Yoshida, and Yasuhiro Hatsugai : Phys. Rev. Lett. 123, 196402 (2019).

281

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: (a) Schematic lattice structure of the three dimensional BBH model, (b) corner statesand (c) Z4 Berry phases (See. Ref.[2] )Figure 2: (a) J1 − J2 Heisenberg spin chain of integer S(≥ 1) and (b) Z2 Berry phase of S = 4(8 site system with periodic boundary condition) (See Ref. [5] )[5] Shota Fubasami, Tomonari Mizoguchi and Yasuhiro Hatsugai: Phys. Rev. B 100, 014438(2019).
[6] Tsuneya Yoshida, Koji Kudo, and Yasuhiro Hatsugai: Scientiﬁc Reports 9, 16895 (2019).
[7] Tsuneya Yoshida and Yasuhiro Hatsugai: Phys. Rev. B 100, 054109 (2019).
[8] Tsuneya Yoshida, Robert Peters, Norio Kawakami, Yasuhiro Hatsugai: arXiv:2002.11265[9] Tsuneya Yoshida, Tomonari Mizoguchi, and Yasuhiro Hatsugai: arXiv:1912.12022[10] Koji Kudo and Yasuhiro Hatsugai : arXiv:2004.00859.

282

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Kinetics of phase transition and polyamorphism
Kazuhiro Fuchizaki, Kei Watanabe, and Hiroki Naruta
Department of Physics, Ehime University, Matsuyama 790-8577

In FY2019, we have undertaken two subjects, as reported brieﬂy below. The ﬁrst task
has been almost completed, and its full reportwill soon be submitted elsewhere. The second
one is still at a preliminary stage and will be
ongoing in FY2020.
Growth of density fluctuations at the beginningof a phase separation
The concept of spinodal has been examined
for an Ising system [1]. However, no explicit
discussion has been found for a ﬂuid system,
which is believed to belong to the same unitary class. Ushcats has suggested [3], extending the equation of state beyond the thermodynamically stable region, that the spinodal line of the modiﬁed Lennard-Jones (mLJ)
system [2] approaches the liquid-gas coexistence (binodal) line. Our prediction based on
the coarse-graining limit for the coarse-grained
free energy, estimated by applying the blockspin coarsening technique, supports Ushcats’
conjecture [4]. It is then highly anticipatedthat the “dynamics” of a system also depends
on a coarsening level.
We conducted isothermal–isobaric molecular
dynamics (MD) simulations for an mLJ system
consisting of 4 × 106 particles to examine thedynamical process of liquid–gas phase separation. Length, time, and temperature are ex√pressed in units of σ, mσ 2 /ϵ, and ϵ/kB [5],respectively, where σ and ϵ are the fundamental length and energy scales of the mLJ potential function and kB denotes Boltzmann’s constant. The critical temperature, pressure, anddensity of the mLJ system are Tc = 1.0762(2),pc = 0.09394(17), and ρc = 0.331(3), respectively. We treated two systems with diﬀer-

283

Figure 1: The peak position of SL is plotted against time with the same color for every
coarsening scale of L. Those at ρc (0.02) aredelineated by solid (dotted) lines.

ent density; 0.02 and ρc . The ﬂuid systemwell-equilibrated at 20Tc was instantaneously
brought to 0.7Tc to undergo phase separation.
The lower- and critical-density systems were
expected to be quenched in the metastable andunstable regions, respectively, judging fromthe shape of the coarse-grained free energy.
The term, “local density,” has been quite
often used in mesoscopic descriptions. However, it has been far unclear what is meantby “local.” In this case, we can deﬁne the local density unambiguously using the length L,
the coarse-graining scale based on which thecoarse-grained free energy was deﬁned [4].
Based on this well-deﬁned “local” density
and its ﬂuctuations around the average density, we deﬁned the structure factor SL . Figure 1 shows the time evolution of SL after
quenching. On the short-time side (t < 2),
L predominantly determines the peak positionof SL , whereas it approaches the value determined by the average density on the long-timeside (t > 2).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

To examine in detail the L-dependence of
the wavelength at which structural destabilization occurs, SL was scaled by its peak
position and height. The dynamical process
in another state, obtained by quenching thecritical-density system to 0.97Tc , was also examined. We could identify in the short-time
region the new universal process (Figure 2), in
which phase separation proceeds in a statistically self-similar fashion irrespective of the average density, quenching temperature as wellas the coarsening length. We name this stage
a “super-early” stage.

assertion.
An isochoric–isothermal MD simulation generated an equilibrated mLJ ﬂuid consisting of2048 particles. We employed such a small number of particles because Goddard et al. used
for a similar size for an LJ ﬂuid [6]. Similarﬁnite-size eﬀects would then be involved in the
results. We chose for this purpose three stateswith density 5.00 × 10−2 , ρc , and 0.600 along
the isotherm 1.001Tc , where Tc is the aforementioned critical temperature of the mLJ system [6]. The density is again expressed interms of the mLJ units.
The entropy of the three states was also calculated using the λ-integration [7], which is too
costly but can give the numerically exact result. The entropies based on the method of
Goddard et al. could not well reproduce theλ-integration based ones. We should undertake a critical review of their basic idea.

References[1] K. Kaski, K. Binder, and J. D. Gunton,
Phys. Rev. B 29, 3996 (1984).
Figure 2: The scaled structure factors at three
diﬀerent states fall into a single curve whenplotted against scaled wavelength, implying
the existence of universality in a phase separation process right after a quench.

[2] Y. Asano and K. Fuchizaki, J. Chem.
Phys. 137, 174502 (2012).

Estimating entropy of a fluid
A method proposed by Goddard et al. [6] hasbeen widely used for evaluating entropy of adisordered system even with such a kind of network structure. The entropy is generally estimated from the density of states (DOS), which
is obtainable through Fourier inversion of thevelocity autocorrelation. Goddard et al. haveclaimed that a DOS of a ﬂuid state can be constructed from those of solid and gas states [6].
This claim does not have any physical basis.
Although an LJ ﬂuid was used to testify theirclaim [6], we employ as another simple liquid
an mLJ system to thoroughly examine their[5] K. Okamoto and K. Fuchizaki, J. Phys.
Soc. Jpn. 86, 034003 (2017).

284[3] M. V. Ushcats, J. Chem. Phys. 141,
101103 (2014).
[4] K. Fuchizaki and K. Watanabe, J. Phys.
Soc. Jpn. 87, 114006 (2018).

[6] S. Lin, M. Blanco, and W. A. Goddard,
J. Chem. Phys. 119, 11792 (2003).
[7] J. Q. Broughton and G. H. Gilmer, J.
Chem. Phys. 79, 5095 (1983).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ground-State Phase Diagram of the S=1/2 Kitaev-G model ona Honeycomb Lattice
Takafumi SUZUKI
Graduate School of Engineering,
University of Hyogo, Shosha, Himeji, Hyogo 670-2280
We have studied the ground-state phase

Next,

we

have

studiedlow-energy

diagram of the S=1/2 Kitaev-G model on a

excitations of an S=1 Ising spin chain with thehoneycomb lattice [1] and quantized DS=2

negative single-ion anisotropy in magnetic

excitation spectra by confinement in an S=1

fields. We have calculated the dynamical

spin chain [2].

structure factor with the infinite time-evolving
bock decimation (iTEBD) method [4]. We haveFirst, we have investigated the ground-statefound that when the transverse magnetic field isphase diagram of the S=1/2 Kitaev-G model on

absent, both a DS=2 excitation continuum anda honeycomb lattice with the numerical exact

one-magnon isolated mode appear in the low-diagonalization method, DMRG and cluster-

lying

series expansion method [3]. By changing theexcitation.

continuum

magnitude of interactions on each bond, the

is

This

DS=2

excitation

quantized

by

the

weak

longitudinal magnetic field. The quantized DSmodel connects with three characteristic points,=2 excitation spectra originate from thewhere the model is described by spin chains,confinement of two domain walls and theisolated dimers, or an isotropic honeycomb-

excitation energies of the quantized DS=2

lattice model. The obtained results havespectra are well explained the negative zeros inclarified that in the spin chain limit, two

the Airy function.

Tomonaga-Luttinger (TL) liquid phases andReferences

three non-TL liquid phases appear when the[1] Y. Yamada, et al., in preparation.

ratio of the Kitaev interaction and the G[2] T. Suzuki and S. Suga, J. Phys. Soc. Jpn. 88

interaction changes. In the dimer limit, the(2019) 053702.

dimerized state with the lowest energy is |tx⟩ =[3] J. Oitmaa, et al., Series Expansion Methods(| ↑↑⟩−i| ↓↓⟩)/ 2, when the positive G interactionforand the negative Kitaev interaction are

Strongly

Interacting

LatticeModels,Cambridge University Press, 2006.

considered. We have found that this |tx⟩ state[4] H. N. Phien, et al., Phys. Rev. B 86 (2012)

can survive up to the isotropic point.

245107.

285

Figure 2 shows a two-component fluid under thermal conduction separated by a semipermeable membrane. The osmotic pressure
is determined from the balance of the chemical potentials in the isothermal state, but the286
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Figure 1 shows a one-dimensional system ofparticles under thermal conduction that interact with each other at the Leonard-Jones potential, and each particle is subjected to a constant external force (gravity). Various local
thermodynamic quantities such as temperature, density, pressure, and chemical potential
were determined by molecular dynamics simulations, and from these quantities the free energy and entropy of the whole system were estimated. The thermodynamic relation is foundto give the free energy change of the whole system when the temperature equivalent to thetotal kinetic energy of the system and the spatial average pressure are adopted as temperature and pressure for the system, respectively.
The equation of state has an additional effectfrom the second order of the external force,
implying a limit to the global view of the thermodynamic system under the external force.
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中間温度<

Figure 1: Heat conduction system under an
本題：これに定常熱流を流す
external force.
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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Macroscopic properties characterized by an extended
thermodynamic functions to nonequilibrium
Naoko NAKAGAWA
Department of Physics, Ibaraki University
2-1-1 Bunkyo, Mito, Ibaraki 310-8512

Thermodynamic functions such as entropy
and free energy play an essential role in equilibrium systems. In order to extend these powerful functions to various non-equilibrium systems, such as thermal conduction systems andexternal force-driven systems, we have performed numerical experiments on the systems
shown in Figs. 1 and 2.

T+2

定常熱流 Jq

Figure 2: Two component fluid separated by asemi-permeable membrane.
局所平衡が成り立つことを仮定して系の定常状態を調べる
11

chemical potentials are not spatially uniform in
the thermal conduction state. In order to explore the principle of determining the osmoticpressure under thermal conduction, molecular
dynamics simulations are performed and thedependence of the osmotic pressure on various parameters is investigated. We used the
LAMMPS in order to achieve efficient results.

References[1] N. Nakagawa and S.-i. Sasa: J. Stat. Phys.
177 (2019) 825.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of data-driven science tomaterials science
Koji Hukushima
Department of Basic Science, University of Tokyo
3-8-1 Komaba, Meguro-ku, Tokyo 153-8902

In recent years, data-driven science methods
have been attracting attention and have been
applied to condensed matter physics and materials sciences. There are two main purposes toanalyze the data obtained as a result of experiments and numerical experiments. One would
be to extract the mathematical structure behind the data, and the other would be to makepredictions to get the next data.
In this project, we carried out the tasks corresponding to the above-mentioned two purposes as actual problems. As the former problem, the model Hamiltonian was estimatedfrom experimental data with a magnetic compound. As an example of the latter problem, we have conducted research on datadriven scientific methodologies in crystal structure search.

interactions or physical quantities are also discussed. These are the advantages of samplingfrom the posterior distribution. The obtained
eﬀective model is useful to predict hard-tomeasure properties such as spin gap, spin configuration at the ground state, magnetic specific heat, and magnetic entropy.
Next, we studied the eﬃciency of Bayesian
optimization as a method of selecting the next
candidate when searching for a crystal structure. Bayesian optimization is a global optimization machine learning technique for a
black-box function that requires a large amountof computation to be evaluated. A crystal
structure is represented by a numerical vector called a descriptor that is used to quantify how similar structures are. This descriptor is an input of the crystal structure searchwith Bayesian optimization. The eﬃciency ofthe optimization significantly depends on the
choice of the descriptor. We evaluated its efficiency with a varying parameter value in thedescriptor[1]. Applying the crystal structure
search to crystalline silicon shows that the efficiency of the search depends heavily on theparameter value. We find that the eﬃciency
is linked to the distribution of the descriptor.
Therefore, we introduce an information measure of the distribution to estimate an appropriate parameter value for performing the crystal structure search eﬃciently. The measure
can also be used to predetermine an appropriate parameter value. The validity of the measure is confirmed with its applications to siliconoxide and yttrium cobalt alloy.

First, we proposed a data-driven methods toextract the spin Hamiltonian with uncertainty
from multiple experiments. Using our method,an eﬀective model of KCu4 P3 O12 is determined from the experimentally observed magnetic susceptibility and magnetization curves
with various temperatures under high magnetic fields. An eﬀective model is the quantum Heisenberg model on a zigzag chain witheight spins in which four independent parameters are contained. Based on Bayesian statistics, these four parameters were estimated using MCMC sampling from the posterior distribution with experimental data as input.
Our method yields that J1 = 8.54 ± 0.51 meV,J2 = −2.67 ± 1.13 meV, J3 = −3.90 ± 0.15
meV, and J4 = 6.24±0.95 meV, describes thesemeasured results well. Evaluation of these error bars is possible only by evaluating noise. [1] N. Sato, et al: Phys. Rev. Materials 4,
The relations among the estimated magnetic (2020) 033801.

287

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Uniﬁed understanding of early-time nonequilibrium
relaxation in Monte Carlo simulations
Yoshihiko NONOMURA
MANA, National Institute for Materials Science
Namiki 1-1, Tsukuba, Ibaraki 305-0044

χ(t, T ) ∼ (T −Tc )−γ fsc [ctσ +ln(T −Tc )γ ], (1)which means that all the oﬀ-critical relaxation
data near Tc are scaled on a single curve.
Here we assume that the relaxation process
along the Kibble-Zurek mechanism [3], namely
the controlled annealing process in accordancewith critical relaxation, is expressed by theabove scaling curve, and try to reconstruct theannealing process from the NER data in thetwo-dimensional (2D) Ising model. Althoughvarious attempts within the standard powerlaw annealing are not successful, the following
stretched-exponential modiﬁed KZ process,T (t) = T0 + Td exp[−C(t/τ )σ ],(2)
Tf − aTiTi − Tf
T0 =, Td =; a = e−C , (3)1−a1−agives consistent results for L = 4096 with the106

σ = 1/5
σ = 1/3
σ = 1/2
L = 4096

5

10

104

χ(t)

Recently we numerically revealed that thecritical nonequilibrium relaxation (NER) behaviors in cluster algorithms are described by
the stretched-exponential simulation-time dependence of physical quantities in various spin
systems [1], and we derived such a relaxation
formula phenomenologically [2].
Quite recently, we found a general derivationof a scaling for oﬀ-critical relaxation in localand cluster-update algorithms. As an example, we consider the magnetic susceptibility incluster-update algorithms. From the initialtime critical relaxation χ(t; Tc ) ∼ exp(ctσ )and the temperature dependence in equilibrium χ(t = ∞, T ) ∼ (T − Tc )−γ , we haveχ(t, T )(T − Tc )γ ∼ exp[ctσ + ln(T − Tc )γ ], orreconstructedfrom NER data

C=2

KZ simulation

103
102
101
100

0

20

40

60

80

100

t [MCS]
Figure 1: Simulation-time dependence of themagnetic susceptibility in the 2D Ising modelin the SW algorithm for the modiﬁed KZ process explained in the main text. The dashedand solid lines are the simulated and reconstructed data based on Eq. (1), respectively.
relaxation process in the Swendsen-Wang algorithm with a set of parameters for a rather
slow relaxation: Ti = 1.5Tc , Tf = Tc , τ = 100,
C = 2, and σ = 1/5, 1/3, 1/2 with the exact
critical temperature Tc as shown in Fig. 1.

References[1] Y. Nonomura, JPSJ 83, 113001 (2014);
YN & Y. Tomita, PRE 92, 062121 (2015),
93, 012101 (2016), 101, 032105 (2020).
[2] YT & YN, PRE 98, 052110 (2018).
[3] C.-W. Liu et al., PRB 89, 054307 (2014);
Refs. therein (including originals by KZ).

288

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Generalization of temperature scaling in early-timenonequilibrium relaxation
Yoshihiko NONOMURA
MANA, National Institute for Materials Science
Namiki 1-1, Tsukuba, Ibaraki 305-0044

χ(t, T ) ∼ (T −Tc )−γ fsc [ctσ +ln(T −Tc )γ ]. (1)We conﬁrm this temperature scaling by analyzing the NER process of the three-dimensional
Heisenberg model in the Swendsen-Wang algorithm from the perfectly-disordered states [3].
Here we take the L × L × L system with theperiodic boundary condition for L = 560, thelargest size used in Ref. [3]. The data up to 225
Monte Carlo steps are scaled with Eq. (1) in
Fig. 1. Minimizing the mutual residuals using
our previous estimates with the NE-ES, Tc =1.442987(2)J/kB and σ = 0.47(1) [3], we have
γ = 1.3945 ± 0.0019, c = 1.2593 ± 0.0043, (2)which is consistent with the previous estimate
from detailed simulations, γ = 1.3960(9) [6].

100γT = 1.4436 J/kB
T = 1.4438 J/kB
T = 1.4440 J/kB
T = 1.4442 J/kB
T = 1.4445 J/kB
T = 1.4450 J/kB
T = 1.4460 J/kB
T = 1.4480 J/kB
T = 1.4500 J/kB
T = 1.4520 J/kB

χ(t,T)(T-Tc)

Recently we numerically revealed that thecritical nonequilibrium relaxation (NER) behaviors in cluster algorithms are described by
the stretched-exponential simulation-time dependence of physical quantities in various classical spin systems [1, 2, 3] and in a quantum
phase transition [4], and derived such a relaxation formula phenomenologically [5]. There
we utilized the nonequilibrium-to-equilibrium
scaling (NE-ES) which connects initial-timeand equilibrium relaxation behaviors.
Here we generalize this derivation to oﬀcritical behaviors. As an example, we consider
the magnetic susceptibility. From the initialtime critical relaxation χ(t; Tc ) ∼ exp(ctσ )and the temperature dependence in equilibrium χ(t = ∞, T ) ∼ (T − Tc )−γ , we haveχ(t, T )(T − Tc )γ ∼ exp[ctσ + ln(T − Tc )γ ], or

10-1

10-2

10-3

10-4
-10

-8

-6

-4

-2

0

2

4

ctσ+ ln(T-Tc)γ

6

8

10

Figure 1: Temperature scaling plot of the magnetic susceptibility in the 3D Heisenberg model
for various temperatures in a semi-log scale using the estimates of Tc and σ in Ref. [3].

References[1] Y. Nonomura, J. Phys. Soc. Jpn. 83,
113001 (2014).
[2] Y. Nonomura and Y. Tomita, Phys. Rev.
E 92, 062121 (2015).
[3] Y. Nonomura and Y. Tomita, Phys. Rev.
E 93, 012101 (2016).
[4] Y. Nonomura and Y. Tomita, Phys. Rev.
E 101, 032105 (2020).
[5] Y. Tomita and Y. Nonomura, Phys. Rev.
E 98, 052110 (2018).
[6] M. Campostrini, M. Hasenbusch, A. Pelissetto, P. Rossi, and E. Vicari, Phys. Rev
B 65, 144520 (2002).

289

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Finite-temperature properties of theKitaev-Heisenberg models on kagome and triangularlattices
Takami TOHYAMA
Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585

Frustrated quantum spin systems such as
the Heisenberg and Kitaev models on various
lattices have been known to exhibit various
exotic properties not only at zero temperature but also for ﬁnite temperatures. Inspiredby the remarkable development of the quantum frustrated spin systems in recent years, we
decided to investigate the ﬁnite-temperature
properties of the S = 1/2 Kitaev-Heisenberg
models on kagome and triangular lattices.
For calculating accurate low-temperature
properties, we developed two types of improved version for ﬁnite-temperature Lanczos
method (FTLM) [1]: replaced FTLM and orthogonalized FTLM. In standard FTLM [2], avery large number of samplings of initial vector is required to obtain good accuracy at low
temperatures. The low-temperature FTLM [2]is known as one of the solutions to this problem. However, this method has a diﬃculty
for large-scale calculations because it requires
huge random access memory to keep all vectors in the Krylov subspace. In RFTLM, lowlying eigenstates obtained by the ground-state
Lancoz method are used in the patrition function and other thermodynamic quantities. In
OFTLM, initial randome vectors are prepared
to be orthogonal to the low-lying eigenstates.
We also developed a Lanczos code that equips
a technique to save the memory for the Hamiltonian by dividing H into two subsystems.
These techniques lead us to calculate ﬁnitetemperature proprieties up to 36 lattice sites
with good accuracy even at low temperatures.

The newly developed RFTLM was also usedin the calculation of speciﬁc heat and magnetic susceptibility for S = 1/2 frustrated J1 J2 Heisenberg model on kagome, triangular,
and square lattice up to 36 sites [3].
In both kagome and triangular lattices for
the Ktaev-Heisenberg model, multiple peaks
are conﬁrmed in the speciﬁc heat. To ﬁnd
the origin of the multiple peaks, we calculate
the static spin structure factor. The origin of
the high-temperature peak of the speciﬁc heatis attributed to a crossover from the paramagnetic state to a short-range ordered state
whose static spin structure factor has zigzag
or linear intensity distributions in momentum
space. In the triangular Kitaev model, the order by disorder due to quantum ﬂuctuation occurs. On the other hand, in the kagome Kitaev
model it does not occur even with both quantum and thermal ﬂuctuations [1].

References[1] K. Morita and T. Tohyama: Phys. Rev.
Research 2 (2020) 013205.
[2] P. Prelovsek and J. Bonca: Ground stateand ﬁnite-temperature Lanczos methods,
in Strongly Correlated Systems, Numerical Methods, Vol. 176 of Springer Series in
Solid-State Sciences (Springer, 2013).
[3] P. Prelovsek, K. Morita, T. Tohyama,
and J. Herbrych: Phys. Rev. Research 2(2020) 023024.

290

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Constructing the electronic structure database for themolecular design of pigments utilizing near infrared light
Yu KOMATSU
National Institutes of Natural Sciences Astrobiology Center
National Astronomical Observatory of Japan
2-21-1 Osawa, Mitaka, Tokyo 181-8588
NIR

are shown with 12 kinds of metals in fourradiation are being anticipated for dye-sensitizedsolvents. The data will be combined with ansolar

existing dataset like QM9 for further analysis to

Novel

dye

cells

molecules
andabsorbingimaging.

Moreover,search for functional molecules effectively.

cyanobacteria, oxygenic photosynthetic bacteria,
turn to utilize chlorophyll f, which is the reddest

The computation in related work has beenchlorophyll, for photochemistry after growing

done using supercomputers of Tokyo Institute ofunder the far-red light [1]. Thus, the red limit ofTechnology

photosynthesis has been updated. In this study,

Observatory of Japan, as well.

andNational

Astronomicalin order to explore redder molecules withpossibly working as photosynthetic pigments,
the database has been constructed using ab initio
calculations for ring molecules like porphyrins
with certain properties, combined with highthroughput methods.
Thephysical-chemicalquantitiesofmolecules, were estimated at DFT level asfollows: [total energies in ground and excited

Fig. 1: Estimated ionization potentials andstates, orbital energies, ionization potentials

electronic affinities for (a) bacteriochlorophylls(IPs), electronic affinities (EAs), bindingb,energies for central metals, electronic structures

dibenzoporphycenes with different central

for each orbital, …]. Dye molecules aremetals in 4 kinds of solvent conditions (CAM-

calculated with different central metals (Mg, Ca,

B3LYP/Def2tzvp//B3LYP-D3/Def2tzvp).

Ni, Zn, Sr, Pd, Cd, Ba, Pt, Hg, Pb and H2） in

References

vacuum and water, methanol and benzene with

[1] D. J. Nürnberg et al.,: Science 360 (2018)

PCM. In Fig.1, IPs and EAs for three pigments

1210.

291

(b)

phthalocyanines

and

(c)

meso-

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Application of numerical renormalization groupmethod in condensed- matter physics
Kenji HARADA
Graduate School of Informatics, Kyoto University, Kyoto 606-8501, JapantensorIn the case of the (2+1)-dim. tensor

renormalization group (TRG) methods [1-4]network, the performance of the TRG

to various condensed matter systems. We

method is not stable. The average density

tried to use them for the non-equilibriumof active objects is not consistent with thesystems.

Monte Carlo results, not near a critical

We

have

appliedthepoint.

The directed percolation (DP) show aTheaccuracyoftheobliquecontinuous phase transition in the phaseprojection in the TRG method is bad.

diagram in the long-time limit. We have

However, due to the higher complexity ofstudied the phase diagram through thethe TRG method, we could not increase theRenyi entropy by using a TEBD method on

bond-dimension of tensors even using thethe matrix product states representation ofsystem B. The reduction of the complexity

a state-probability distribution [5]. In theof the TRG method is a future work tocase of one-dimensional DP, we have foundimprove the accuracy of the TRG method.

a critical relaxation at the critical point

Reference

and a new phase transition point in the[1] M. Levin and C. P. Nave, Phys. Rev.

active phase of the one-dim. DP.

Lett. 99, 120601 (2007).

The state-probability distribution of thed-dim. DP can be written as a (d+1)-dim.

[2] Z. Y. Xie, J. Chen, M. P. Qin, J. W.

tensor network. In the case of one-dim. DP,

Zhu, L. P. Yang, and T. Xiang, Phys. Rev.

the TRG shows better accuracy than the

B 86, 045139 (2012).
[3] G. Evenbly and G. Vidal, Phys. Rev.

TEBD method.

Lett. 115, 180405 (2015).

To check the existence of the new[4] S. Yang, Z.-C. Gu, and X.-G. Wen,transition point in the activity phase of

Phys. Rev. Lett. 118, 110504 (2017).

higher dim. DP, we tried to apply the TRG[5] K. Harada and N. Kawashima,method on the two-dim. DP by a massively

Phys. Rev. Lett., 123, 090601, (2019).

parallel computer on the ISSP.

292

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Clarification of thermal transport spectra in hierarchicalstructured organic bulk materials
Takuma Shiga
Department of Mechanical Engineering,
The University of Tokyo, Hongo, Bunkyo, Tokyo 113-8656
Material design of cellulose nanostructureThis force field is composed of bond stretching,has been recently paid much attention becausebond angle, dihedral angle, van der Waals, andcellulose structure was identified by X-ray andCoulombic interaction. For non-bonding, we

neutron scattering spectroscopies. Cellulose

used the combination of particle-particle particle

nanomaterial is expected as candidates such as

meth and cutoff methods [2]. In the calculation,transparent

thermalwe applied periodic boundary conditions along

insulator since it has high degree of self-

all directions. After equilibration with T=300 K,

organization and high mechanical property.

hot and cold thermostats with T=330 K and

Turning

thermalT=270 K were attached to the simulation cell as

conductivity of cellulose thermal insulators suchillustrated in Fig. 1. Heat flux and temperature

as aerogel and foam is around 15-18 mWm-1K-1,

gradient were evaluated after the system reaches

and it is lower than widely-used glass wool andnon-equilibrium steady-state, and then thermal

urethane foam. However investigation of

conductivity was evaluated through the Fourier's

microscopic heat conduction mechanism oflaw. All calculations were done by LAMMPS

cellulose nanomaterial is very limited. In order

package.

totofurther

conductive

thermalimprovefilm

andinsulation,

thermalinsulation

performance, it is necessary to get insight into
the knowledge on cellulose nanocrystal andfibrils.
We have evaluated heat conduction and its
size effect of I-b type cellulose nanocrystal andFig. 1 Schematics for (a)cellulose nanocrystal

single chain by performing non-equilibrium(CNC) and (b)single chain cellulose.
Size effect of thermal conductivity ofmolecular dynamics (NEMD) simulation. In thethecellulose nanocrystal is shown in Fig. 2. As

GLYCAM06 [1] force field which reproduces

thermal conductivity increases with long-axis

thermal expansion coefficient of cellulose well.

length increasing, we found that phonon

NEMD

calculation,

we

employed293

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

transport inside cellulose nanocrystal is quasiballistic. This feature is attributed to strong
covalent bond of intra-interaction. From theobtained results and linear-relationship between
an inverse of thermal conductivity and an
inverse of long-axis length (Lc), we estimatedthe thermal conductivity of bulk cellulose
nanocrystal as 4.50±0.60 Wm-1K-1, which isFig. 2 Thermal conductivity of CNC (solid line)

similar with reported literatures.

and cellulose single chain (dashed line) as a

As for single cellulose chain, it was expectedfunction of the conduction region length. The

that thermal conductivity of single chain is larger

inset shows extrapolation of inverse of thermal

than that of nanocrystal however these two

conductivity in infinite conduction region length.

thermal conductivities are actually quite similar
with each other, which is different with thereported works on polyethylene [3]. Similar to
the results of poly-dimethylpolysiloxane [4],this result can be understood because non-linear
vibration of side structure arising from thermal
fluctuation impedes phonon transport along
long-axis direction. The non-linear vibration ofside structure is strongly dependent on dihedral

Fig. 3 Thermal conductivity of original single

angle interaction and then we calculated thermal

cellulose chain (solid line), stiff chain (dashedconductivity by strengthening or softeningline) and soft chain (dash-dotted).

spring constant of dihedral angle, which are

References

shown in Fig. 3 denoted as stiff and soft chains.

[1] S. Hashmi, et al., Int. J. Clin. Exp. Pathol., 8

While strength of dihedral interaction increases(2015), 8786.

thermal conductivity, heat conduction along[2] R.W.Hockney, et al., “Computer simulation

long-axis direction is found to be insensitive tousing particles”, Adam Hilger, NY,(1989).

the softening of dihedral interaction.

[3] A. Henry, et al., Phys. Rev. Lett., 10123(2008), 235502.
[4] T. Luo, et al., J. Appl. Phys., 109-7(2011),
074321.

294

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Heat conduction analysis for phononic crystal
Takuma Shiga
Department of Mechanical Engineering,
The University of Tokyo, Hongo, Bunkyo, Tokyo 113-8656
It has been known that phononic crystal

Figure 1(b) shows thickness-dependent in-plane(PnC) such as superlattice and thin-film with air-thermal conductivity of silicon thin-films atholes leads to significant modulation of phonon

T=300 K. We found that the thickness

dispersion relation, which finally results in large

dependence is largely different with the

reduction

convectional theory considering size effect.

ofthermalconductivity

whilecrystallinity remains. In order to qualitatively
evaluate a thermal conductivity reduction, we
need to directly calculate thermal conductivityof PnC by means of microscopic simulation.
Before considering actual PnCs, we haveconsidered heat conduction of silicon thin films
with a thickness of an order of nanometer byperforming anharmonic lattice dynamics (ALD)
simulation. For interatomic force constants
which are needed in ALD calculation, we
employedtheoptimized

Stillinger-Weberpotential [1]. Surface orientation of silicon film
is set to (001) and 20´20 sampling mech for twodimensional Brillouin zone is chosen for the
calculation of scattering rate [2].

Fig. 1 (a) phonon dispersion relation of silicon

Figure 1(a) shows phonon dispersion relation

thin film with 10 nm thickness. (b) thickness-of silicon thin-film with the thickness of 10 nm.

dependent thermal conductivity at T=300 K.

Because of the presence of surface, there are

References

surface phonon modes labeled by S1-S5. From

[1] Y. Lee, et al., Phys. Rev. B 85, 125204 (2012).

the analysis of eigenvectors, we identified S1 and[2] T. Tadano, et al., J. Phys. Condens. Mater 26,

S2 are Love and Rayleigh waves, respectively.

225402 (2014).

295

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Comprehensive study on transition between heat conduction
and radiative heat transfer
Takuma Shiga
Department of Mechanical Engineering,
The University of Tokyo, Hongo, Bunkyo, Tokyo 113-8656
It has been so far revealed that thermal

we realized the framework for investigatingtransport across two substrates with nanogap istransition between heat conduction and near-

known to be attributed by phonon-polariton

field radiation.

resonance and tunneling of acoustic phonons
and therefore such a near-field heat transfer canexceed black-body limit. In order to explore
thermally-functionalized devices utilizing nearfield heat transfer such as thermal switch,
thermal rectifier, and so on, microscopic

Fig. 1 Spectral thermal boundary conductancemechanism of transport regime changing fromacross the interface between Ar and heavy-Ar

near-field heat transfer to heat conduction issolids at different temperatures.

needed to be investigated.
In order to realize such investigation, we
chose a combination of spectral heat current andnon-equilibrium molecular dynamics (NEMD)
simulations.

Figuredependent

spectral1

shows

frequency-

thermalboundary

conductance at the interface across solid argon
and heavy-mass argon crystals for different

Fig. 2 Frequency-dependent dielectric function

temperatures.
inelastic

As

terms

of

temperature

increases,of b-cristobalite SiO2 at T=300 K.

interfacial

scattering

References

contribute to overall heat conduction. In addition,[1] K. Sääskilahti, et al., Phys. Rev. B 90,

we134312 (2014).

calculated

dielectric

functionofb-cristobalite SiO2 on the basis of fluctuation-[2] Y. Chalopin, et al., Appl. Phys. Lee. 104,

dissipation theorem. These two results are in

011905 (2014).

good agreement with previous works [1,2], and296

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& "            
¼

¼



¼

¼



¼

¼

¼

¼

¼

¼

RS
sXY1

  

H

sF

sN
RT

−3.0
−3.0 −2.0 −1.0

¼

N

0.0

1.0

2.0

Δ

3.0

.  3 4        #&          )
            !   & "                  (  1 $         1  1    !    $        "'                         5      $ )  &          &  !(0"   $     ,  !6+4"   $   $               ,  !57"            .   $        )    8   
   $  &  '         $                 )   %     !."$      !."$   !9:"$  !9:"$    !+ "$     !+0"$   !"$ ;< !;"$
    ;< !;"         .$ ;$  ;      &  .  2
  =  1  >$              !?     $   1 1       " '¼297

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo     .         ;            9: 
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 ! "    &     &              &           8  ,            
57          8     &   !  "   .     !  /"      '     $      8  ,  &    ! #"  &  &   #!  "$      $  
                      8  ,   &          +0          +   4    '   $  @ 
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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Spin multipole dynamics and spin transport infrustrated magnets
Hiroaki ONISHI
Advanced Science Research Center, Japan Atomic Energy Agency
Tokai, Ibaraki 319-1195

O−−− (q, ω) =1
1
− Im ⟨0|Oq−−−†
O−−− |0⟩,π
ω + E0 − H + iη qwhere Oq−−− is the Fourier transform of−−
Oi−−− = Si− Si+1
Si+2
. Note that we perform
one DMRG run to obtain the spectral weight
for a set of q and ω, so that we need to do
many runs to scan a wide range of the q-ωspace. The computations are accelerated byparallel simulations using the system B of the
ISSP supercomputer.
We present intensity plots of O−−− (q, ω) in
Fig. 1. We find a finite gap in the quadrupole
regime [Fig. 1(a)], while we observe a gaplessmode at q = π in the octupole regime in accordance with quasi-long-range antiferro-octupole
correlations [Fig. 1(b)]. Since a bound threemagnon cluster is excited with zero energy in22

ω / J2

(a)

1

1

0
2

0
2

(b)

ω / J2

In a spin-1/2 J1 -J2 Heisenberg chain withferromagnetic J1 and antiferromagnetic J2
in a magnetic field, there appear a seriesof spin multipole liquid ground states, i.e.,quadrupole, octupole, hexadecapole, etc. To
clarify magnetic and transport properties in
the quadrupole state, we have studied spinand quadrupole excitation spectra [1] and spin
Drude weight [2] by numerical methods. We
have argued that low-energy excitations aregoverned by bound two-magnon pairs, so thatmagnon pairs would carry spin current.
Here, we extend our focus to the octupole
regime. By using a dynamical DMRG method,
we examine the dynamical octupole structure
factor at zero temperature, given by

1

1

0

0
0

0.5

1

q/π

Figure 1: O−−− (q, ω) at (a) J1 /J2 = −2 andM = 0.35 and (b) J1 /J2 = −3 and M = 0.35,
where M is the magnetization. DMRG resultswith 40 sites.
the octupole state, we envisage that magnon
clusters would contribute to the spin transport.
The analyses of current correlation functions
and wavepacket dynamics are also on going toclarify the relationship between magnetic andtransport properties.

References[1] H. Onishi, J. Phys. Soc. Jpn. 84, 083702(2015); J. Phys.: Conf. Ser. 592, 012109(2015); Physica B 536, 346 (2018).
[2] H. Onishi, J. Magn. Magn. Mater. 479,
88 (2019).

299

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular Dynamics Simulation of Ferroelectrics
Using a Shell Model V
T. Hashimoto
Research Center for Computational Design of Advanced Functional Materials (CD-FMat),
National Institute of Advanced Industrial Science and Technology (AIST),
Tsukuba Central 2, 1-1-1 Umezono, Tsukuba, Ibaraki 305-8568, Japan

Amorphous BaTiO3 can be formed by sputtering. Its structure is assumed to be a random
network of TiOn local bonding units (LBUs).
By X-ray absorption fine-structure (XAFS)
spectroscopy, n was found to be 6[1]. But, due
to the experimental diﬃculty, the LBU linkage for amorphous BaTiO3 is not clear. We
have developed a classical molecular dynamics(MD) simulation code that can handle shellmodels that reproduce physical properties of
BaTiO3 [2], and applied it to the study of amorphous BaTiO3 .
In the shell model, each atom is composed ofa core and a shell. The intra-atomic core-shellinteraction is expressed by V (r) = c2 r2 /2 +c4 r4 /24, where r is the core-shell distance andc2 and c4 are parameters. The inter-atomic interaction is through the Coulomb interaction
and the Buckingham type shell-shell interaction V (r) = A exp(−r/ρ) − C/r6 , where r is
the inter-atomic shell-shell distance and A, ρ,
and C are parameters. The computations werecarried out in constant temperature and constant pressure (NPT) ensembles. The pressure
and the temperature were controlled by the
Parrinello-Rahman method and the massive
Nose-Hoover chain method, respectively. The
externally applied pressure was set to 0 Pa.
Because we cooled the system slow enough,the densities were very close to each other, andthe susceptibilities were also very close to eachother, both in agreement with experiments[3].
As shown in Fig. 1, the probability of TiO6

1
nTiO

Probability

0.8

1
2
3
4
5
6

0.6
0.4
0.2
0

n[n]Ti[m]Ti

5

6
7
8
5
4.5
4
3.5
3
2.5
2 apex
1.5
1 edge0.5 face044 45 46 47 48 54 55 56 57 58 64 65 66 67 68 74 75 76 77 78 84 85 86 87 88

11
10
9
8
7
6
5
4
3

nBa[m]Tim
4mn

Figure 1: The probability of [m] Ti and thenumber of Ti around O (nTiO ) (upper panel),and n[n] Ti[m] Ti and nBa[m] Ti (lower panel).
was the largest, and the probability of NBOs
(purple) was larger for smaller m. The numberof Ti (Ba) around [m] Ti was larger (smaller)
for larger m. [7] Ti and [8] Ti were in an O rich,Ti rich, and Ba poor environment with fewer
NBOs and many edge or face-sharings, while[5] Ti was in an O poor, Ti poor, and Ba richenvironment with many NBOs.
[1] A. I. Frenkel et al.: Phys. Rev. B 71
(2005) 024116.
[2] S. Tinte et al.: J. Phys.: Condens. Matter
16 (2004) 3495.
[3] T. Hashimoto and H. Moriwake: Physica
B: Condens. Matter 579 (2020) 411799.

300

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Transport properties of the antiferromagneticclassical XXZ model in two dimensions
Kazushi AOYAMA
Department of Earth and Space Science, Graduate School of Science, Osaka University
Machikaneyama-cho, Toyonaka-shi, Osaka 560-0043

Transport phenomena in magnetic systems
reflect dynamical properties of interacting
spins, such as magnetic excitations and fluctuations. In this work, we theoretically investigate transport properties of two-dimensional
antiferromagnetic insulators, putting emphasis
on how the occurrence of a phase transition isreflected in spin and thermal transports. In
the classical nearest-neighbor (NN) antiferromagnetic XXZ model on the square lattice,)∑(
H = −J
Six Sjx + Siy Sjy + ∆Siz Sjz , (1)⟨i,j⟩the anisotropy ∆ plays a role to control theuniversality class of the transition, i.e., either
a second-order transition at TN into a magnetically ordered state or the Kosterlitz-Thouless(KT) transition at TKT , which respectively occur for the Ising-type (∆ > 1) and XY -type(∆ < 1) anisotropies, while for the isotropic
Heisenberg case of ∆ = 1, a phase transition
does not occur at any finite temperature. The
dynamics of the spins Si is determined by thefollowing semiclassical equation of motion:dSi= Si × Heﬀ
i ,
dt
∑
Heﬀ
= J
(Sjx , Sjy , ∆Sjz ),(2)ij∈N (i)where N (i) denotes all the NN sites of i.
The spin current and the associated spins are respectively given by
conductivity σµν∑Jzs (t) = J
rij (Si × Sj )z ,
⟨i,j⟩
s
σµν

=

1
T L2

∫ ∞

z
z
dt ⟨Js,ν(0) Js,µ(t)⟩, (3)0301

where rij and L denote a vector connecting twosites i and j and the linear system size, respectively. We numerically integrate Eq. (2) withinitial equilibrium spin configurations generated by Monte Carlo simulations and calculate
z (0) J z (t)⟩ at eachthe time correlations ⟨Js,ν
s,µtime step. By using the second order symplectic method, we perform long-time integrations
typically up to t = 100 |J|−1 − 800 |J|−1 withthe time step δt = 0.01 |J|−1 until the timez (0) J z (t)⟩ is completely lost.
correlations ⟨Js,νs,µThe thermal conductivity κµν can also be calculated in a similar way.
It is found that the spin current probes thediﬀerence in the ordering properties, while thethermal current does not. Figure 1 shows
the temperature dependence of the longitudis for the Ising-type
nal spin conductivity σxx(∆ = 1.05), XY -type (∆ = 0.95), andHeisenberg-type (∆ = 1) spin systems. Fors exhibits a diverthe XY -type anisotropy, σxxs ∝gence at TKT of the exponential form, σxx√
exp [B/ T /TKT − 1 ] with B = O(1), while
for the Ising-type anisotropy, the temperatures is almost monotonic withdependence of σxx
out showing a clear anomaly at TN and sucha monotonic behavior is also the case in the
Heisenberg-type spin system [see the dashedcurve in Fig. 1 (c)] [1]. Noting that in the
XY -type spin system, the inter-free-vortex distance ξs diverges toward TKT in the form of√ξs ∼ exp [(π/2)/ T /TKT − 1 ], the significant
s at Tenhancement of σxx
KT can be understoodas a manifestation of the topological nature of

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(a)ing finite at any finite temperature. It is foundthat the longitudinal spin-current conductivity
exhibits a divergence at the Z2 -vortex transition temperature Tv , while the thermal conductivity only shows a monotonic temperaturedependence with no clear anomaly at Tv [2].
Our results suggest the strong association
between the spin transport and the bindingunbinding topological transition of vortex excitations.

L=24
L=48
L=96
L=192

Δ=1.05108σxsx 6

TN

4
2

(b)

35
30
s 25
σx x 20
15
10
5
0

(c)

Δ=0.95

L=24
L=48
L=96
L=192
L=384

TKT

References
L=24
L=48
L=96
L=192
L=384

Δ=1

10
8

σxsx 6[1] K. Aoyama and H. Kawamura, Phys. Rev.
B 100, 144416 (2019).
[2] K. Aoyama and H. Kawamura, Phys. Rev.
Lett. 124, 047202 (2020).

4
2
0

0.2

0.4

0.6

T/ |J |

0.8

1.0

Figure 1: The temperature dependence of thes inlongitudinal spin-current conductivity σµµ
the (a) Ising-type (∆ = 1.05), (b) XY -type(∆ = 0.95), and (c) Heisenberg-type (∆ = 1)
spin systems. In (a) and (b), red arrows indicate the magnetic and KT transition temperatures, TN /|J| ≃ 0.75 and TKT /|J| ≃ 0.6,
respectively. In (c), a dashed curve representss (T ) curve extrapolated to the thermothe σxx
dynamic limit of L → ∞.
a vortex whose lifetime τv gets longer toward
TKT due to the diﬀusive vortex motion characterized by the relation τv ∝ ξs2 .
Such an anomalous spin transport is also
found in the NN antiferromagnetic Heisenberg
model on the triangular lattice. In contrast to
the XXZ antiferomagnets on the square lattice, the triangular-lattice antiferromagnet is afrustrated system. In the latter frustrated system, a KT-type binding-unbinding topologicaltransition of Z2 vortices is predicted to occur
at Tv , although spins do not order except at
T = 0 with the spin correlation length ξs be-302

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Dynamic Mechanical Properties of Slide-Ring Gels
using Coarse-Grained MD Simulations
Koichi Mayumi

Material Innovation Research Center (MIRC) and Department of Advanced Materials
Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5
Kashiwanoha, Kashiwa, Chiba 277-8561, Japan
Polyrotaxane (PR) is a supramoleculara coarse-grained model of PR with 7-

polymer composed of many ring molecules, α-membered rings which can slide freely along

cyclodextrins (CDs) and one linear polymer,

the axial chain[2]. By cross-linking rings of thepoly (ethylene glycol) (PEG), threading on

PRs, we prepared SR gels. We conducted uni-these rings. By cross-linking rings belonging

axial elongation simulations of the SR gels,to PRs, Okumura and Ito succeeded inand obtained Young’s moduli ESR, which were

fabricatinggels

lower than theoretical values by the classicalcalled slide-ring gels (SR gels)[1]. SR gels do

affine network model. Then, we analyzed the

not have direct cross-links between polymer

partial chain length distribution in SR gelschains, but topological interlock by figure-of-undereight shaped cross-links composed of two ring

distribution was described by a single

molecules. Because SR gels have slidable

exponential function in un-deformed state,cross-links, they show unique mechanicalwhile it became bimodal by stretching: longer

properties. For example, SR gels show lower

and shorter chains appeared.

supramolecularpolymer

uniaxial

deformation.

While

the

Young’s moduli than conventional fixed crosslinking polymer gels. So far, no molecularmodels have succeeded in representing thequantitative relationship between the sliding
motion of the cross-linking points and the low
Young’s moduli of SR gels. In this study, weinvestigate the relationship between the slidingof figure-of-eight cross-links and Young’s
moduli by means of coarse-grained molecularFig. 1. λ dependence of the average legth ofdynamics simulations.

long and short chain.
The average length of short and long chains

For the modeling of SR gels, we fabricated303

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyochange linearly with λ (Fig.1). We defined thisdecay rate of the segment number of theshorter partial chain length as Nslide. By
considering the chain movement through theslidable cross-links, we have succeeded inestablishing a molecular model for SR gelsbased on the classical three chain model [3](Fig. 2.), and obtained the symple equation :𝐸

𝐸

1Fig. 3. The Young’s moduli of SR gels plottedagainst the cross-linking deensity.

𝑁
𝑁

Where EAffine is the theretical prediction by

Referencesclassical threee-chain model, N0 is the average

1. Okumura Y.; Ito K. Adv. Mater., 2001,

partial chain length in undeformed state.

13, 485
2. Y. Yasuda et al., Macromolecules, 2019, 52,3787.
3. James, H. M.; Guth, E. J. Chem. Phys. 1943,
11, 455.
4. Y. Yasuda et al., ACS Macro Letters, underreview.

Fig. 2. Schematic illustration of the proposed
In order to verify this equation, we compare
the Young’s moduli obtained from thesimulation results and theoretical estimation.
We found that this estimation is realistic
enough to reproduce the simulation results.
Thus we succeeded in.

quantatatively

evaluateing the effect of the sliding on theelasticity of the slide-ring gels.

304

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Microscopic Dynamics of Polyrotaxanes using FullAtomistic MD Simulations
Koichi Mayumi
Material Innovation Research Center (MIRC) and Department of Advanced Materials
Science, Graduate School of Frontier Sciences, The University of Tokyo, 5-1-5 Kashiwanoha,
Kashiwa, Chiba 277-8561, Japan
Polyrotaxane (PR) is a supramolecularpolymer which consists of an axial linear
polymer and multiple ring-shaped molecules
threaded on the chain. A unique feature of PR
is that the rings can slide and rotate along theaxial polymer, and this feature has beenutilized for fabricating biomaterials[1] andtopological gels[2]. However, the internal
dynamics such as the sliding and rotation havenot been disclosed yet. In this study, weinvestigated the internal molecular dynamics
of PR composed of α-cyclodextrins (CDs) and

Figure 1. Simulation snapshot of the full-poly (ethylene glycol) (PEG) chain in solution

atomistic model for (a) PRs, (b) free CD, (c)byfree PEG, and (d) MSD for translational

means

of

full-atomistic

molecular

dynamics (MD) simulations [3].
We

measured

the

mean

diffusion of CD in PR(red solid line), freesquaredCD(red dotted line), and free PEG (blue dotted

displacement and estimated the diffusionline)

coefficient of free PEG, free CD, and CD in
PR. The simulation results agree well with theTable 1. Diffusion coefficients of CD in PR,

diffusion coefficients measured by the quasi-

free CD, and free PEG from the asi-elastic

elastic neutron scattering experiment (Table 1).

neutron scattering (QENS) experiment andFrom this result, we consider that our model is

MD simulation.

realistic enough. Then we tried the analysis of
intramolecular motion: the sliding dynamics.

305

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

In order to evaluate the sliding dynamics in PR,

In conclusion, we succeeded in representing

we tracked the one-dimensional trajectory ofthe diffusion coefficient for the sliding motion

CDof PR by the combination of the jump diffusion

along

PEG.

The

mean

squareddisplacement corresponding to the sliding

term with the Einstein-Stokes equation:

motion (MSDslide) increased linearly with time,𝐷

which suggests that the sliding motion is

∝

𝑘 𝑇
exp
𝜂

𝐸
𝑘 𝑇

diffusive (Fig. 2.). From the time dependenceThis relationship is valuable for controlling theof MSDslide, we calculated from the diffusion

sliding speed in polyrotaxanes.

coefficient for the sliding motion Dslide at 300
K as 1.42Å/ns, which is quite smaller value
than that of the translational diffusion of CD in
PR.

Fig. 3 Temperature dependence of the
diffusion coefficient of free CD, free PEG
and sliding motion.
Fig. 2. MSDslide of CD along the PEG chain.

References
In order to clarify the molecular origin of this(1). Yui, N. et al., Chem. Eur. J. 2006, 12,

slow sliding dynamics, we analyzed the6730

temperature dependence of Dslide (Fig. 3). We(2). Okumura, Y.et al., Adv. Mater. 2001,

found that the diffusion coefficients of the13, 485

sliding dynamics was dominated by the energy(3). Yasuda, Y. et al., J. Am. Chem. Soc.

barrier between CD and PEG. This energy

2019, 141 (24), 9655.

barrier was 8.92 kJ/mol, which corresponds to(4). Liu, P. et al., J. Phys. Chem. C 2012,

the energy potential barrier for CD on PEG,

116, 17913.

2kcal/mol = 8.37 kJ/mol [4].

306Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Comparison of X-ray pinhole topographs experimentallyobtained and computer-simulated based on the Ewald-Laue andTakagi dynamical theories
Kouhei OKITSU
Institute of Engineering Innovation, School of Engineering,
The University of Tokyo, 2-11-16 Yayoi Bunkyo-ku Tokyo 113-8656

Fig.1 [Sx(T-T)], [Ex] and [Sx(E-L)] (x∈{h, v}) show T-T simulated, experimentally obtainedand E-L&FFT simulated eight-beam pinhole topographs for horizontally (x = h) andvertically (x = v) polarized incident X-rays [2].

The present author verified the simple relation(x = v) polarized incident X-rays whose photon

between the n-beam Ewald-Laue (E-L) and Takagi

energy was adjusted or assumed to be 18.245 keV.

(T-T) X-ray dynamical theories explicitly [1-4] forThe

the first time. It can be described with Fourier

polarizationtransformation. Then, the behavior of diffracted

synchrotron radiation by using the four-quadrant

X-rays in a perfect crystal can be described by bothphase retarder system [1, 2, 4] at the BL09XU ofthe E-L and T-T dynamical theories.

SPring-8. A [1 -1 1]-oriented floating zone silicon

experiment
state

was
of

performed
the

with

the

monochromatedFigs. 1 [Sx(T-T)], [Ex] and [Sx(E-L)] (x∈{h, v})

crystal with a thickness of 9.6 mm was used as theshow T-T simulated, experimentally obtained andsample. The indices of reflections are as described

E-L&FFT

pinholein Fig. 1 [Sh(T-T)]. The T-T simulated topographs

topographs for horizontally (x = h) and verticallywere computed by integrating the T-T equation

simulated

eight-beam

307

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Fig. 2 Enlargement of the 0 6 6 transmitted-reflected images in Fig. 1 [2].
with the finite-difference method. However, theconcerning the too large R factors in protein

E-L&FFT topographs were obtained by fast

crystallography by estimating them with n-beam

Fourier transforming the solution of the E-L

approximation in place of the conventional two-

dynamical theory.

beam approximation.

References

Figs. 2 [Sx(T-T)], [Ex] and [Sx(E-L)] areenlargements of the 0 6 6 transmitted-reflected[1] K. Okitsu, Y. Imai, and Y. Yoda: Recent

images in Figs. 1 [Sx(T-T)], [Ex] and [Sx(E-L)].

Advances in Crystallography, (2012) pp. 67-86.

Good agreements among Figs. 2 [Sx(T-T)], [Ex]InTech Open. http://dx.doi.org/10.5772/47846.

and [Sx(E-L)] are found both for x=h and for x=v,[2] K. Okitsu, Y. Imai, Y. Yoda and Y. Ueji: Acta

respectively. However, evident discrepancies are

Cryst. A75 (2019) 474-482;

also found between the cases of x=h and x=v.

https://doi.org/10.1107/S2053273319001499.

The present author has a hypothesis that too[3] K. Okitsu, Y. Imai, and Y. Yoda: Acta Cryst.

large R factors for protein crystals is caused by

A75 (2019) 483-488;

interferences of multiple-reflected wave fields andhttps://doi.org/10.1107/S2053273319002936.

bankruptcy of the two-beam approximation that[4] K. Okitsu: J. Jpn. Soc. Synchrotron Rad. Res.

has been used for over 100 years. The present

33 (2020) 61-80 [Invited].

author has prepared to verify this hypothesis308

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical verification of the higher-order ETH inquantum XXZ spin ladder
Eiki IYODA
Department of Physics, Tokai University
Kitakaname, Hiratsuka-shi, Kanagawa 259-1292

Recently, isolated quantum many-body systems, which are realized in artificial systems such as cold-atoms or superconducting
qubits, have attracted much attention, because
they are useful to study fundamental problems in statistical mechanics. Especially, it
has been shown that even an isolated quantum many-body system exhibits thermalization. The eigenstate thermalization hypothesis(ETH) [1] is a promising mechanism of thermalization, which is closely related to quantum
chaos. Many numerical studies have shownthat ETH holds in non-integrable systems.
We propose a higher-order generalization of
the ETH, to which we refer as the k-ETH (k =1, 2, · · ·) [3]. The lowest order ETH (k = 1) isthe conventional ETH. The k-ETH gives many
conditions which are obtained by comparing
Hamiltonian dynamics with the Haar-random
unitary of the k-fold channel. As a non-trivial
contribution of the higher-order ETH, we showthat the Page correction of the kth Renyi entanglement entropy of individual energy eigenstates originates from the k-ETH.
In this study, we numerically investigated 2ETH for the one-dimensional spin-1/2 Heisenberg XXZ ladder model, which is composedby two chains whose lengths are p and p + 1
respectively. In order to numerically investigate 2-ETH, we should discuss finite size scaling of indicators of 2-ETH by changing thesystem size. The 2-ETH gives many conditions. For example, 2-ETH states that diagonal and oﬀ-diagonal matrix elements such as

Figure 1: (a) d-dependence of I2 (SX ). (b) λdependence of a.
⟨Ei Ej |O|Ei Ej ⟩ equal some value. There aretotally d2 equalities, where d is the dimensionof the energy shell. We adopt I2 (O) as an indicator of 2-ETH, which is defined as the maximum value of the deviation of the d2 equalities. I2 (O) is a straightforward extension of
the indicator of strong 1-ETH [2]. By numerically exact diagonalization, we calculate I2 (O)by changing parameters about energy shell andthe Hamiltonian.
We numerically calculated I2 (SX ), where SX
is the partial swap operator which swaps theregion X between the original system and a
replicated system. Figure 1(a) shows the ddependence of I2 (SX ) with λ = 1, where
λ is the coupling constant in the rungs andtunes the integrability of the model. In nonintegrable systems, the indicator I2 (SX ) decays
polynomially with d, which implies the 2-ETH
for SX holds in non-integrable systems.
We fit the numerical data of log I2 against
a fitting function f (d) := −a log d + b. Figure1(b) shows the λ-dependence of the exponent

309

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

a. In the non-integrable cases (λ ̸= 0), theexponent a takes a suﬃciently large value. Especially, when the size of the region X equals
p, the exponent a ∼ 1, which is consistent withthe typicality prediction.
In this report, we have numerically shownthat the higher-order ETH holds by using theindicator I2 (O). Numerical studies about finite size scaling with other indicators and theweaker version of higher-order ETH are left as
future issues.

References[1] M. Rigol, V. Dunjko, and M. Olshanii,
Nature 452, 854 (2008).
[2] H. Kim, T. N. Ikeda, and D. A. Huse,
Phys. Rev. E 90, 052105 (2014).
[3] K. Kazuya, E. Iyoda,
arXiv:1911.10755.

T. Sagawa,

310

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Analysis on Structuring and Dynamics of Ionic Liquid
Forming Electric Double Layer as a Local Interfacial Field
Ken-ichi FUKUIDepartment of Materials Engineering Science, Graduate School of Engineering Science,
Osaka University, Machikaneyama, Toyonaka, Osaka 560-8531
The interfacial ionic-liquid (IL) behavior
causing bias stress in the electric double layer
organic field effect transistor (EDL-OFET) (Fig.
1) has been investigated in the molecular scaleusing MD simulations combined withexperimental techniques [1].
The MD simulations were performed withGROMACS-5.0.7. The rubrene substrate was oflinear dimensions 7.2165 × 7.1930 × 2.7760 nm.
EMIM-FSI ion pairs were sandwiched between
the rubrene substrate (2.7760 nm) and vacuum
layer (~9.5 nm). Simulations were performed forthe uncharged rubrene surface (σ = 0) and for the
positively charged surfaces (σ = 0.6, 1.2, and 1.8
μC cm-2). Single point charges were placed oneach carbon atom consisting of a tetracene
backbone of a rubrene molecule corresponding to
the HOMO of rubrene, and its magnitude wasdetermined by the overall surface charge density
σ. The systems were equilibrated at a constantvolume for 100 ps, followed by a constantvolume simulation for 20 ns.
Fig. 2 shows the plane-averaged charge density
profiles with respect to the amount of injectedcharge into rubrene electrode and number density
profiles of atoms in EMIM cation and FSI anion,
respectively, at the charge density of 1.8 μC cm-2.
At this potential, EMIM cations and FSI anions
form a checkerboard structure with their major
molecular axis perpendicular to the surface. Thus,
negative atoms of -SO2F of FSI anions arepointing the rubrene surface (O×2 and F). Thisconfiguration probably causes the bias stress by
efficiently trap the hole carrier at the interface
with structured interfacial IL as observed by force
curve measurements with EC-FM-AFM [1].

Fig. 1: (a) Molecular structures of rubrene andEMIM-FSI. (b) Schematic of EDL-OFET using
rubrene semiconductor and IL gate dielectrics.

Fig. 2: (a) Plane-averaged charge density profiles
with respect to the amount of injected charge into
rubrene electrode. (b),(c) Number density profilesof atoms in the EMIM cation and the FSI anion,
respectively, at the charge density of 1.8 μC cm-2.
Each line corresponds to the shaded atom withthe same color. Gray-shaded area is the rubreneelectrode region. Dotted line at z = 0.04 nm
suggests the position of negative charge density
next to the rubrene electrode surface.

Reference[1] D. Okaue, I. Tanabe, S. Ono, K. Sakamoto, T.
Sato, A. Imanishi, Y. Morikawa, J. Takeya, K.
Fukui, J. Phys. Chem. C 124 (2020) 2543.

311

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Calculation of ordered structures and their optical properties
of soft materials
Jun-ichi FUKUDA
Department of Physics, Kyushu University, Motooka 744, Nishi-ku, Fukuoka 819-0395
This year we have studied how a topologicalthe effect of the variation of the numericaldefect in a thin cell of a nematic liquid crystal

aperture. We have found that the core of alook under optical microscope. Such defects are

topological defect appears as a dark spot, andcommonly observed in experimental labs

also that the spot becomes sharper as thestudying

numerical aperture increases. More details will

liquidcrystals.

However,usual

be presented in a manuscript in preparation.

identifications of topological defects in anematic liquid crystal relies on the observation

Another subject is the lattice orientation of aof the orientation profile around the topological

cubic lattice of cholesteric blue phase liquid

defects. How the image should be at the centercrystalof topological defects has given little attention

orienting surfaces. Previous experiments foundso far. It is because the length characterizingthatthe defect core is ~10nm, much smaller than theorientation with respect to the direction of theresolution of optical imaging.

surface orientation. We have simulated the

the

in

contact
cubic

with

latticeunidirectionallyexhibits

specific

We have made use of the techniquestructures of cholesteric blue phases in such adeveloped previously [1] which reproduced

setup using the Landau-de Gennes theory

excellently the microscope images of a thin cell

describing the orientational order of the liquidof a chiral liquid crystal. We solve the fullcrystal by a second-rank tensor. This study is

Maxwell equations for the electromagnetic

now under way.

wave to investigate the response of the liquid
crystal to monochromatic incident light with

References

given wavevector. By doing calculations for[1] A. Nych, J. Fukuda, U. Ognysta, S. Žumer

different

and I Muševič, Nature Phys. 13, 1215 (2017).

incident

wavevectors,

one

can

construct a microscope image, whose details[2] M. Takahashi et al. J. Phys. D: Appl. Phys.

are presented in Ref. [1].

51, 104003 (2018)

Calculations have been done to investigate

312Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ultrafast relaxation of inhomogeneous electron
distribution around the Dirac cone in graphene
Shota ONO
Department of Electrical, Electronic and Computer Engineering, Gifu University
Gifu 501-1193

(β)

!% #$

!"#

!"/
!"#

!"!
$!"#

!"#

%&*"+'()%&!"!'()%&,-'()

!"!
$!"#
$!"#

(ν)

∂nq /∂t = (∂n/∂t)ph-e , where fks is the electron distribution function with the wavevector k = (kx , ky ), the valleys ν =K and K’,(β)
and the band index s = ±1. nq is thephonon distribution function, where β and q
denote the phonon mode and wavevector, respectively. The collision terms include theelectron-electron (e-e) and the electron-phonon(e-ph) scattering contributions. The e-e interaction matrix element is calculated by using
the expression given in Ref. [3]. The expression for the e-ph interaction matrix elements
given in Ref. [4] were used to compute thescattering rates, while diﬀerent e-ph couplingstrengths [5] were used for the coupling withthe Γ and K phonons, respectively. The initialcondition for the electron distribution is imposed to show the inhomogeneous population
around the Dirac cones [6].
Figure 1 (upper) shows the time-evolution(ν)
of fk,+1 : The excited electrons inhomogeneously populated around the Dirac cone initially go to the K point due to the e-e scattering mainly, followed by electron thermalization due to both the e-e and e-ph scattering.
The electron relaxation is slowed down from∼ 50 fs to more longer when the e-e scattering is neglected (lower). Using the electron
distribution, the time-evolution of absorption!".

%&,-'()%&*"+'()%&!"!'()

!"!

!% #$

It has been known that the inhomogeneouselectron distribution can be created around the
Dirac cone of monolayer graphene after photon absorption [1]. Motivated by recent experiment using ultrafast laser pulse [2], we simulate the ultrafast dynamics of the photoexcited Dirac electrons coupled with the optical phonons by solving the Boltzmann equa(ν)
tion: ∂fks /∂t = (∂f /∂t)e-e + (∂f /∂t)e-ph and

!"!
!" #$

!"#

$!"#

!"!
!" #$

!"#

$!"#

!"!
!" #$

!"#

Figure 1: The time-evolution of the electron
distribution around the Dirac cone: In upper
figure, both the e-e and e-ph scattering are considered, while in lower figure the e-ph scattering is considered only.
spectra can also be calculated. We expect thatthe present study will stimulate further experimental work on this system.
The author thank I. Katayama (Yokohama
National University) for useful discussions.

References[1] A. Grüneis et al.: Phys. Rev. B 67 (2003)
165402.
[2] S. Nara et al.: JPS 2018 Autumn, 11aPS20.
[3] T. Ando: J. Phys. Soc. Jpn. 75 (2006)
074716.
[4] S. Piscanec et al.: Phys. Rev. Lett. 93(2004) 185503.
[5] M. Lazzeri et al.: Phys. Rev. B 78 (2008)
081406(R).
[6] M. Trushin et al.: Phys. Rev. B 92 (2015)
165429.

313

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Boltzmann equation solver for nonequilibrium
electrons and phonons in solids
Shota ONO
Department of Electrical, Electronic and Computer Engineering, Gifu University
Gifu 501-1193

By taking the wavevector average of the
distribution functions, we calculate the timeevolution of the electron distribution f (ε) andthe phonon distribution n(ω), where ε and ω
are the electron energy and the phonon frequency, respectively. The time-evolution off (ε) and n(ω) is regulated by the Boltzmann
equation ∂f (ε)/∂t = (∂f /∂t)e-e +(∂f /∂t)e-ph +(∂f /∂t)laser and ∂n(ω)/∂t = (∂n/∂t)ph-e ,where the laser excitation as well as the e-e
and e-ph collision terms are considered.
We apply our BENEP code to the calculation of the femtosecond infrared photolumi-

0.0 ps0.2 ps
0.5 ps1.0 ps3

15x10

PL (arb.)

It is of importance to establish a theoretical scheme for studying the ultrafast electron dynamics of laser-excited solids, where
the nonequilibrium electron distribution approaches thermal distribution within a picosecond time scale through the electron-electron(e-e) and electron-phonon (e-ph) scattering.
Recently the author has developed the Boltzmann equation solver to calculate the timeevolution of the electron and phonon distribution [1], where the free-electron, the Debye
phonon, and the deformation potential models are used to describe the electron densityof-states (DOS), the phonon DOS, and theEliashberg function (the e-ph coupling function), respectively. In the present study, basedon ab initio approach to calculate these threefunctions, we develop the Boltzmann Equation solver for Nonequilibrium Electrons andPhonons, BENEP, which enables us to study
the ultrafast electron and phonon dynamics
of realistic materials absorbing a femtosecond
laser pulse. It would be useful to analyze
the pump-probe experimental data beyond thewell-known two-temperature model [2].

10

5

0
0.2

0.4

0.6
0.8
Photon energy (eV)

1.0

1.2

Figure 1: The time-evolution of PL in silver:
The excitation density, the eﬀective Coulombinteraction strength, and the electron diﬀusion
time are assumed to be 460 J/cm3 , 0.37 eV,
and 0.5 ps, respectively.
nescence (PL) of metals. Figure 1 shows thetime-evolution of PL spectra in silver: The PL
spectra changes with time because the electron
distribution thermalizes through the e-e scattering and because the electron energy is transferred to phonons. We find that the agreement
between the numerical simulation and the experimental data is good, which will be demonstrated in our future paper [3].
The author thank T. Suemoto (Toyota Physical and Chemical Research Institute) for useful discussions.

References[1] S. Ono: Phys. Rev. B 97 (2018) 054310.
[2] P. B. Allen: Phys. Rev. Lett. 59 (1987)
1460.
[3] S. Ono and T. Suemoto, arXiv:2004.09000.

314

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Entanglement in Remote Electron-phonon Systems
Created by Photoirradiation
Kunio ISHIDA
School of Engineering and Center for Optics Research and Education
Utsunomiya University, Yoto, Utsunomiya, Tochigi 321-8585
Recent experiments on quantum entanglement

We derived relevant composite modes obtained

between remote systems has revealed that theby the Heisenberg equation of motion for 𝑐𝑖 , andirradiated photons mediates quantum correlation

found that the heterodyne detection of it will

between noninteracting material systems[1,2].

help us distill the information on phonon

Since,

and/orcorrelation which slowly increases after a certain

dynamical behavior has not been understoodnumber of phonons is created. As shown in thetheoretically, we study the dynamics ofprevious

entanglement

remotebetween remote diamond crystals[1], thesystems by irradiation of a quantized light pulse.

entanglement is generated as a result of

We employed a model of coupled electron-

measurement on the scattered light, i.e.,phonon-photon systems described by[3]measurement corresponds to a disentanglement

however,

its

generation

mechanism

between𝑗

𝜎 +1
2Solving

entanglement

quantum correlation before measurement is also𝑗time-dependent

phononthe projection hypothesis, this means that the+ {∑3𝑖=1 𝜈𝑖 (𝑐𝑖 † + 𝑐𝑖 ) + 𝜆}𝜎𝑥 ].

the

on

process between photons and phonons. Underℋ = ∑3𝑖=1 𝛺𝑖 𝑐𝑖 † 𝑐𝑖 + ∑2𝑗=1 [𝜔𝑎𝑗† 𝑎𝑗 + {𝜇(𝑎𝑗† +𝑎𝑗 ) + 𝜀} 𝑧

study

important to find appropriate methods for

Schrödinger

entanglement control. These results will help us

equation by numerical calculation on the Systemdesign a method of coherent control of

B at ISSP, we found that the quantum mutual

entanglement generation.

information for phonons reveals the dynamics ofphonon entanglement generation.

References
entanglement[1] K. C. Lee, et al., Science 334, 1253(2011).

generation dynamics are also studied and we[2] F. Borjans, et al., Nature 577, 195 (2020).

showed that the scattered light, e.g., Stokes light,[3] K. Ishida, Eur. Phys. J. D73, 117 (2019).

Detection

methods

ofcarries information on the phonon entanglement.

315

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular simulation of patchy particles
Takamichi TERAO
Department of Electrical, Electronic, and Computer Engineering,
Gifu University, Yanagido 1-1, Gifu, 501-1193
In colloidal systems, many studies have been

structures of colloidal crystals have been

performed to clarify the properties of sphericalanalyzed for various crystal structures. It has

particles with isotropic interactions. Recently,

been revealed that a wide photonic bandgap

there has been much interest in the studies ofexists in a colloidal crystal with diamondpatchy particles with anisotropic interactions. It

structure. Melting transition of such crystals

is of interest to create novel functional

have been studied by Monte Carlo simulations,materials using these particles. In this study, theand it was confirmed that the crystals withstructural formation of patchy particles was

diamond structure becomes thermodynamicallystudied by molecular simulations using cluster

stable if the attractive interaction energyMonte Carlo method. To describe the effective

between patchy particles is about 10kBT.

interaction between patchy particles, the KernFrenkel model has been employed [1].
First, computer simulations are performedfor 2-patch particles. Each particle has degrees
of freedom of rotation in three-dimensional
space, and its motion was constrained in aplane. In order to clarify the phase diagram, weanalyzed the structure of the system using thegeneralized local bond order parameter that we
Fig. 1: Snapshot of tetrahedral patchy particles.

have developed in previous studies [2]. As aresult, a fluid phase, a hexagonal phase, aKagome phase, and their coexistence phase

References

have been observed.

[1] F. Romano, E. Sanz, P. Tartaglia, and F.

Next,

we

studiedtetrahedral

Sciortino: J. Phys.: Condens. Matter 24 (2012)

patchyparticles in a three-dimensional system (Figure

064113.

1), and the stability with diamond structure was[2] R. Mizuno, K. Okumura, J. Oguri, and T.

numerically investigated. The photonic band

Terao: Mol. Simul. 45 (2019) 743.

316

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Eﬀects of Dzyaloshinskii-Moriya interactions andexchange randomness on low-temperature specificheats of spherical-kagome spin-systems
Yoshiyuki Fukumoto
Department of Physics, Faculty of Science and Technology, Tokyo University of Science
2641 Yamazaki, Noda, Chiba 278-8510

For cluster magnets described by Heisenberg models, in general, stepwise structures
are expected in zero-temperature magnetization curves. However, for a spherical-kagome
system {W72 V30 } [1], which contains 30 vanadium ions with S = 1/2, it was reported
that there is no such structure up to 50 T
in a magnetization measurement at 0.5 K [2].
So far, the eﬀects of (i) a distribution in thestrength of the exchange interaction [2] and(ii) the Dzyaloshinskii-Moriya (DM) interaction [3] have been investigated. If in (i) the distribution width is about 30% of the average exchange interaction, or if in (ii) the DM interaction strength is about 10% of the exchange interaction, it has been shown that the low temperature magnetization process of {W72 V30 }can be explained.
In this study, we focus on the eﬀects of (i)and (ii) on the specific heat. To be specific, wefirst notice the fact that the recently reported
experimental results for the low-temperature
specific heat of {W72 V30 } in several magnetic
fields do not match the calculated results in the
Heisenberg model; (a) the peak at about 2K inthe calculated result is not seen in the experimental result, and (b) the observed magneticfield dependence is very smaller than the calculation [4]. In order to resolve these two discrepancies, (a) and (b), we use the method ofthermal quantum pure state [5] to calculate thespecific heat, taking (i) and (ii) into account.
As a result, regarding (a), we conclude that317

the distribution of low-energy singlet states isaﬀected by the distribution of exchange interactions to wipe out the low-temperature peak.
The important finding is that the lowest singlet excitation-energy in the Heisenberg model
is a fraction of the lowest triplet excitationenergy, which leads to the distribution widthof exchange interaction being about 10% of theaverage exchange interaction (a fraction of theprevious study [2]). Regarding (b), we foundthat the DM interaction can have the eﬀect ofsuppressing the magnetic-field dependence ofthe energy eigenvalues, whose mechanism canalso be illustrated by the two-spin model.
In conclusion, the specific heat of the 30-site
system has been quantitatively evaluated up
to suﬃciently low temperatures, and we havequalitatively discussed the diﬀerences and similarities between the eﬀects of two types of perturbations (i) and (ii) on the specific heat inmagnetic fields and the magnetization process.

References[1] N. Kunisada et al., PTEP 2014, 41I01(2014).
[2] J.
Schnacketmat/1304.2603v1.

al.,

arXiv:cond-[3] Y. Fukumoto et al., J. Phys. Soc. Jpn. 87,
124710, 2018.
[4] T. Kihara et al., PRB 99, 064430 (2019).
[5] S. Sugiura and A.Shimizu, Phys. Rev.
Lett. 108, 240401(2012).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Data-driven determination of a spin Hamiltonian of
KCu4P3O12
Ryo TAMURAInternational Center for Materials Nanoarchitectonics,
National Institute for Materials Science,
1-1 Namiki, Tsukuba, Ibaraki, 305-0044

The origin of physical properties in materials is often understood through an eﬀectivemodel in materials science. Many methods
have been developed in order to construct theeﬀective model for a target material and they
are mainly divided into two groups. One is abinitio calculations which determine the model
parameters in an assumed eﬀective model only
by giving basic information of the target material. The other is a data-driven approachin which model parameters are determined so
as to fit the experimentally measured data inthe target material. In the latter case, from aview point of eﬀective model estimations, datadriven techniques are considered to be eﬃcientfor the acceleration of automatic search for appropriate model parameters[1] and the extraction of relevant model parameters[2, 3, 4].
Here, by a data-driven approach, aspin Hamiltonian as an eﬀective model ofKCu4 P3 O12 is determined. The crystal structure of KCu4 P3 O12 is defined by a =7.433
Å, b = 7.839 Å, c = 9.464 Å, α = 108.28◦ ,β = 112.68◦ , γ = 92.73◦ , and space group:
P1̄[5]. Cu(II) ions have S = 1/2 isotropic
Heisenberg spin, but magnetic properties ofthis compound have not been reported yet.
The lattice structure of Cu ions can be regarded as a zigzag chain consisting of eight Cuions. Thus, a quantum Heisenberg model ona zigzag chain is targeted for a spin Hamiltonian of KCu4 P3 O12 to be estimated. We estimate superexchange interactions between Cu

ions in this target model by a data-driven approach with susceptibility and magnetization
curves experimentally measured. The estimated model parameters are J1 = −8.54 meV,J2 = −2.67 meV, J3 = −3.90 meV, andJ4 = 6.24 meV, which describe the measured
results well.
Once an estimated spin Hamiltonian is established, we predict, through theoretical analysis of the Hamiltonian, various magnetic
properties which cannot be or have not beenmeasured, such as magnetic specific heat, magnetic entropy, spin configuration, and spin gap.
These predictions are helpful to propose a further experimental plan and design.
This work is the collaboration work withKoji Hukushima, Akira Matsuo, Koichi Kindo,and Masashi Hase.

References[1] R. Tamura and K. Hukushima, PLoS
ONE 13, e0193785 (2018).
[2] H. Takenaka, K. Nagata, T. Mizokawa,and M. Okada, J. Phys. Soc. Jpn. 83,
124706 (2014).
[3] R. Tamura and K. Hukushima, Phys. Rev.
B 95, 064407 (2017).
[4] H. Fujita, Y. O. Nakagawa, S Sugiura, and M. Oshikawa, Phys. Rev. B 97,
075114 (2018).

318

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[5] H. Eﬀenberger, Zeitschrift für Kristallographie 180, 43 (1987).

319

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Establishment of new analysis method
for extend X-ray absorption fine structurewith sparse modeling
Hiroyuki KUMAZOE
Institute of Industrial Nanomaterials, Kumamoto University
Kurokami, Chuo-ku, Kumamoto, 860-8555

Measurement of extended X-ray absorption
fine structure (EXAFS) is one of the primarymethods to obtain local structure information
around a specific element with atomic scale.
We are building a new method for the analysis
of EXAFS by the sparse modeling. This year,
we focused on Bayes free energy as an information criteria for choosing the regularization
parameter.
To perform the sparse modeling on the EXAFS signals, we employed a simplified modelof the EXAFS formalism based on the singlescattering approximation [1]:y(k) =χ(k) · k 3
=

N
X
k2
j=1

Rj2

exp



−2k 2 σj2Rjexp −2Λ× (aj sin 2kRj + bj cos 2kRj ),(1)matrix, X incorporates other terms in Eq. (1).
In this method, some elements of the coefficient, w is are suppressed to exactly zero withthe moderate value of λ.
Let us consider the sparse regression
problem for the LASSO estimations within
Bayesian inference to choose the regression parameter, λ. In Bayesian inference, this linear
regression problem is optimized by maximizing the posterior probability. Here, we introduce the Bayesian free energy [2, 3] as an information criterion to optimize a regularization
parameter and to extract the physical model
appropriately. As a result, we estimated theradial distribution function with fewer bases
than in previous studies [1].
This work was supported by JST CREST
Grant Number JPMJCR 1861, Japan.

where, y(k) is the k 3 weighted EXAFS signal, χ(k) as a function of the photoelectronwavenumber, k. Rj is the distance from thefocused atom, j. σj is the Debye–Waller factor for atom, j. Λ is the mean free path. To
obtain the local structure information, we convert Eq. (1) to a linear regression problem andsolve it with L1 regularization.
12ŵ = arg min ky − Xwk2 + λkwk1 , (2)2wReferenceswhere the regression coefficient is w =(. . . , aj , bj , . . . )T .
The response vector, ycomes from the target data and the predictor[3] Y. Mototake, Y. Igarashi, H. Takenaka,
K. Nagata, and M. Okada, J. Phys. Soc.
Jpn. 87, 114004 (2018).

320[1] I. Akai, K. Iwamitsu, Y. Igarashi,
M. Okada, H. Setoyama, T. Okajima, and
Y. Hirai, J. Phys. Soc. Jpn. 87, 074003(2018).
[2] Y. Igarashi, H. Takenaka, Y. NakanishiOhno, M. Uemura, S. Ikeda, andM. Okada, J. Phys. Soc. Jpn. 87, 044802(2018).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Competiton between dipolar and short-range
interactions on the magnetic thin films
Hisato KOMATSU, Yoshihiko NONOMURA, and Masamichi NISHINONational Institute for Materials Science, Namiki, Tsukujba, Ibaraki 305-0044

Magnetic thin films are known to exhibit avariety of orderings when the exchange andthe dipolar interactions compete with eachother [1]. These systems are described by thefollowing Hamiltonian:∑H = −J⟨i,j ⟩+D′−ηSi · Sj∑  Si · Sj
i<j

∑(

i

(a) η=0,H=0


z

Si

r3
)2

ij

−H

−

3(S i · r ij )(S j · r ij


)

5
rij



∑

z

Si .

i

321

1.0

0.5

0.5

0.0

0.0

-0.5

-0.5

-1.0

-1.0

(c) η=0,H=2(1)

Here, r ij = t (xij , yij , 0) ≡ j − i means thediﬀerence between the position i and j. Previous studies revealed that this system has the
spin-reorientation(SR) transition between the
stripe and the planar ferromagnetic phase [2, 3]
driven by the anisotropy η. However, thesestudies are limited to the cases when the magnetic field H does not exist.
We investigate the relation between the
structure of the ordered phase and the parameters η and H using the Monte-Carlo(MC)simulation. In the simulation, naive MC algorithm require O(N 2 ) simulation time, andthus we adopt the O(N ) SCO algorithm [4].
The coupling constant of interactions are fixed
as J = D′ = 1. Figures 1 and 2 show the snapshots and the η − T phase diagrams given by
our investigation, respectively. These figures
show that the SR transition exists no matter
whether H is zero or nonzero.
The numerical calculations of this study
were mainly performed on the Numerical Materials Simulator at National Institute for Ma-(b) η=5,H=0
1.0(d) η=5,H=2
1.0

1.0

0.5

0.5

0.0

0.0

-0.5

-0.5

-1.0

-1.0

Figure 1: Snapshots of the system at several
cases. The vectors and color mean the values of(S x , S y ) and S z , respectively. The parametersη and H are fixed at (a)η = 0, H = 0, (b)η =5, H = 0, (c)η = 0, H = 2, and (d)η = 5, H =2, and the temperature T = 0.1. Note that thewidths of the stripes depend on H.
terials Science. We applied for the uage of
the ISSP Supercomputer in preparation for the
maintenance period of this simulator. However, we have ended this period without needfor the new large-scale simulation, and do nothave used the ISSP Supercmputer.

References[1] K. De’Bell, A. B. MacIsaac, and J. P.
Whitehead, Rev. Mod. Phys. 72, 225(2000).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo[2] J. P. Whitehead, A. B. MacIsaac, and K.
De’Bell, Phys. Rev. B 77, 174415 (2008)[3] M. Carubelli, O. V. Billoni, S. A. Pighin,
S. A. Cannas, D. A. Stariolo, andF. A. Tamarit, Phys. Rev. B 77, 134417(2008).
[4] M. Sasaki and F. Matsubara, J. Phys. Soc.
Jpn. 77, 024004 (2008).

(a)10
8

stripe

η

6

para
4
2 planar ferro
0
0.0

0.5

(b)10
8

1.0

1.5

T
stripe

η

6

para
4
2 planar ferro
0
0.0

0.5

1.0

1.5

T

Figure 2: The η −T phase diagrams at (a)H =0 and (b)H = 2. The closed and open circles mean the first- and the second-order phasetransition.

322

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Competiton between dipolar andDzyaloshinskii-Moriya interactions on the magnetic
thin films
Hisato KOMATSU, Yoshihiko NONOMURA, and Masamichi NISHINONational Institute for Materials Science, Namiki, Tsukujba, Ibaraki 305-0044}

on the value of D′ and η. It makes the triangular lattice under certain conditions, and thesquare lattice under the others. Furthurmore,
the chiral magnetic phase also shows thechange of the direction of the structure depending on the parameters. We calculate theorientational order parameter of these phases,
and investigated the condition under which
each structure appear.
The numerical calculations of this study
were mainly performed on the Numerical Materials Simulator at National Institute for Materials Science. We applied for the uage of
the ISSP Supercomputer in preparation for the
maintenance period of this simulator. However, we have ended this period without needfor the new large-scale simulation, and do nothave used the ISSP Supercmputer.



References

[1] S. D. Yi, S. Onoda, N. Nishikawa, andJ. H. Han, Phys. Rev. B 80, 054416(2009).

Studies in recent years revealed that the spin
systems with the Dzyaloshinskii-Moriya(DM)interaction have various types of magnetic
structures such as the skyrmion lattice or thechiral magnetism [1]. Most of these studies
does not consider the eﬀect of the dipolar interaction between the magnetic moments ofthe spins, although it can not be removed.
We investigate the two-dimensional square lattice where the DM, the nearest-neighbor ferromagnetic, and the dipolar interactions compete with each other, by the Monte-Carlo(MC)simulation.
The Hamiltonian we consider in this study
is given as follows:∑

H = −J⟨i,j ⟩−D

Si · Sj∑{(S i × S i+ex )x + (S i × S i+ey )y

i 

+D′

∑  Si · Sj
i<j

−η

∑(

i



Siz

3
rij

)2

−H

−

3(S i · r ij )(S j · r ij ) 

∑

5
rij

Siz .

(1)

i

Here, r ij = t (xij , yij , 0) ≡ j − i means thediﬀerence between the position i and j. We
fixed the coupling constant of short range interaction as J = D = 1. In the simulation,
naive MC algorithm require O(N 2 ) simulation
time, and thus we adopt the O(N ) SCO algorithm [3].
As we can see in the figure 1, the skyrmion
lattice changes its structure depending mainly

323[2] M. Sasaki and F. Matsubara, J. Phys. Soc.
Jpn. 77, 024004 (2008).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

(a)

(b)

(c)

Figure 1: Snapshots of the skyrmion latticephase at (a)D′ = 0.0, η = −1.2, H = 0.2,(b)D′ = 0.0, η = 0.0, H = 0.5, and (c)D′ =
0.6, η = 2.0, H = 1.5. The temperature ofeach one is fixed at T = 0.1. The skyrmions
make the square lattice at the cases (a) and(c), whereas they make the triangular latticeat (b). Note that direction of the square lattice
is diﬀerent in (a) and (c).

324

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Investigation of Dynamics of a Supercooled Liquid andProteins using the Free-Energy Landscape
Takashi YOSHIDOME
Department of Applied Physics, Graduate School of Engineering, Tohoku University, Sendai
980-8579
Free-energy landscape (FEL) picture has

the two proteins at 400 K to observe unfolding

been used for understanding the properties ofprocess. Then the trajectories were analyzed. It

glass transition and protein folding [1,2]. The

was found that the experimental result was

free-energy landscape is defined as a function

successfully reproduced.

of a particle configuration [2]. In the present

The calculations were performed using thestudy, we have investigated the dynamics of a

L4cpu and F18acc in the system B, and L4cpu

Lennard-Jones system in a supercooled statein the system C. We used our custom-madeand the dynamics of two proteins upon

program [3] for computing the free-energy

unfolding process from the viewpoint of thelandscape of a Lennard-Jones system and for

FEL.

MC simulations. As for the study of proteinaunfolding, MD simulations were performed

crystallization process in a supercooled state.

using the program GROMACS [5]. The MD

The computation of free-energy landscape wastrajectories were analyzed using our custom-

conducted using the protocol we have proposed

made programs.

We

first

computed

the

FEL

for

[3]. The initial configuration was preparedusing a Monte-Carlo (MC) simulation at a

References

temperature above the freezing temperature. We[1]have successfully obtained a FEL upon

Applications to Clusters, Biomolecules andcrystallization.

Glasses (Cambridge University Press, 2004).

D.

Wales:

EnergyLandscapes:[2] T. Odagaki: J. Phys. Soc. Jpn. 86 (2017)

As for the protein dynamics upon unfolding
process, we focused on the two proteins (goat082001.

alpha-lactalbumin and human lysozyme). It has[3] T. Yoshidome, A. Yoshimori, and T.

experimentally shown that they have quite

Odagaki: Phys. Rev. E 76 (2007) 021506.

similar native structures but different structures[4] H.J.C. Berendsen, D. Van der Spoel, and R.

at the transition state. We first performed all-van Drunen, Comput. Phys. Commu. 91 (1995)

atom molecular dynamics (MD) simulations of

43.

325

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Non-monotonic Behavior of the Binder Parameter inPotts Models
Hiroshi WATANABE
Department of Applied Physics and Physico-Informatics, Keio University
Yokohama, Kanagawa 223-8522, Japan
Satoshi MORITA, Yuichi MOTOYAMA, and Naoki KAWASHIMA
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277–8581

4.5
4

L = 32
L = 64
L =128(a)Binder Ratio

3.5
3
2.5
2
1.5
1
0.76

0.78

0.8

0.82

0.84

Temperature
1

(b)
0.8
Binder Ratio

The Binder parameter, a.k.a, the forth-order
cumulant, is a useful tool for analyzing the critical phenomena [1]. Since the scaling dimension of the Binder parameter is zero, its value
does not depend on the system size at the criticality. While the Binder parameter usually amonotonic function for the systems involving
continuous phase transition, it sometimes exhibits non-monotonic behavior. For example,
a hump appears in the Binder parameter near
the criticality of the Potts model. It exhibit
system size dependence, and therefore, it is
not trivial whether the universal scaling function itself has a hump or not. Additionally, it
is known that the amplitude of the hump depends on the definition of the order parameter.
However, the reason has not been clarified yet.

0.6
0.4
L = 32
L = 64
L =1280.2
00.76

To study the peculiar behavior of the
Binder parameter, we investigate the FortuinKastelyen graph representation. We find thatthe graph representation of the Binder parameter consists of two parts, namely, the low- andhigh-temperature components, and the peculiar behavior of the Binder parameter is causedby the low-temperature one. We also find thespin representation of the high-temperaturecomponents of the Binder parameter, which isa monotonic function. We study the J1 − −J2
frustrated Ising model [2] and find that the
non-monotonic behavior of the Binder parameter can be removed.

0.78

0.8

0.82

0.84

Temperature

Figure 1: The Binder parameters of the J1 −−J2 frustrated Ising model with (a) the conventional and (b) the proposed definitions.
The former exhibits humps while the latterdoes not.
[1] K. Binder, Z. Phys. B Cond. Matt. , vol.
43, pp. 119-140 (1981).
[2] S. Jin, A. Sen, and A. W. Sandvik, Phys.
Rev. Lett. vol. 108, pp. 2-6 (2012).

326

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulating phonon cross section using density
functional theory
Naoki Murai
Materials and Life Science Division, J-PARC Center, Japan Atomic Energy Agency
Tokai, Ibaraki 319-1195, JapanThe studies of lattice dynamics, phonons,in crystalline materials are of fundamental importance as they provide key insights into theunderstanding of some relevant physical properties such as superconductivity and thermal
conductivity. Historically, the direct observation of phonon dispersion using inelastic neutron scattering (INS) by Brockhouse opened
the ﬁeld of phonon spectroscopy as an energyand momentum-resolved technique[1]. Since
then, especially with the development of modern time-of-ﬂight spectrometers at spallation
neutron sources[2], INS has emerged as a powerful tool that allows eﬃcient determination ofphonon dispersion. Meanwhile, as an alternative method, inelastic x-ray scattering (IXS)
has demonstrated its potential to precisely
measure phonon dispersion[3]. Thus, the ﬁeldof phonon spectroscopy has grown quickly overthe past the few decades, and the developmentof new instruments oﬀers a unique opportunity
to explore lattice dynamics in novel materials.
So far, we have been working on phonon dispersion measurements using the state-of-theart INS spectrometers at J-PARC. The present
project was carried out as a joint experimental
and numerical study of lattice dynamics properties in novel materials. In particular, thanks
to recent advances in density functional theory(DFT) calculations, it is now possible to perform ab initio phonon calculations whose only
input information is the chemical compositionof the materials.
In the present research project, we per-formed ab initio phonon calculations, with aparticular focus on unconventional superconductors and thermoelectric materials. Phonon
calculations were performed using the density
functional perturbation theory (DFPT)[4], as
implemented in quantum espresso code[5,6].
Figure.
1 shows representative results obtained for SnS, which is predicted
to be an attractive thermoelectric candidate.
Here, all calculations were performed using the plane-wave pseudopotential method
and the generalized gradient approximation(GGA) for the exchange correlation functional in the Perdew-Burke-Ernzerhof (PBE)
parametrization[7]. Pseudopotentials and energy cutoﬀs of plane-wave basis were chosen
according to the results of convergence tests
provided in the standard solid-state pseudopotential (SSSP) library[8], in which the precisionand performance of publicly available pseudopotential libraries are extensively tested tofacilitate the optimal choice of pseudopotentials. In the present work, we used ultrasoft
pseudopotentials from the GBRV library[9]with cutoﬀs of 70 Ry and 560 Ry for the expansion of the wave functions and charge densities, respectively. The Brillouin zone integration was performed over a 12 × 12 × 12 k mesh.
Dynamical matrices were computed on 6×6×6
meshes in q space, which were then interpolated to determine the full phonon dispersion.
Comparing the experimental phonon dispersion of SnS with DFPT calculations, we foundthat DFPT calculations are quite successful in327

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

predicting the experimental phonon frequencies. From the calculated phonon eigenvalues
and eigenvectors, we also computed the dynamical structure factor S(Q, ω), which provides an estimation of the phonon intensity. A
comparison with the neutron scattering data
revealed that the experimental phonon intensities of SnS were perfectly reproduced by thissimulation.
The present work thus serves to highlightthe potential to use DFPT phonon calculations
to simulate phonon cross sections as well as
phonon frequencies. A more detailed report is
now in course of preparation and will be published elsewhere.

References[1] B. N. Brockhouse and A. T. Stewart Phys.
Rev. 100, 756 (1995).
[2] K. Nakajima et al., Quantum Beam Sci.
1, 9 (2017).
[3] A. Q. R. Baron, High-Resolution Inelastic
X-Ray Scattering, in Synchrotron Light
Sources and Free-Electron Lasers: Accelerator Physics, Instrumentation andScience Applications, edited by E. J.
Jaeschke, S. Khan, J. R. Schneider, and J.
B. Hastings (Springer International Publishing, Cham, 2016) pp. 1643–1719, (seealso arXiv:1504.01098).
[4] S. Baroni et al., Rev. Mod. Phys. 73, 515(2001).
[5] P. Giannozzi et al., J. Phys. Condens.
Matter 21, 395502 (2009).
[6] P. Giannozzi et al., J. Phys. Condens.
Matter 29, 465901 (2017).
[7] J. P. Perdew, K. Burke, and M. Ernzerhof,
Phys. Rev. Lett. 77, 3865 (1996).
[8] G. Prandini et al., npj Computational
Materials 4, 72 (2018).
[9] K. F. Garrity et al., Computational Materials Science 81, 446 (2014).

Figure 1: Calculated phonon dispersion of SnS.
To facilitate the comparison between theory
and experiment, the dynamical structure factor, S(Q, ω), is weighted on the calculated
phonon dispersion curves.

328

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular dynamics simulations of water confined incarbon structures with the reactive force field
Tomoko MIZUGUCHI
Faculty of Materials Science and Engineering, Kyoto Institute of Technology
Matsugasaki, Sakyo-ku, Kyoto 606-8585

Many studies have been done on water in
confinement by both theoretical and experimental techniques and revealed that the properties of confined water may strongly diﬀer
from that of bulk water. It is clearly importantto properly evaluate the influence of confinement on water for various applications such as
ion channels or drug delivery. Until last year,
we had performed molecular dynamics (MD)simulations of confined water in nanoporous
silica with the reactive force field (ReaxFF)using the supercomputer at ISSP. We examined the influence of hydrophilic surface on
the physical properties of water, specifically,
the hydrogen bond structure and dynamics [1].
This year, I embarked on MD simulations using ReaxFF for water in a carbon nanotube asa model of a hydrophobic pore to clarify the
influence of interface on water.
ReaxFF allows us to incorporate bondbreakage and formation, which are particularly important on interface, in MD simulations with a lower computational cost thanquantum-mechanics-level calculations. I usedfour ReaxFF parameter sets: (i) developedby Monti et al. for biomolecules (protein2013) [2], (ii) by Zhang and van Duin to improve the weak interaction between hydrocarbon and water from protein-2013 force field(CHON-2017 weak) [3], (iii) by Yeon and van
Duin to simulate hydrolysis reactions at silica/water interface (Yeon2015) [4], and (iv)by Pitman and van Duin for clayzeolite com-posites (Pitman2012) [5]. I prepared a singlewalled carbon nanotube solvated in water andobserved the inflow and outflow of water into
the nanotube. The diameter of the carbon
nanotube (CNT) was set 2.7 nm for comparison with our previous results in the silica/water system. All simulations were conducted in the NPT ensemble (T = 300 K and
P = 1 atm) using the Nosé-Hoover thermostat
and barostat with LAMMPS pre-installed in
the supercomputer at ISSP. The ReaxFF MD
simulations were carried out with a time stepof 0.25 fs through the USER-REAXC packageof LAMMPS.
When the protein-2013 and Pitman2012
force fields were used, water flowed into the
CNT and filled it in 250 ps. In the 250-ps simulation using the Yeon2015 force field, water
flowed into the CNT somewhat. It seems toneed more time to fill in the CNT with water.
In fact, when I started the simulation with astructure where the CNT was filled with water,
the CNT remained filled with water. On theother hand, water went out of the CNT using
the CHON-2017 weak force field. Some experiments show that water spontaneously flows
inside the CNT, thus the CHON-2017 weakforce field seems not to be suitable for the
CNT/water system. But we should carefully
verify the result. I am now planning to carryout DFT calculations to compare with the simulation results using ReaxFF.

329

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] T. Mizuguchi, K. Hagita, S. Fujiwara andT. Yamada: Mo. Sim. 45 (2019) 1437.
[2] S. Monti, A. Corozzi, P. Fristrup, K. L.
Joshi, Y. K. Shin, P. Oelschlarger, A. C.
T. van Duin, and V. Barone: Phys. Chem.
Chem. Phys. 15 (2013) 15062.
[3] W. Zhang and A. C. T. van Duin: J. Phys.
Chem. B 122 (2018) 4083.
[4] J. Yeon and A. C. T. van Duin: J. Phys.
Chem. C 120 (2016) 305.
[5] M. C. Pitman and A. C. T. van Duin: J.
Am. Chem. Soc. 134 (2012) 3042.

330

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Manipulation of electronic states with nanostructures: model
construction and its application
Toshikaze KARIYADOInternational Center for Materials Nanoarchitectonics,
National Institute for Materials Science, Namiki, Tsukuba, Ibaraki 305-0044
We focus on computing orbital magnetic

The improved program has been used tosusceptibility, which is relatively easy to

calculate the orbital magnetic susceptibility ofmeasure in experiment, to characterize novel

Sr3PbO, a Dirac material with antiperovskiteband structure such as Dirac/Weyl fermions.

crystalline structure. Temperature and carrier

There are some situations in which computation

number dependence of the susceptibility isof orbital magnetic susceptibility requires large

obtained using a tight-binding model derived

computing resources. One example of such afrom the ab-initio calculation. The improved

situation(i)

program enables us to have better results in low

nanostructured system, which is the main topic

temperature. It turned out that the susceptibilityof this project. Nanostructures lead to large

at low temperature is affected mainly by the

number of sites in a unit cell, which in turnchange in the temperature dependence of the

makes the computation hard. Another situation

chemical potential associated with the change

is when we handle with (ii) real materials.

in the density of states.

is

when

we

deal

with

Generically, taking more orbitals into accountAnother topic in this project is thegives better precision at the cost of computing

investigation on the bilayers of atomically thinpower. Furthermore, in order to characterizematerials with some mismatch showing moire

singular band structures like Dirac/Weyl cones,

pattern. A generic theory on the symmetry-fine sampling of k-points is inevitable.

based constraints on the interlayer coupling is

A useful strategy to improve the efficiency
ofcomputationisapplying

proposed [1], which is inspired by data sets ofmassivethe interlayer coupling in bilayer graphene

parallelization on k-point sampling, which had

obtained by systematic ab-initio calculations.

been done in the preceding project last year.
This year, we have made some corrections inReferences

memory handling to push up the maximum[1] T. Kariyado and A. Vishwanath, Phys. Rev.

system size allowed in the same facility.

Research 1 (2019) 033076.

331

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Statistical Properties in a Branching Network
Satoshi YUKAWA, Kei TAKAYA, and Takeru WATANABE
Department of Earth and Space Science, Osaka University
Machikaneyama, Toyonaka, Osaka 560-0043

0.025
A = 2, arid
A=4
A=6
A=8
A = 10, humid
θ = 72°

0.02

0.015

N(θ)

In a river network, there are many interesting statistical laws, such as Hack’s law andHorton’s law. Recently another statistical law
was found in the distribution of bifurcation
angle.[1, 2] The distribution has a universal
characteristic angle depending on the aridityof the climate:[3] For the humid area, the angle is 2π/5 = 72◦ and, on the other hand, forthe highly arid area, it takes a smaller angle ofalmost 45◦ . The angle 2π/5 is theoretically explained for the Laplacian growth network, but
the smaller angle is not.
In this supercomputer project, we developa theoretical model to understand the aridity
dependence of the network based on the coupled map lattice model.[4] The model is constructed on a square lattice with water and soil
variables. Dynamical rules are too complicatedto be expressed here. The resultant networks
generated by computer simulation are shownin Figs. 1.

0.01

0.005

0
0

20

40

60

80

100

θ(°)

120

140

160

180

Figure 2: Bifurcation angle distribution forseveral aridity parameters A.
of the distribution decreases. There is, however, discontinuous behavior around the characteristic angle in the distribution. The origin
of such behavior is unclear. We need additional
computer simulations.

References[1] O. Devauchelle, A. P. Petroﬀ, H. F. Seybold, and D. H. Rothman: Proceedingsof the National Academy of Sciences 109(2012) 20832.

(a) humid case(b) arid case

Figure 1: Simulated network structures
Distribution of the bifurcation angle can beobtained from the simulated network. The result is presented in Fig. 2. We observe slightaridity dependence in the ﬁgure. Increasingaridity index, the peak at the characteristic angle becomes much larger. Besides the lower tail[2] S. Yukawa, T. Watanabe, and K. Hara:
Journal of the Physical Society of Japan88 (2019) 024901.
[3] H. Seybold, D. H. Rothman, and J. W.
Kirchner: Geophysical Research Letters 44(2017) 2272.
[4] B. Murray and C. Paola: Earth Surface
Processes and Landforms 22 (1997) 1001.

332

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Study of Cell Guiding Mechanism in
Cellular Tissue
Katsuyoshi Matsushita
Department of Biological Science, Osaka University
Toyonaka, Osaka 563-0043

Cells have function in the organisms. In thedevelopment of organisms, cells are not always
born in the suitable place which the cells function. In these cases, cell migration play a significant role to transport the cells to the suitable place. As a prominent observation, there
is a case that the transport length of the cell
migration reaches mm scales much larger thanthe cell’s typical scale of 10µm [1]. In suchcases, the migration should be properly guided
by surrounding tissues to transport the cell for
its suitable position. The guiding mechanism
is still unclear and is expected to utilize chemical signals.

effective in the case of cell transport on tissue.
We show that the migration direction ofcells on the tissue aligns in the same direction
even when the cells are suspended. The order in cell migration is induced as a polarity
memory effect [6, 7]. The net transport velocity exhibits a non-linear transport and becomes a finite value above a threshold adhesion
strength. Furthermore, the transport distanceis longer than 102 times of the cell scale. This
result show potential of the heterophilic adhesion with polarity as the guiding mechanism ofcell transports.

As a candidate of the chemical signal, thechemical cell-cell adhesion is one of most powerful candidate. The possibility of the cell-celladhesion on the explanation of the long distance transport of cells is not sufficiently examined. In this work, we have investigatedthe cell migration on tissue which is guided by
the cell-cell adhesion. We employed the Cellular Potts model and examine cell-cell adhesion
effect on the cell migration in tissue [2].

References

We consider the model consists of suspended
transported cells on cellular tissue on the
Cellular Potts model[3] and one dimensionaltransport of the cells. The cells and tissue interacts with the heterophilic cell-cell adhesion,
As a guiding mechanism of the cell migration
direction, we consider the polarity of the cellcell l adhesion. The polarity is a hypothetical factor for guiding collective cell migrations
with long distance [4, 5] and is expected to be[1] C. Lois and A. Alvarez-Buylla, Science
264, 1145 (1994).
[2] K. Matsushita: submitted to PRE.
[3] F. Graner and J. Glazier, Phys. Rev. Lett.
69, 2013 (1992).
[4] K. Matsushita: Phys. Rev. E 97, 042413(2018).
[5] K. Matsushita: Phys. Rev. E 95, 032415(2017).
[6] K Matsushita, K Horibe, N Kamamoto,S Yabunaka, K Fujimoto, Proc. Sympo.
Simul. Traffic Flow 25, 21 (2019).
[7] Matsushita, K Horibe, N Kamamoto, K
Fujimoto, J. Phys. Soc. Jpn. 88, 103801(2019).

333

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetism in the System with the Multiple-Spin
Exchange Interactions
Chitoshi YASUDA
Department of Physics and Earth Sciences, Faculty of Science,
University of the Ryukyus, Okinawa 903-0213, Japan
Helium-3 (3 He) atoms adsorbed ongraphite form the commensurate solid layer
regarded as the spin-1/2 quantum spin
system on a triangular lattice at certain
density of 3 He. In the exchange process of
3 He atoms, there are not only an exchange
between two neighbor atoms but also thatamong three or more neighbor atoms. The
exchange integrals of three- and four-spin
cyclic exchange interactions are larger
than that of two-spin exchange interaction.
Furthermore, the comparison between thetheoretical and experimental studies showsthat eﬀects of the five- and six-spin exchangeinteractions are not negligible. Thus, in
relation to the solid 3 He, the multiple-spin
exchange (MSE) model on the triangularlattice has been extensively studied. Groundstates and thermodynamic properties of the
MSE model on the triangular lattice havebeen investigated using various methods,e.g., the mean-field approximation[1,2], theMonte Carlo simulations, the exact diagonalization, and the spin-wave theory[3,4].
In particular, the model has attracted
attention owing to the existence of novel
states such as the quantum spin liquid andthe spin-nematic state and the eﬀects offluctuations on ordered phases with chirality.
However, the study becomes diﬃcult for thecomplexity of the system with the various
interactions on the triangular lattice.
Recently, a new quantum spin liquid is experimentally observed in the solid 3 He layer.
This layer is a monolayer 3 He adsorbed ongraphite preplated with atomic layers of deuterium hydride. At low density of 3 He, it
was suggested that there exists the quantum spin liquid with novel dependences of334

the heat capacity and the magnetic susceptibility on temperature. In particular, the lowtemperature heat capacity is proportional to
2/3 power of temperature, which is an unprecedented behavior in the quantum spin
system. The details of this experimental
work are not yet clear, however, it is suggested that the solid 3 He layer is a honeycomb lattice.
We investigate the MSE model on thehoneycomb lattice using numerical methods,
which were applied in works of the MSE
model on the triangular lattice. In thepresent project, we concentrate the classical MSE model with the two-spin interaction and the six-body ring exchange interaction. The ground state is investigated using the conjugate gradient method. In thismethod, we need to prepare many random
spin states as the initial states because of
avoidance of the trap to a metastable state.
For large six-body ring exchange interactions,
we found the classical ground state with themulti-sublattice structure. We also advanceresearch on thermodynamic properties using
the exchange Monte Carlo simulations.

References[1] C. Yasuda, Y. Uchihira, K. Kubo, J.
Mag. Mag. Mater. 310, 1285 (2007).
[2] C. Yasuda, Y. Uchihira, S. Taira, K.
Kubo, J. Phys. Soc. Jpn. 87 104704(2018).
[3] C. Yasuda, D. Kinouchi, K. Kubo, J.
Phys. Soc. Jpn. 75, 104705 (2006).
[4] S. Taira, C. Yasuda, T. Momoi, K.
Kubo, J. Phys. Soc. Jpn. 88, 014701(2019).

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simulation Analysis of Collision of Two Filaments Driven by
Protein Molecular Motors
Kazuo SASAKI
Department of Applied Physics, Graduate School of Engineering, Tohoku University,
Sendai, 980-8579
It is known that protein filaments driven bysimulations of the particles for several particle

protein motors distributed on the glass surface

densities and parameters of the model, and theirform vortices when the density of filaments iscollective motion was analyzed from thehigh [1]. We studied this collective motion by

viewpointcomputer simulation. In this year, we focused on

percolation transition was found to occur as thethe following two systems. One is the system

particle density was increased if the interaction

consisting of two filaments and a lot of protein

between particles was week, while a new

motors [2]. The other is the system in which thephenomenon, the character of which is to be

filaments were simplified as point particles.

clarified, was observed in the case of strongof

percolation

theory[4]. AIn the first system, we studied the collisioninteraction. Formation of vortices was not

between two protein filaments, which is closely

observed, probably due to the simplicity of therelated to the emergence of the vortices. Fourmodel.

types of collisions were found experimentally

The calculations were performed using the[1]: parallel, anti-parallel, stop, and crossing; theL4cpu in both the systems B and C. We used our

probability of which type was observed strongly

custom-made program for the calculations.

depended on the incident angle between two
filaments. We simulated the collision of the two

References

filaments for various incident angles. We have[1] Y. Sumino, et al.: Nature 483 (2012) 448.

successfully reproduced the dependences of the[2] Y. Ishigure and T. Nitta: Langmuir 30 (2014)

probabilities on collision angle for parallel, anti-

12089.

parallel, and stop of collision types.

[3] F. Peruani, T. Klauss, A. Deutsch, and A.
Voss-Boehm: Phys. Rev. Lett. 106 (2011)

In the second system, we simplified themodel of protein filaments in accordance with

128101.

the previous study [3]: The filaments were[4] D. Stauffer and A. Aharony: Introduction To

modeled as self-propelled particles; and they

Percolation Theory, 2nd ed. (Taylor & Francis,

moved on a lattice. We performed Monte-Carlo

London, 1992).

335

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Elucidation of the coercivity mechanism by statisticalphysical approaches
Masamichi Nishino
National Institute for Materials Science,
Tsukuba, Ibaraki 305-0044, JapanThe neodymium (Nd) permanent magnet,
Nd2 Fe14 B, which has strong coercivity, is anindispensable material in modern technologies, applied to information-storage devices,hybrid and electric vehicles, generators, etc. [1]This magnet has also another interesting feature. It exhibits a temperature-induced spinreorientation (SR) transition. The spin dynamics on the SR transition in the magnet has
not been clarified. The temperature dependence of the ferromagnetic resonance (FMR)
frequency is an open question.

quency above TR in connection to the temperature, magnetization along to the easy axis,
and the fluctuation of the magnetization along
to the hard axis (hard plane). We found that
this formula is a good description for overalltemperature region, and the last factor (fluctuation of transverse magnetization) in the formula is important for the qualitative nature of
the FMR frequency.
TR
200

In the present work we studied the temperature dependence of the FMR frequency at zeroexternal field. [2] The FMR spectrum I(f ) is
calculated by the auto-correlation function of
spins (power spectrum) for an atomistic modelof the Nd magnet. The temperature dependence of the FMR frequency fR is plotted byblue diamonds in Fig. 1.
We find that fR exhibits a drastic changearound TR (SR transition temperature) andnon monotonic temperature dependence. In
particular, it is found that fR ∼ 0 below TR .
This is totally diﬀerent from the dependenceof conventional magnets with a single uniaxial
anisotropy energy, in which a monotonic decrease of the FMR frequency is observed. We
clarified the mechanism for fR ∼ 0 below TR .
At zero temperature the state of the tilted spinalignment is stable, and the precession aroundthe ground-state (GS) easy axis (parallel to
the GS magnetic moments) does not occur.
We also derived the formula for the FMR fre-f [GHz]

150

100

50

0
0

200

400

600

800

1000

T [K]

Figure 1: Temperature dependences of fR(blue diamonds) for the atomistic Nd magnet
model..

References[1] S. Hirosawa, M. Nishino,
Miyashita, Adv. Nat. Sci:
Nanotechnol. 8 (2017) 013002.

and S.
Nanosci.

[2] M. Nishino, and S. Miyashita, Phys. Rev.
B 100 (2019) 020403(R).

336

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Transition in the memory effect of paste
Akio NAKAHARA
College of Science and Technology, Nihon University
7-24-1 Narashino-dai, Funabashi, Chiba 274-8501
A dense colloidal suspension, called a paste,

reproduce the transition from memory of shear

remembers the direction of its motion, such as

to vibration, we find that we have to abandon thevibration and shear, and these memories in paste

assumption of simple shear flow and solve more

dominate the preferential direction for cracks torealistic flow motion under vibration.

propagate. When a paste remembers vibration,
cracks propagate in the direction perpendicular
to the direction of the vibration, while, when apaste remembers shear, cracks propagate along
the shear as is shown in Fig. 1 [1-2].
(a) Setup(b) Velocity field

Fig. 2: Direction of a simple shear applied to apaste in numerical simulations.

Fig. 1: Crack patterns induced by memory effect.
(a) Memory of vibration (b) Memory of shear.
To explain the formation of striped crack
pattern, we performed numerical simulations ofFig. 3: Elongated clusters along shear flow withshear motion of colloidal suspension using

its solid volume fraction of paste 3.3%.

LAMMPS. Colloidal particles attract each other

References

via Lennard-Jones potential and receives[1] L. Goehring, A. Nakahara, T. Dutta, S.

Stokes’s drag force from surrounding fluid.

Kitsunezaki and S. Tarafdar, Desiccation

When we assume a simple shear as shown in Fig.

Cracks and their Patterns (Wiley, 2015).

2, we obtain formation of elongated clusters[2] Japan patent JP 6565067, Material Mixing

along shear, as shown in Fig. 3, which dominates

Method, A. Nakahara, Y. Matsuo, M. Ito andpreferential direction for cracks to propagate. To

R. Yoneyama (2019)337

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Study of One Dimensional Frustrated
Quantum Spin Systems
Kazuo HIDA
Professor Emeritus, Division of Material Science,
Graduate School of Science and Engineering,
Saitama University, Saitama, Saitama 338-8570

We investigate the ground-state phases ofspin-1 alternating-bond diamond chains described by the following Hamiltonian [1]:
H=

N [
∑
(1)
(1)
(1 + δ)S l τ l + (1 − δ)τ l S l+1

Hence, each ground state consists of an array ofn successive Tl = 1 pairs separated by singlet
dimers. This phase is called a DCn phase. If
no singlet dimers are present, the ground stateis equivalent to that of a mixed spin chain,

l=1
(2)

+ (1 + δ)S l τ l](1) (2)+ λτ l τ l ,
(1)

(2)

+ (1 − δ)τ l S l+1

H=
(1)

(2)

where S l , τ l , τ l are spin-1 operators. The
lattice structure is depicted in Fig. 1.
(1)

τl
1+δ

1−δ

λ
Sl
1+δ

Sl+1
1−δ
(2)

τl

Figure 1: Structure of a spin-1 alternatingbond diamond chain. S = τ (1) = τ (2) = 1.
The exchange parameters are denoted by λ,1 + δ, and 1 − δ, where λ and δ control thestrengths of frustration and bond alternation,
respectively.
Each ground state consists of an array ofspin clusters separated by singlet dimers owing to an inﬁnite number of local conservation
law,
(1)

∀l [T 2l , H] = 0, (T l ≡ τ l(2)+ τ l ).

(2)

A pair of spins with Tl = 0 is a singlet dimer.
For λ > 2, the state with Tl = 2 is not allowed.

338

N [
∑
(1 + δ)S l T l + (1 − δ)T l S l+1
l=1]+ λ(Tl (Tl + 1) − 4) (Tl = 1 or 2)(3)

with inﬁnite length. For strong frustration, we
ﬁnd a series of quantum phase transitions asin the case of alternating-bond mixed diamondchains with spins 1 and 1/2[2]. For intermediate frustration, we ﬁnd the nonmagnetic Haldane or dimer phases according to whether thebond alternation is weak or strong. For weak
frustration and weak bond alternation, we
ﬁnd the ferrimagnetic states with spontaneous
magnetizations m = 1/6 (F1/6 phase) and 1/3(F1/3 phase) per site. The F1/6 phase is accompanied by a spontaneous translational symmetry breakdown. This phase vanishes for strong
bond alternation[1]. The presence of a narrow
partial ferrimagnetic phase is suggested near
the point (λ, δ) = (λc , δc ) ≃ (1.0832, 0.2598).
The phase diagram determined by the numerical calculation for the Hamiltonian (3) using ﬁnite-size DMRG and inﬁnite-size DMRG
methods is shown in Fig. 2 except for the partial ferrimagnetic phase whose width is estimated to be so narrow that it is invisible inthis scale.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] K. Hida, J. Phys. Soc. Jpn. 89, 024709(2020)[2] K. Hida, K. Takano, and H. Suzuki, J.
Phys. Soc. Jpn. 79, 044702 (2010).

1
(a)
δ

DC∞
Dimer
(λ,δ)
=(1.03261,0.42495)

F1/3
(λ,δ)
=(2.5338,0.2598)

0.5

(λ,δ)
=(1.0832,0.2598)
DC0
F1/6
DC∞
Haldane
0

1

DC1

2

3

λ

4

1
(b)
δ
DC∞
Dimer

0.5

(λ,δ)
=(1.03261,0.42495)

F1/3

(λ,δ)
=(1.0832,0.2598)
F1/6
DC∞
Haldane
0
0.9

1

1.1

λ

Figure 2: (a) Overall ground-state phase diagram. Small open circles are the phase boundaries between DCn and DC(n − 1) phases. Forn ≥ 4, these phase boundaries are only shownby solid lines to avoid complications. Other
phase boundaries are shown by the large open
circles and solid lines. The exact DC0-DC1
phase boundary is shown by the thick dotted line. The open square is the accumulation point of inﬁnite series of critical points at
δ = δc (≃ 0.2598). The ﬁlled squares are triple
points. (b) The enlarged phase diagram in thesmall λ region. The thick dotted line is the approximate relation for δ ≃ 1. (from Ref. [1])339

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Construction of A New Method for Analysis of Crystallization
Mechanism from Amorphous Precursor Using Molecular
Dynamics Simulation Method and Unsupervised Machine
Learning
Hiroki NADA
National Institute of Advanced Industrial Science and Technology (AIST),
16-1 Onogawa, Tsukuba, Ibaraki 305-8569

crystallization from disordered systems in

The control of crystallization fromdisordered systems, such as amorphous

MD simulation studies.

crystalAn MD simulation of a supercooledengineering. However, our understanding

Lennard-Jones melt was performed usingof the mechanism of crystallization from

ISSP supercomputer. The methodology

disordered systems is still poor. This is

was utilized to evaluate the structural

because the structure of disorderedsimilarity between the melt and its

systems can hardly be elucidated by

crystalline form, which was regarded as

experimental means.

the geometrical similarity of the pair-

and

melt,

is

essential

to

Molecular dynamics (MD) are often

distribution function between them, at

helpful to elucidate the structure ofeach period during crystallization. An

disordered systems. A question is how toabrupt change of the structural similarity,

evaluate

which corresponded to crystal nucleation,thetime-evolution

of

the

structure in disordered systems during

wassuccessfully

detected.

Itiscrystallization properly.

anticipated this methodology contributes

Recently, a new methodology forto elucidation of the mechanism ofevaluation of the structural similarity

crystallization, even for multicomponent

betweensystems,

different

phases

using

the

such

as

crystallizationofdimensional reduction, which has beencalcium carbonate from its amorphousdeveloped as a method of unsupervised

precursor.

machine learning, is proposed [1]. The
purpose of this project is to demonstrate

Referencesthat this methodology contributes to[1] H. Nada: ACS Omega 3 (2018) 578.

elucidatingthemechanismof340

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

The analysis of the dynamical response to the opticalbistability
Tatsuhiko SHIRAIGreen Computing Systems Research Organization, Waseda University
Waseda-chou, Shinjuku-ku, Tokyo 162-0042

We have studied a dynamical response ofan optical bistable system to a time-periodic
driving ﬁeld. The optical bistability has beenfound in cavity systems with an external driving ﬁeld. As a function of laser intensity, there
is a ﬁnite interval with bistability of a hightransmission state (HTS) and a low transmission state (LTS). When the intensity of the
input laser is time-periodically modulated beyond the bistable regime, the system shows adynamical phase transition when the period of
the modulation changes. At large period, thesystem stays in a diﬀerent stable state depending on whether the laser intensity is increasingor decreasing. On the other hand, at small period, the system is kept in either the HTS or
the LTS. Here, we show that the Floquet dissipative map is useful to characterize the dynamical phase transition. The Floquet dissipative
map is given by a time-evolution operator ofa quantum master equation, and it characterizes the limit cycle and the decay rate of therelaxation dynamics. We found that the decayrate exhibits qualitatively diﬀerent system-size
dependence before and after the phase transition, and it shows a ﬁnite-size scaling of spinodal phenomena around the transition point.
This work was published to Physical Review
A [1].

operator L as a matrix. Naively, the number of elements in L increases exponentiallywith the number of spins N , which gives astrong restriction on N in the numerical simulation. However, we made use of the fact thatthe present model has a symmetry under exchange of spins. This symmetry reduces thenumber of non-zero elements in L to the orderof N 3 [2, 3, 4]. We have used this property andperformed simulations up to N = 100.
This research was supported by MEXT as
the “Exploratory Challenge on Post-K Computer project (Challenge of Basic ScienceExploring Extremes through Multi-Physics
and Multi-Scale Simulations).

References[1] T. Shirai, S. Todo, and S. Miyashita:
Phys. Rev. A 101 (2020) 013809.
[2] S. Sarkar, and J. S. Satchell: EPL 3(1987) 797.
[3] M. Gegg, and M. Richter: New J. Phys
18 (2016) 043037.
[4] T. Shirai, S. Todo, H. de Raedt, and
S. Miyashita: Phys. Rev. A 98 (2018)
043802.

In this work, we develop a numerical algorithm to eﬃciently solve the dynamics governed by the quantum master equation consisting of many spins. To do it numerically,
it is necessary to express the time evolution341

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study for superconductivity insuperstructured strongly correlated materials with
two-particle self-consistent approach
Kazutaka NISHIGUCHI
Graduate School of Science, Technology, and Innovation, Kobe University
1-1 Rokkodai-cho, Nada-ku, Kobe 657-8501, Japan– High-Tc superconductivity in multi-layer
cuprates –We have theoretically studied superconductivity in multi-layer cuprate, which is a series ofsuperstructured strongly correlated materials.
Here 1–5-layer Hubbard model has been considered as an effective model for multi-layer
cuprate superconductors. Then we have investigated the multi-layer superconductivity bysolving the linearized Eliashberg equation forthe superconducting gap function within the
two-particle self-consistent (TPSC) approach.
We have also developed the TPSC approach so
as to treat the multi-layer systems. Many degrees of freedom arising from the multi-layer
properties have been treated by the massive
parallelization in ISSP Supercomputer Systems.
– Possible superconductivity induced by spinorbit coupling in carrier doped Sr2 IrO4 –Possible superconductivity in in carrie- doped
iridium oxide insulator Sr2 IrO4 have studied
by a weak-coupling approach[1]. We havetreated t2g 3-orbital Hubbard model with alarge spin-orbit coupling (SOC) as an effectivemodel for carrie- doped Sr2 IrO4 . Numericallysolving the linearized Eliashberg equation forthe superconducting (SC) gap function withthe random phase approximation (RPA), we
have systematically examined both singlet andtriplet SC gap functions with possible pairing
symmetries and their parameter dependence.
For the realistic SOC λ and Hund’s coupling

J/U relevant to Sr2 IrO4 , namely, for a large
λ and small J/U region, we find that the
intra-band antiferromagnetic (AF) pseudospin
jeff = −l + s fluctuations favor a dx2 −y2 -wave
pseudospin jeff = 1/2 singlet pairing in theelectron-doping (Figure 1). We also find thatthe dx2 −y2 -wave pairing is more stabilized withincreasing the SOC and decreasing the Hund’s
coupling. Furthermore, we show for a small
λ and large J/U region that an s± -wave singlet pairing is favored in the hole-doped region(Figure 2). The origin of the s± -wave pairing
is due to the interband pair scattering arisingfrom the intra-orbital AF spin s fluctuations.
Although the possibility of a pseudospin triplet
pairing is considered, we find it always unfavorable for all parameters studied here. We
have also developed the multi-orbital and spindependent RPA so as to treat the multi-orbital
systems with spin-orbit coupling. Many degrees of freedom arising from the multi-orbitaland spin properties, namely, spin-orbit coupling, have been treated by the massive parallelization in ISSP Supercomputer Systems.
– Electronic structures of doped SrTiO3 as
H2 -generation semiconductor photocatalyst –We have performed the first-principles calculations based on the density functional theory toobtain electronic structures of doped SrTiO3
as a H2 -generation semiconductor photocatalyst. We have set the dopants to be a Rh
and Sb atom and replaced the Ti sites withthem in the 3 × 3 × 3 SrTiO3 supercell. The

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo
0.6

0.9

0.8 0.7

0.3

0.2

0.4

0.5
0.6

0.9
0.8

0.6

0.7

0.5
0.6

Figure 1: Contour plot of the largest eigenvalue of the linearized Eliashberg equation
for the dx2 −y2 -wave pseudospin singlet pairingin the parameter space of the electron density n and the SOC λ for U = 0.8 eV, andJ/U = 0.05. The red (blue) region represents
the dx2 −y2 -wave pseudospin singlet SC (x-AF)
phase.

Figure 2: Contour plots of largest eigenvalueof the linearized Eliashberg equation for thes± -wave pseudospin singlet pairing in the parameter space of n and λ for U = 0.9 eV and
J/U = 0.3. The red region represents the s± wave pseudospin singlet SC phase.
[2] VASP (The Vienna Ab initio Simulation
Package): https://www.vasp.at

O-vacancies have also been considered as theintrinsic defect in the realistic experimental situations. The first-principles calculations havebeen performed by using VASP (The Vienna
Ab initio Simulation Package)[2], in which thehybrid functionals (HSE06) are adopted to reproduce the accurate band gap of SrTiO3 , andthe massive band and k-point parallelization
are used in ISSP Supercomputer Systems. The
numerical calculations have shown from thedensity of states that the Rh-doping produces
the impurity levels within the band gap as both
donor and acceptor levels. We have also observed that the Sb-doping works as electrondoping and then removes the acceptors in the
Rh+Sb-doping systems. In addition, the Ovacancies also works as electron-doping, whichleads SrTiO3 to the n-type semiconductors.

References[1] K. Nishiguchi, T. Shirakawa, H. Watanabe, R. Arita, and S. Yunoki: J. Phys.
Soc. Jpn. 88 (2019) 094701.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Ising machines from a viewpoint ofstatistical mechanics
Shu TANAKA
Green Computing Systems Research Organization, Waseda University
27 Wasedacho, Shinjuku, Tokyo 162-0042

We have studied the performance of Isingmachines from a viewpoint of statistical mechanics. The Ising machines have been attracting attention in recent years as a computer thathas the potential to solve combinatorial optimization problems with high speed and accuracy. Very recently, quantum annealing machines, simulated annealing machines, and various other types of Ising machines have beendeveloped. In order to draw out the potential of the Ising machine, it is more important
to develop not only the hardware of the Isingmachine but also the algorithm and softwarein accordance with the established mathematical framework. We conducted research on thefollowing two topics on the basis of this trend.
(A) A guiding principle for embeddingin simulated-annealing based Ising machines
When we use the Ising machine, the costfunction and constraints of the combinatorial
optimization problem are first expressed in the
Hamiltonian of the Ising model or equivalentform. Herein, we refer to the Ising model as thelogical Ising model. Next, we represent the logical Ising model on the limitations of the network of spins in an Ising machine. The operation is called embedding. In embedding algorithms, there are hyperparameters that should
be adjusted to improve the computational performance, and how to adjust them is still unknown. In order to solve this question, we
have succeeded in constructing a method of
embedding algorithm based on the calculationof the correlation function by the transfer matrix. The results suggest an improvement in
the computational performance of simulated
annealing-based Ising machines against typicalexisting embedding algorithms [1].
This work was done in collaboration with
Dr. Tatsuhiko Shirai (Waseda Unviersity).
(B) The performance of black-box optimization using Ising machines from aviewpoint of statistical mechanical informatics
We have previously proposed a new methodof black-box optimization using the Ising machine [2]. The results suggest that this method
is superior to existing methods in the search
for metamaterials with excellent thermal radiation characteristics. The theoretical basis forthe superiority of this method is clarified fromthe perspective of statistical mechanical information.
This work was done in collaboration with
Dr. Ryo Tamura (National Institute for Materials Science, The University of Tokyo).

References[1] T. Shirai, S. Tanaka, and N. Togawa,submitted. preprint version is available via https://www.dropbox.com/s/
o8alkr8ch05ahtr/bare_jrnl_compsoc.
pdf[2] K. Kitai, J. Guo, S. Ju, S. Tanaka, K.
Tsuda, J. Shiomi, and R. Tamura: Phys.
Rev. Research 2 (2020) 013319.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Nonequilibrium phase transition and slow dynamics
in the dense hard sphere systems
Masaharu ISOBE
Nagoya Institute of Technology
Gokiso-cho, Showa-ku, Nagoya, 466-8555

The hard disk/sphere systems are one of
the simplest models, which have been actively
investigated in both equilibrium and nonequilibrium statistical physics. In this project,
we investigated non-equilibrium phenomenain the hard disk/sphere model system withmodern algorithms, especially for Event-Chain
Monte Carlo(ECMC) [1] and Event-Driven
Molecular Dynamics(EDMD) [2], where we
propose the “Hybrid Scheme”, namely, ECMC
for equilibration and EDMD for calculation of
dynamical properties [3, 4].
Dynamic facilitation and direct evidence ofvoid induced structural relaxations in glass formers:
On approaching glass transition, the viscosity of the supercooled liquid would be increased
rapidly. It often behaves as solid with disorder
structure within observation timescale. One of
the challenging issues is to understand whether
the essential properties of glass-forming materials are fundamentally thermodynamic or dynamic in origin. However, the microscopic origin of structural (so-called α) slow relaxationin deeply supercooled liquids at an atomic
scale has remained elusive due to the limitation of both electron microscopy experiments
and computer simulation. Although many theoretical models have been proposed and debated actively, one of a perspective that favors a dynamic origin is called Dynamic Facilitation (DF) theory [5, 6, 7]. DF theory was
known to explain a wide range of empiricallyobserved dynamical features of thermal super-cooled liquids and glasses. The applicability ofDF theory to athermal systems, i.e., systemsof hard particles where the relevant control parameter is pressure rather than temperature,under “super-compressed” conditions was investigated by employing novel eﬃcient algorithms [1, 2, 3]. The novel methodologies
allowed studying in detail the true equilibrium dynamics of high-density systems, whichis consistent with the predictions of DF theory. In such athermal molecular systems under“super-compressed” conditions — where what
is facilitated is the ability of the constituent
particles to structurally relax — giving rise
to correlated and cooperative dynamics, in amanner predicted by theory [8].
In collaboration with the experimentalgroup in Hong Kong, we resolve the coarsegrained trajectories obtained by colloidal experiments to conﬁrm DF theory. The results
undergo a transition from collective “creeping” to the string-like “hopping” motion on approaching the glass transition, where mobile ofparticles can be rearranged in string-like manners or compact geometries. Still, the compact
ones decomposed into connected sequences ofstring-like hopping motion. Furthermore, sucha string-like motion has an ultra-high returning hopping probability, which is proved to be
the leading contributor to the kinetic arrest forslow relaxation. One of the paradoxical issues
in DF theory is how a starter of string-like
hopping has suﬃcient room for the ﬁrst hop
in highly dense packing fraction. A void as a345

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

defect in the crystal structure can diﬀuse one
after another on the crystal lattice positions incase of dense mono-disperse systems. However,in a dense amorphous structure, there are few
voids with a size of particle diameter. Instead,
we found the quasi-voids distributed withina few neighboring shells. The suﬃcient freevolumes come from accumulated quasi-voids
within a local area as a soft spot might induce
the origin of string motion, where free volumes
transport along to the string-like hopping motions. These hypotheses are now carefully investigated by molecular dynamics simulation,
where the results would show direct evidenceof the scenario based on DF theory [9].

[9] C.-T. Yip, M. Isobe et al.: in preparation.

References[1] E. P. Bernard, W. Krauth, and D. B. Wilson: Phys. Rev. E 80 (2009) 056704.
[2] M. Isobe: Int. J. Mod. Phys. C 10 (1999)
1281.
[3] M. Isobe: Mol. Sim. 42 (2016) 1317.
[4] M. Isobe: “Advances in the Comutational Sciences — Proceedings of the Symposium in Honor of Dr Berni Alder’s
90th Birthday”, edited by Eric Shwegler, Brenda M. Rubenstein, and Stephen
B. Libby, World Scientiﬁc, Chapter 6(2017) 83.
[5] D. Chandler and J. P. Garrahan: Annu.
Rev. Phys. Chem. 61 (2010) 191.
[6] L. O. Hedges, R. L. Jack, J. P. Garrahan and D. Chandler: Science 323 (2009)1309.
[7] A. S. Keys, L. O. Hedges, J. P. Garrahan,
S. C. Glotzer, and D. Chandler, Phys.
Rev. X, 1 (2011) 021013.
[8] M. Isobe, A. S. Keys, D. Chandler, and J.
P. Garrahan: Phys. Rev. Lett. 117 (2016)
145701.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Glass phases induced by correlations
Chisa Hotta
Department of Basic Science, University of Tokyo
Meguro-ku, Komaba, Tokyo 153-8902

We studied the possibility of having a finite
temperature glass phases driven by the corelation eﬀect. Conventional spin glasses in realistic spatial dimensions, d = 2, 3 are realized in a series of Edwards-Anderson models
with classical interactions between spins, Jij ,which distribute at around Jij = 0. There, thedegree of disorder the only energy scale thatcompetes with the thermal fluctuation. Evenin such case the spin glass phases breaking thetime reversal symmetry is allowed to exist at
finite temperature only when d ≥ 3. We studied two diﬀerent types of models [1,2].
One is the classical vector spin Heisenberg
model on a pyrochlore lattice with additional
Ising-like lattice degrees of freedom, σi [1]; σi =±1 indicate the displacement of the lattice siteat each vertex, in and out of the tetrahedra,and the exchange interaction Jσi ,σj between
Heisenberg spins depends on the location of
displacements of sites that the spins live on.
Although there is no quenched randomness inthe system, the elastic energy term ∝ σi σj andthe spin exchange energy term Jσi ,σj Si · Sj arecorrelated with each other via Jσi ,σj and workas dynamical randomness to each other. The
two degrees of freedom finally undergo a simultaneous glass transition, which is detectedby the scaling analysis on the auto-correlation
functions[1].
The other one is the quantum transverse
Ising model on a triangular lattice with verysmall quenched bond randomness[2]. Thistime, the transverse field first works on thespin degrees of freedom and drives the system
to a KT phase, and successively to the clock-347

phase, where the three-sublattice magnetic ordering appears. Introducing a very small bondrandomness breaks the regular three-sublattice
structure of the clock phase into pieces of domains, cooporatively with the emergent glass
behavior of the spin degrees of freedom. The
spins and lattices(bond order) work to eachother as an emergent random fictitious field,
which is the origin of the finite temperature
spin glass in d = 2 system.
There are two common aspects between
these two cases. First, the model has a finite spin coupling constant J, and energy scale
represnting the quenched disorder is either absent or very small, which is contradictory to
the case of conventional spin glass whose energy is scaled by the quenched disorder. However, since these J’s are defined on frustrated
lattices, the interactions themselves are notenough to stabilize any kind of magnetic orderings. This allows the emergent energy scaleof disorder to dominate the low energy prooerties of the system. Second point is that theinterplay of the two diﬀerent species of degrees
of freedom can stabilize the glass phase much
more easily than had been considered before.
Each of the degrees of freedom have a tendency
to order and are on the verge of transition. The
correation with other degrees of freedom would
not allow them to have a regular order, andboth cooporatively goes into the glass phase.

References[1] K. Mitsumoto, C. Hotta, and H. Yoshino,
Phys. Rev. Lett. 124, 087201, (2020).
[2] C. Hotta, K. Ueda and M. Imada, in preparation.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetic structures of multiple-Q states infrustrated itinerant magnets
Takashi UCHIDA
Hokkaido University of Science
4-1, 7-15, Maeda, Teine-ku, Sapporo 006-8585

Recently, the magnetic structures ofmultiple-Q states have attracted attention
since the topologically protected vortexlike magnetic structures such as magnetic
skyrmions emerge as 3Q multiple helical spin
density waves in the Dzyaloshinskii-Moriya(DM) interaction driven systems under magnetic ﬁeld. In addition to these systems, thefrustrated systems without the DM interaction have been found to reveal magnetic
skyrmions [1, 2]. In the present work, wehave applied the molecular spin dynamics(MSD) method [3] to the triangular-lattice
single-band Hubbard model without the
DM interaction to investigate the magnetic
structures of multiple-Q states realized aroundthe antiferromagnetic-ferromagnetic phaseboundary.
The MSD method is based on the functional integral method with the static approximation for the spin ﬂuctuation theories andthe isothermal molecular dynamics method.
The method allows us to ﬁnd automaticallythe magnetic structures of a large system withthousands of atoms in a unit cell at ﬁnite temperatures.
In the numerical calculations the most timeconsuming process is the magnetic force calculation at each time step, where the local electronic structures are calculated in real
space by means of the recursion method. We
have adopted the automatic parallel calculation scheme and found it to be eﬀective in saving both computing time and CPU resources.

We have performed the magnetic structure
calculations on the supercell with 20×20 triangular lattice, which is embedded in a large cluster consisting of 3 × 3 supercells, each of which
are connected by the periodic boundary condition and are subject to the self-consistent uniform eﬀective medium. Under zero magnetic
ﬁeld and the ﬁxed value of the temperature
T /t = 0.0005, we have changed the Coulombinteraction strength U/t = 5 ∼ 8 and the electron number n = 1.29 ∼ 1.36. The various
multiple-Q states such as 2Q, 4Q, 2Q+1Q were
found to be realized near the ferromagnetic
boundary. Of these, the 2Q states are accompanied by small spontaneous magnetization. It
is not clear, however, whether the calculated
multiple-Q states are topologically protectedstructures or not. This is partly because thatthe main Q state is often accompanied by small
satellite components, which make the wholemagnetic structure complex. In order to makeclear the magnetic structures of the multipleQ states, the magnetic structure calculations
with the site-dependent self-consistent eﬀective medium are now in progress.

References[1] T. Okubo, S. Chung, and H. Kawamura:Phys. Rev. Lett. 108 (2012) 017206[2] Y. kakehashi, D. Koja, T. Olonbayar, and H.
Miyagi: J. Phys. Soc. Jpn. 87 (2018) 094712.
[3] Y. Kakehashi, S. Akbar, and N. Kimura:Phys. Rev. B57 (1998) 8354.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetization reversal process in classical spin systems
Taichi Hinokihara
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
We studied a reveal the magnetization reversal process by using the classical spin Heisenberg modelwith the dipole-dipole interactions (DDI).
Recently, theoretical studies for the coercivity based on the atomistic-scale spin model are increasing
due to the development of the first-principles calculations.
While these studies enable us to obtain material-dependent properties, the computational cost also
increases to simulate such the model.
The problem becomes severe for studying the coercivity of magnet because it strongly depends on
the long-range interaction, DDI [1,2].
In this project, we focused on the following two subjects: (i) develop efficient methods to simulate
this system. (ii) propose a coarse-graining method to construct a macro spin model from theatomistic scale system obtained from the first-principles calculations.
For the subject (i), we recently developed the novel efficient method for the simulation of the
dynamics of spins, called time quantified Monte Carlo with the stochastic cutoff method(TQMC+SCO).
As an example, the computational cost for the spin update is for the three-dimensional DDI systemeven when the system consists of the complicated lattice structure.
We analytically prove that the TQMC+SCO gives the same Fokker-Planck equation with thestochastic Landau-Lifshitz-Gilbert (s-LLG) equation, which is widely used for the simulation of spin
dynamics.
Namely, the ensemble average of the magnetization trajectory calculated by the TQMC+SCO is thesame as that by the s-LLG.
We also evaluated the validity of the present method by demonstrating the magnetization reversal
process and comparing it to the result obtained by the s-LLG.
Figure 1 shows three magnetization-trajectories of the total magnetization along z-axis: s-LLG
without DDI, s-LLG with DDI, and TQMC+SCO with DDI.
This simulation is performed in the 10×10×10 spin system with exchange coupling 𝐽 , the349Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

anisotropy 𝐾 = 0.1𝐽, the DDI 𝐷 = 0.05𝐽, and the temperature 𝑇 = 0.2𝐽.
We performed the magnetic field = 0.085𝐽 to drive the magnetization reversal process.
This figure clearly shows two results: (a) the DDI plays an essential role in the system with DDI, and(b) both s-LLG and TQMC+SCO gives the almost same magnetization trajectory.
We have submitted our paper, and it is now under review [3].
Besides, we recently found the other way of the bond-update process, which is suitable for the GPU
calculation.
We are now preparing this paper.
Each macro spin motion follows this landscape.
Next, the exchange coupling between themacro spins is selected to optimize the physicalproperties such as domain-all width.
We study the validity of our model bycomparing it to other physical properties suchas the total-magnetization and the susceptibility.
We are now preparing this paper.

References
Fig.

1:

Magnetization

reversalprocess[1] Taichi Hinokihara, Masamichi Nishino,

calculated by s-LLG without DDI (black), s-

Yuta Toga, and Seiji Miyashita: Phys. Rev. B

LLG with DDI (red), and TQMC+SCO with

97 104427 (2018).

DDI (blue).

[2] Yuta Toga, Masamichi Nihsino, Seiji
Miyashita, Takashi Miyake, and Akimasa

For the subject (ii), we constructed the macro-

Sakuma: Phys. Rev. B 98 054418 (2018)

pin Hamiltonian from the atomistic-scale spin

[3]

model of Nd2Fe14B in the following procedure.

Munetaka Sasaki, and Seiji Miyashita, arXiv:

First, we construct the free-energy landscape

1811.00237v2 (2019)

for the single macro spin from the atomisticscale spin model.

350

Taichi Hinokihara, Yuta Okuyama,

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Quantum simulation for quantum many body systems using
noisy-intermediate-scale quantum computers
Keisuke Fujii
Graduate School of Engineering Science,
Osaka University, 1-3 Machikaneyama, Toyonaka, Osaka 560-8531
to describe molecular electronic wavefunctions

Noisy Intermediate-Scale Quantum (NISQ)
devices, or medium-scale quantum computersquantitatively.

Ourmethodmitigatesthewhose qubits are not fault-tolerant, are expected

problem by decomposing VQE calculation for ato be realized within a few years. As Google

large system into a lot of VQE calculations forshowed in 2019 [1], NISQ devices may be able

small systems. We applied this method toto perform some tasks faster than the state-of-various molecules to verify accuracy andthe-art classical computer. Such tasks should be

efficiency by numerically simulating the outputs

sufficiently simple and suitable for a quantumof quantum circuits. The largest system wecomputer, because of its incapability to remove

investigated was the Benzene molecule with theerrors in the computation process. Particularly,

cc-pVDZ basis sets. We note that it is unfeasible

calculations for quantum many-body systems

to perform the simulation of the original VQE

and quantum chemical systems are expected toalgorithm on classical computers as it requires

be promising applications of NISQ devices.

228 qubits for this system.

In this project, we have developed a method

Our numerical simulation is based on theto compute properties of quantum many-bodyfollowing programs: a fast quantum circuit

systems, especially molecules in quantum

simulator Qulacs [3] developed by our group;chemistry, with NISQ devices and performed

OpenFermion library [4] which can handle

numerical simulations of them by using the ISSP

mapping fermionic Hamiltonians to qubit

supercomputer. Concretely, we invented a

Hamiltonian; a quantum chemistry libraryperturbative approach based on the variational

PySCF [5]. Our code was highly parallelized

quantum eigensolver (VQE) algorithm [2],using MPI, as our perturbative VQE method canwhich is a quantum-classical hybrid algorithm tobe performed in an embarrassingly parallel

compute the ground state energy of a system.

fashion owing to its additive scheme.

One of the obstacles to utilize NISQ devices in

K.F. would like to thank Wataru Mizukami

quantum chemistry is that the number offor his help and collaboration throughout thisavailable qubits is limited and often not enoughproject.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

References[1] F. Arute et al., Nature 574, 505-510 (2019).
[2] A. Peruzzo et al., Nat. Commun. 5, 4213
(2014).
[3] Qulacs, https://github.com/qulacs/qulacs[4] J. McClean et al., arXiv:1710.07629[5] Q. Sun et al., WIREs Comput. Mol. Sci. 8,
e1340 (2017).

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on Complex Systems by Generalized-Ensemble Algorithms
Takuya HAYASHI, Daiki MATSUBARA, and Yuko OKAMOTO
Department of Physics, Graduate School of Science, Nagoya University
Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8602
We had two projects regarding generalized-

per one water molecule [4] isensemble algorithms applied to complex

𝑆 = 0.815533 ± 0.000066.

systems.

This estimate is in good agreement with the

The density of states (DOS) is one of theresults of several other research groups. The

most important physical values in statisticalresults also imply that we need to develop amechanics.

new simulation model in order to estimate the

Recently,

weproposedasimulation protocol, REWL-MUCAREM [1],residual entropy with more accuracy.

in order to obtain the DOS with high accuracy
even in large systems by combining the
Replica-Exchange

Wang-Landau(REWL)

method [2] and the Multicanonical ReplicaExchange Method (MUCAREM) [3]. The
effectiveness of REWL-MUCAREM wasdemonstrated by using the 2-dimensional
Ising model in [1].

Figure 1: The estimates of residual entropy ofWe also applied the REWL-MUCAREM

ice Ih by several research groups.

protocol to the ice Ih system in order toestimate the residual entropy with highIn the second project, we have proposed

accuracy. The residual entropy of ice has

thebecome one of good examples to test the

Method (GCREM) [5], which is one of theefficiency of sampling algorithms. However,multidimensional replica-exchange methods

it seems that there is slight disagreement[6]. This method achieves a random walk inamong the estimates by various calculation

the temperature and chemical potential space,methods (see Fig.1). In this work, we give ouri.e., variables of grand canonical ensemble, inlatest estimate of the residual entropy by

one simulation. In this study, we applied

REWL-MUCAREM protocol.

GCREM to the LJ potential system andOur latest estimate of residual entropy

Grand

Canonical

Replica-Exchange

succeeded in drawing a phase diagram353

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

includinggas-liquid

first-order

phasetransition, second-order phase transition, andsupercritical fluid (see Fig.2). We also
calculated the critical point as (𝑇c∗ , 𝜇𝑐∗ ) =(1.18 ± 0.01, −3.34 ± 0.01). This is in good
agreement with the results of previous study

(a)

(b)

[7].
GCREM could sample various structuralphases in one simulation run (see Fig.3): It
was possible to sample the states of different
numbers of particles such as gas, liquid,
supercritical fluid, because the number of(c)particles in the grand canonical ensemble

Figure 3: Snapshots of the LJ particle systemvaries. By using the structure that definesobtained from a single GCREM run. Fig.3 (a)each of these states, structural analysis based

corresponds to Gas phase, (b) corresponds toon, e.g., radial distribution functions andLiquid phase, and (c) corresponds to supercluster formation, became possible.

critical phase.

References[1] T. Hayashi and Y. Okamoto, Phys. Rev. E.
100, 043304 (2019).
[2] T. Vogel, Y. W. Li, T. Wüst and D. P.
Landau, Phys. Rev. Lett. 110, 210603 (2013).
[3] Y. Sugita and Y. Okamoto, Chem. Phys.
Lett. 329, 261 (2000).
Figure 2:[4] T. Hayashi, C. Muguruma, and Y.

The phase diagram on reduced

temperature and chemical potential space.

Okamoto, in preparation.

The black line indicate 1st order phase[5] D. Matsubara and Y. Okamoto, J. Chem.

transition points and the edge is the 2nd order

Phys. 152, 194108 (2020).

phase transition point, i.e., critical point.

[6] Y. Sugita, A. Kitao, and Y. Okamoto, J.

Dotted lines indicate the critical temperature

Chem. Phys. 113, 6042–6051 (2000).

and chemical potential.

[7] N. B. Wilding, Am. J. Phys. 69, 11471155 (2001).

354

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of a Coarse-Grained Force Field
Designed with a Polar Water Model
Wataru Shinoda
Department of Materials Chemistry, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8653

Coarse-grained (CG) approaches have been
adopted to investigate biological events relevant to the mesoscale. Many models have been
proposed and used for various target systems,
depending on the level of accuracy required in
the CG description. One of the promising CG
FFs, recently renamed as SPICA FF [1, 2, 3],accurately reproduces the experimental thermodynamic properties and structure (distribution function) obtained from AA-MD simulations using the CHARMM FF [4]. However,
the ability of the SPICA FF to predict the morphology of highly charged molecular complexes
in aqueous solution is still limited due to thelack of the polarity with the CG water modeland to the assumption of a high (background)dielectric constant. To overcome this problem,
we developed a CG FF, pSPICA, that is basedon a polar CG water model in order to precisely describe the molecular events that are
difficult to simulate using the SPICA FF with
non-polar water in lipid membrane systems,
such as water defects, membrane electroporation, and morphological changes in the charged
lipid self-assemblies. We follow the parameteroptimization scheme used in the SPICA FF,
namely, the parameters are optimized to reproduce several thermodynamic quantities measured experimentally [1, 2, 3].
In this study, we used the LAMMPS for CGMD simulations, and the simulations were significantly accelerated by GPU. In the pSPICA
FF, the polar CG water particle is composedof a pair of interacting sites, WO and WH

355

!"#

!$#
!" !#
$! "!

Figure 1: (a) Polar CG water, representing
three water molecules, developed in this study.
The blue bead, WO, has a van der Waals radius shown with a black circle. The red bead,WH, is connected to WO via a rigid bond andis positioned within the van der Waals radius ofWO. (b) The CG mapping of a DMPG lipid.
All-atom representation is given in stick and
CG representation is given in transparent particle.

(Fig. 1 (a)), and was designed to represent
three neighboring water molecules in aqueous
solution. The two sites, WO and WH, areconnected by a rigid bond, and have positive
and negative partial charges, respectively. The
choice of the CG sites for lipid molecules is thesame as that in SPICA FF (Fig. 1). The parameters of the CG sites were systematically
optimized to reproduce surface/interfacial tension, density, solvation or transfer free energy,
as well as distribution functions obtained fromall-atom molecular dynamics trajectory generated with the CHARMM FF, following theActivity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

scheme used in the SPICA FF. Lipid membranes simulated using the present CG FF
demonstrate reasonable membrane area andthickness, elasticity, and line tension, which
ensure that the simulated lipid membranes exhibit proper mesoscopic morphology. Using
the pSPICA FF with the supercomputer at
ISSP, we performed a large scale simulation
to investigate the morphology of aggregatesof the lipids dimyristoylphosphatidylglycerol(DMPG) in dilute solution. Thanks to thereasonable variation of line tension and elastic moduli of the lipid membranes dependingon salt concentrations in the pSPICA FF, themorphological changes in the lipid aggregates
showed good agreement with those observed inexperiments (Fig. 2 (a)). CG-MD simulationsof the membrane electroporation processes offlat lipid bilayers and vesicles were successfully
performed by the pSPICA FF. A water channel bridging the lipid bilayer was formed spontaneously in the presence of an electric field
generated by an imbalanced NaCl salt distribution, allowing ion transport across the lipid
bilayer (Fig. 2 (b)). The results were similar to the pore opening process observed using
AA-MD. Thus, the new CG FF enabled us toquantitatively investigate biological events, especially those involving water strings and defects in lipid membranes and ionic molecules.

(a)Salt-free

500 mM NaCl(b)

References[1] W. Shinoda, R. DeVane, and M. L. Klein:
Mol. Simul. 33 (2007) 27.
[2] W. Shinoda, R. DeVane, and M. L. Klein:
J. Phys. Chem. B 114 (2010) 6836.
[3] S. Seo, W. Shinoda: J. Chem. Theory
Comput. 15 (2019) 762.
[4] J. B. Klauda, R. M. Venable, J. A. Freites, J. W. O Connor, D. J. Tobias, C.
Mondragon-Ramirez, I. Vorobyov, A. D.
MacKerell, R. W. Pastor: J. Chem. Phys.
B 114 (2010) 7830.

356

Figure 2: (a) Snapshots of the initial aggregate composed of 5000 DMPG units and thefinally obtained aggregate in salf-free and 500
mM NaCl solution. (b) Snapshot of the electroporation process found in the simulation fora planar membrane system.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Screening of Substitutable Element in Rare-earth
Inter-metallic Compounds
Riki KOBAYASHI
Department of Physics and Earth Sciences, Faculty of Science
University of the Ryukyus, Nakagami, Okinawa 903-0213, Japan300

Total Energy of R5Si3 system200

c-axis/a-axis

Energy (eV)

250
150
100
50
0

Y La Ce Pr NdPmSmEuGd Tb DyHo Er TmYb Lu
Rare earth elements

Figure 1: Total energy of R5 Si3 (R = REEs)
system after structure relaxation.

Recently, we have succeeded in growing single crystals of Ce5 Si3 and Ce5 Ga2 Ge with thetetragonal Cr5 B3 -type crystal structure andfound that the Cr2-sites in the Cr5 B3 -type
crystal structure form the Shastry-SutherlandTetrahedral-Lattice (SSTL). SSTL has four geometrically frustrated two-dimensional layers
in a unit cell, called orthogonal-dimer systems,
and the ground state of Ce2-sites in Ce5 Si3
and Ce5 Ga2 Ge is a spin-dimer due to this geometric frustration. There are no other Cecompounds showing spin-dimers at the groundstate other than Ce5 Si3 and Ce5 Ga2 Ge, which
are important targets for the study of heavy
fermion systems with geometric frustration.
However, few rare-earth compounds with the
Cr5 B3 -type crystal structure have been reported, and this lack of targets is a bottle-

1.90
1.85
1.80
1.75
1.70
1.65
1.60
1.55
1.50

Aspect Ratio of R5Si3 crystal structures

Y La Ce Pr Nd PmSm Eu Gd Tb Dy Ho Er Tm Yb Lu
Rare earth elements

Figure 2: Aspect ratio of R5 Si3 (R = REEs)
crystal structures.

neck for the above research. In this study, thestructural stability of R5 Si3 (R=Rare earth elements) is investigated by comparing the total energy of R5 Si3 obtained by ﬁrst-principles
calculations to ﬁnd new Cr5 B3 -type materials.
The calculations were performed using theVienna Ab-initio Simulation Package (VASP),
which is capable of generalized gradient density approximation (GGA), and the K-points
and energy cut-oﬀ values were based on the
8 × 8 × 4 mesh and VASP recommendations,
respectively[1]. In this study, both quasiNewtonian and conjugate gradient algorithms
are used to calculate the structural relaxation,and it is conﬁrmed that there is no signiﬁcantdiﬀerence in the results between the two algorithms.
Figure 1 shows the total energy of R5 Si3357

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

from ﬁrst-principles calculations. Pm5 Si3 andSm5 Si3 were excluded from the graphs because
Pm is a radioactive isotope with a short halflife, and Sm5 Si3 did not converge in the SCF
calculation. The present calculations revealed
that the total energy is lower in the compounds containing Eu and Yb elements thanin the others, and it may be diﬃcult to obtaina Cr5 B3 -type crystal structure in these compounds.
Figure 2 shows the aspect ratio of the lattice parameter of R5 Si3 . Systematic changes in
the aspect ratios were observed for compounds
containing light REE from Y to Nd. This indicates that a speciﬁc axis of the unit cell may
shrink due to lanthanide contraction.

References[1] G. Kresse and J. Furthmuller, Phys. Rev.
B 54, 11 169 (1996).

358

3.5

SCCMS Projects

359

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-Principles Phase Field Mapping
Kaoru Ohno
Department of Physics, Faculty of Engineering Science,
Yokohama National University, Tokiwadai, Hodogaya-ku, Yokohama 240-8501
In order to predict microstructures of alloys

effects. We succeeded in applying the first-

without relying on any empirical or experi-principles phase field method to this systemmental parameter, we have developed the first-

without using any thermodynamic parameter

principles phase field method by combining

and identifying the element partitioning

cluster expansion theory, potential renormali-

effect, i.e., enrichment of V in the β grainzation theory and density functional theory andboundary and Al in the α phase at 977 ºC.

applied it to NiAl alloys that are used for

Figs. 1(a) and (b) show the resulting V and Al

example in jet engine turbine blades at highconcentrations, while Figs. 1(c) and (d) showtemperature [1]. This year, we focused on Ti-

the corresponding experimental images [3],6wt%Al-4wt%V (Ti64) alloy, which is one ofwhich look very similar to each other. As a

the most used Ti alloys in industry in a broadconclusion, the present method has an ability

range from aerospace to medical applications.

to predict complex microstructure of alloys.

The mechanical properties and the phasetransformation of Ti64 are strongly influen-

References

ced by the microstructure, which is reliant on[1] S. Bhattacharyya, R. Sahara, and K. Ohno,

the history of processing, thermal treatment

Nature Communications 10, 3451;1-10 (2019).

procedures and alloying element partitioning[2] T. N. Pham, K. Ohno, R. Kuwahara, and S.
Bhattacharyya, J. Phys.: Cond. Mat. 32,

(a)

(c)

264001;1-9 (2020).
[3] S. Huang, et al. J. Alloys Compounds. 791,
575-585 (2019).

V

V(ex)

(b)

(d)

Fig. 1: (a) V and (b) Al concentrations obtainedby the present method [2], and (c), (d) the
corresponding experimental images [3].

Al

Al(ex)

360

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Energy conversion --chemical energy-Osamu SUGINO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Challenge

electrochemical

provide a hint to the hitherto

interface study is to establish a

unexplained structure of H/Pt(111).

quantum theory of electrode and to

It is also important to utilize thepredictofanultimately

efficientsimulation for electrocatalyst design.

energy conversion. To this end we

Platinum alloys are used in thestudied two topics, manifestation ofexisting fuel cells, but they are notnuclear quantum effect on H/Pt(111)

activeand environmental effect on theelectrocatalysts,

oxygen reduction reaction (ORR) on

oxides are attracting attention, buttransition metal oxides. The nuclear

thequantum effect was investigated byunderstood. In collaboration with

applying the first-principles pathexperimental groups, we calculated

integral

dynamics

the correlation of the adsorption(PIMD) under different coverageenergies of the ORR intermediates,

conditions [1]. The hydrogen atoms

O2H, OH, and O; the correlation isaredelocalized

known to be a descriptor of thequantum mechanically under low

activity. For most materials, thecoverageincreasingcorrelation curve does not cross thecoverage, the interatomic repulsion

point for ideal activity, but TiO2 andis

ZrO2 are found to cross it whenmolecular

known

found

to

but,
to

be
with

inducelocalization

enough.

mechanism

bettertransition

metal

has

some

not

noble

been

within an adsorption site; atop, fcc,

doped

or hcp.

The interaction induced

dopants [2]. The activity versus

localization, which had been showndefects relation is consistent withto exist in a low index noble metal

experimental findings. From thesesurfaces, was captured on platinum

results, the joint research group is

and this phenomenon is found tonow planning to realize an ideal

361

with

For

metal

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

catalyst.

C123 19486 (2019).

References[1] L. Yan et al. Phys.

Rev.

B101,

165414 (2020).
[2] Y. Yamamoto et al. J. Phys. Chem.

362

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Molecular Dynamics Simulation Studies ofElectrochemical Properties of Ionic Liquid Electrolytes
Hayato SHIBA1,2 and Patrick A. BONNAUD1
1

Institute for Materials Research, Tohoku University, Katahira, Aoba-ku, Sendai 980-8577
2

Information Technology Center, The University of Tokyo, Kashiwa-no-ha,
Kashiwa, Chiba 277-8589

Ionic liquids (ILs) are salts that are liquid at

We have observed that ions migrate toward

the good reason that they are composed only ofelectrodes of opposite charge upon an appliedions, they are expected to be good candidates

voltage. The fluid structure in vicinal layers

for electrolytes in supercapacitors. They may

that span over roughly 1 nm with respect to theexhibit fast charging times, excellent powerelectrode surface is more pronounced than in

performances, and good aging properties. In

the neutral state. In the core of the gap between

this project, we focused on capacitors based onelectrodes, the higher the applied voltage, theproperties

more

of

Electrical

DoubleLayerstructured

thefluid.

Ions

formedCapacitors (EDLC), in which ionic liquid arealternative layers of cations and anions. Fromconfined between a pair of planar electrodes.

the average total charge sampled on one of theWe employed molecular simulation to study

electrodes, we computed the total gravimetric

underlying molecular mechanisms of electrical

capacitance and observed a fast increase at low

properties in EDLC. we selected an ionic pairapplied voltages before reaching a nearly

widelyconstant behavior beyond 1V. Those results set

studiedexperimentally:

methylimidazolium/

1-butyl-3-bis[(trifluoromethyl)acornerstone

for

the

understandingofsulfonyl] imide. Then, we inserted those ions inmolecular mechanisms underlying electricala simulation box made of two electrodes

properties of EDLC.

separated by a slit-shape gap of 4 and 6 nm up
to a mass density corresponding to given
thermodynamics conditions (300 < T < 400 K
and p~1 atm). We employed LAMMPS in
combination with the constant potential method
to simulate EDLC at the molecular scale, byusing a subroutine by Zhenxing Wang et al.1
Fig. 1: Snapshot of a molecular model for
simulations at constant potential.
1 https://github.com/zhenxingwang/lammps-conp363

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of accuracy verification method on
analytic continuation results using cross validation
Kazuyoshi YOSHIMI1, Yuichi MOTOYAMA1, Yoshinori NAKANISHI-OHNO2
1Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581
2Graduate School of Arts and Sciences, University of Tokyo, Tokyo, 153-8902

Recentdevelopments

incomputationalverification on the results obtained by SpM

sciences have made it possible to construct andusing cross-validation.

analyze effective models for realistic materials.

In SpM, artificial oscillations appear in the low

Quantum Monte Carlo (QMC) calculations are

frequency range due to the cutoff of the bases.

one of powerful methods for finite temperature

To solve this problem, we focused on the Pade

analysis of effective models. To compare withapproximation,

experimental results such as excitation spectra,

analytic continuation in the low-frequency

it is necessary to connect the results of imaginary

region. In our method (SpM-Pade), the costtime simulations in QMC method to real time byfunction which becomes large when themeans of a numerical analytic continuation.

difference between the spectrum and that by

However, there is a problem that small statistical

Pade becomes large in the region where thenoise of the input data has a great influence onspectrum by Pade is stable to noise. We

which

gives

high-precise

the results of the analytic continuation, and there
has been no decisive method to enable highprecision spectral analysis until now.
Recently, we have proposed a method toautomatically select bases which are insensitive
to noise using sparse modeling and to achieve a
numerically stable analytic continuation against

Figure 1 Reconstructed spectrum by the Padenoise (SpM) [1-3]. In addition, SpM can easily(left), the SpM (center), and the SpM-Pade

add physically required conditions as constraints,(right) method. The line denotes the mean value

such as spectral non-negativity and sum rule. In

and the shaded region denotes the standard

this work, we have developed a new method todeviation from 30 independent samples. The

improve the validity of the results obtained byexact spectrum is shown as the black dashed

SpM. We also developed software to enable the

line.

364

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

examined the validity of SpM-Pade using thedeviation. Actual data, such as QMC data, havetest data obtained by adding noise to thea correlation between imaginary time data. In theartificially given spectrum and performing ancurrent simulation, we have ignored these

inverseeffects. We plan to apply SpM-Pade to the QMCtransformation

of

the

analytic

continuation. In order to see the sensitivity todata and investigate its applicability.

noise, the simulations were done for 30

For the cross-validation program, we develop

independent samples. In Fig. 1, we show thea program for large-scale parallel computers soreconstructed spectrum by the Pade (left), thethat it is designed not only to be used for analytic

SpM (center), and the SpM-Pade (right)

continuation but also for various methods. Now,

methods, respectively. It is seen that using Pade

we confirmed that it worked on the ISSP

approximation, the spectrum (solid line) is

supercomputer for the analysis in which thealmost same as the exact one (dashed line)

reduction of the noise of the image was donearound ω=0 and the standard deviation (shadedusing sparse modeling. We plan to release thisarea) is small. With increasing ω , both theprogram as open source software when it can bedifference between the spectrum and the exact

used for various solvers, including the program

one and the deviation become large toward theof SpM [2].

second peak aroundω=2 as expected. In the caseof SpM, the oscillations appear around ω =0

References

and the second peak becomes broad compared to[1] J. Otsuki, M. Ohzeki, H. Shinaoka, and K.

the exact one. However, the small variance

Yoshimi: Phys. Rev. E 95 (2017) 061302.

indicates that this method is insensitive to noise.

[2] K. Yoshimi J. Otsuki, Y. Motoyama, M.

In the case of SpM-Pade, due to introducing the

Ohzeki, and H. Shinaoka: Comput. Phys.

cost function, the oscillations around ω=0 is

Commun. 244 (2019) 319.

suppressed. On the other hand, the noise[3] J. Otsuki, M. Ohzeki, H. Shinaoka, and K.

tolerance is still strong as seen from the small

Yoshimi: J. Phys. Soc. Jpn. 89 (2020) 2061.

365

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio study of quantum spin liquid in molecular
conductors
Takahiro Misawa
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

It has been experimentally reported that theX[Pd(dmit)2 ]2 molecular conductors exhibit
various phases such as antiferromagnetic, spinliquid, and charge-ordered states depending on
the choice of cation (X) [1]. In order to elucidate the origin of this variety of phenomena,detailed analyzes of band structures and transfer integrals based on the extended Hückel
method and first-principles calculations havebeen performed to quantitatively evaluate thematerial dependence of electronic states [2].
On the other hand, systematic analyses incorporating the electron correlation effect, whichplays an important role in the emergence ofvarious phases, have not been carried out due
to the lack of efficient tools and the needfor large computational resources for analysis
in molecular conductors. We note that thederivation of the low-energy effective Hamiltonian including the interaction parameters is
carried out only for EtMe3 Sb[Pd(dmit)2 ]2 [3],which has the quantum spin liquid groundstate.
In this project, using the open-source software package RESPACK [4, 5], we systematically derive effective Hamiltonians for all
available nine β 0 -X[Pd(dmit)2 ]2 (X = Me4 Y ,EtMe3 Y , Et2 Me2 Y and , Y = As, Sb, andP) [6]. In the part of obtaining the global band
structures, we use Quantum ESPRESSO [7].
Furthermore, using the quantum lattice model
solver HΦ [8, 9], we perform the numericallyexact analyzes for the obtained low-energy effective Hamiltonians and show that the mag-netic properties are well reproduced including
the quantum spin liquid behavior observed in
X=EtMe3 Sb. We also show that both the geometrical frustration and the off-site interactions play key role in stabilizing the quantum
spin liquid.
In addition to the ab initio study for themolecular conductors, we perform the ab initio
calculations for the high-Tc cuprates [10, 11].
We also analyze the quantum transport phenomena in the Weyl semimetals [12] and the
topological semimetals [13] using the realtime evolution of the quantum systems. Furthermore, using the many-variable variational
Monte Carlo method [14, 15], we analyze thequantum spin-nematic phase [16], the Kitaev
model under magnetic fields [17], and the dynamical properties of the correlated electron
systems [18].

References[1] R. Kato, Chem. Rev. 104, 5319 (2004).
[2] K. Kanoda, R. Kato, Annu. Rev. Condens. Matter Phys. 2, 167 (2011).
[3] K. Nakamura, Y. Yoshimoto, M. Imada,
Phys. Rev. B 86, 205117 (2012).
[4] https://sites.google.com/view/kazuma7k6r[5] K. Nakamura, Y. Yoshimoto, Y. Nomura,T. Tadano, M. Kawamura, T. Kosugi,

366

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoK. Yoshimi, T. Misawa, Y. Motoyama,
arXiv preprint arXiv:2001.02351.
[6] T. Misawa, K. Yoshimi, T. Tsumuraya,
arXiv preprint arXiv:2004.00970.
[7] P. Giannozzi, O. Andreussi, T. Brumme,
O. Bunau, M. B. Nardelli, M. Calandra,
R. Car, C. Cavazzoni, D. Ceresoli, M. Cococcioni, et al., Journal of Physics: Condensed Matter 29, 465901 (2017).
[8] M. Kawamura, K. Yoshimi, T. Misawa,
Y. Yamaji, S. Todo, N. Kawashima, Comput. Phys. Commun. 217, 180 (2017).
[9] https://www.pasums.issp.u-tokyo.
ac.jp/HPhi/en/[10] M. Hirayama, T. Misawa, T. Ohgoe,
Y. Yamaji, M. Imada, Phys. Rev. B 99,
245155 (2019).
[11] T. Ohgoe, M. Hirayama, T. Misawa,K. Ido, Y. Yamaji, M. Imada, Phys. Rev.
B 101, 045124 (2020).
[12] T. Misawa, R. Nakai, K. Nomura, Phys.
Rev. B 100, 155123 (2019).
[13] T. Misawa, K. Nomura, Scientific Reports
9, 19659 (2019).
[14] T. Misawa, S. Morita, K. Yoshimi,
M. Kawamura, Y. Motoyama, K. Ido,
T. Ohgoe, M. Imada, T. Kato, Comput.
Phys. Commun. 235, 447 (2019).
[15] https://www.pasums.issp.u-tokyo.
ac.jp/mvmc/en/[16] T. Hikihara, T. Misawa, T. Momoi, Phys.
Rev. B 100, 214414 (2019).
[17] K. Ido, T. Misawa, Phys. Rev. B 101,
045121 (2020).
[18] K. Ido, M. Imada, T. Misawa, Phys. Rev.
B 101, 075124 (2020).

367

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Unified Photonic-Electronic Devices
Kazuhiro YABANA
Center for Computational Sciences,
University of Tsukuba, Tsukuba 305-8577
now possible to calculate the ground state andWe develop a first-principles computational
dynamics

electron dynamics of systems of more than a

induced by ultrashort laser pulses based on

few thousand atoms. We intend to make thetime-dependent

new version public in early fiscal year of 2020.

methodtoinvestigate

electrondensityfunctional

theory(TDDFT) in real time. We develop the code
SALMON (Scalable Ab-initio Light-Matter

References

simulator for Optics and Nanoscience) [1] and[1] M. Noda, et.al, “SALMON: Scalable Ab-

make it open to the public at our website,

initio Light–Matter simulator for Optics andhttp://salmon-tddft.jp.

Nanoscience”, Comp. Phys. Comm. 235, 356

SALMON is developed as a unified(2019).

software that include traditional computational[2] K. Yabana, T. Sugiyama, Y. Shinohara, T.

methods

theOtobe, G.F. Bertsch, “Time-dependent density

finite-functional theory for strong electromagnetic

difference time-domain (FDTD) method, andfields in crystalline solids”, Phys. Rev. B85,

linear response calculation for susceptibities

045134 (2012).

based on TDDFT. There are two options for the[3]

coupling: macroscopic[2] and microscopic [3].

Yabana, “Time-dependent density functional

In addition, Ehrenfest molecular dynamics cantheory for interaction of ultrashort light pulse

be combined in the multiscale simulation [4].

with thin materials”, Phys. Rev. B98, 245147

oflight-matterelectromagnetism

analysisinteraction,
usingThis year, we have concentrated on the

S. Yamada, M. Noda, K. Nobusada, K.

(2018).

development of ver. 2 of SALMON. In the new[4] A. Yamada, K. Yabana, “Multiscale time-

version, we intended to improve the readability

dependent density functional theory for aand extensibility of the code by using structuresunified description of ultrafast dynamics:of Fortran extensively. We also paid much

Pulsed light, electron, and lattice motion ineffort to improve the efficiency and scalability

crystalline solids”, Phys. Rev. B99, 245103

for large-scale calculations. Using the code, it is(2019).

368

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Dynamical DMRG study of magnetic excitations inmagnetization plateaus of a frustrated spin ladder
Takami TOHYAMA
Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585

Magnetization plateau (MP) emerges inquantum spin systems due to spontaneously
breaking of translational symmetry. The broken symmetry can induce reconstruction ofelementary excitations, but its microscopic
mechanism and reconstructed quasiparticle
in MP phases have remained unclear. We
theoretically study magnetic excitations in
the MP phases of a frustrated spin ladder(FSL) by using the dynamical density-matrix
renormalization-group (DDMRG) method [1].
The Hamiltonian of FSL is deﬁned as H =∑H⊥ + H∥ + HZ with H⊥ = J⊥ N
i=1 Si,1 · Si,2 ,∑ ∑∑H∥ = 2η=1 Jη i 2j=1 Si,j · Si+η,j , and HZ =∑z , where S−h i,j Si,ji,1 (Si,2 ) is the S = 1/2
spin operator on ith rung in the upper (lower)
chain. Exchange energies of the ﬁrst-neighborbond in a leg, the second-neighbor bond in aleg, and the ﬁrst-neighbor bond in a rung, aredenoted by J1 , J2 , and J⊥ , respectively. We
set J1 /J⊥ = 0.2 and J2 /J⊥ = 0.65. Changing magnetic ﬁeld h, we obtain MPs at m =M/Ms = 1/3, 1/2, and 2/3, where M (Ms ) ismagnetization (saturation magnetization).
We calculate dynamical spin structure factor(DSSF) using DDMRG, where the correction
vector is expanded by the Legendre polynomialwith a Gaussian averaging [2] and a broadening factor is replaced by the width of the Gaussian, for which we set 0.02J⊥ . The system size,
N = 48 rungs, is suﬃcient to discuss dynamical behaviors. The number of states kept in
the DDMRG is m = 600, leading to truncation
error less than 1 × 10−4 .
Figure 1 shows DSSF for momentum along

Figure 1: DSSF for qy = π in the m = 1/3 MP.
rung qy = π as a function of momentum alongleg qx in the case of m = 1/3 [1]. A dispersive feature with zero-energy excitation at
qx = 2π/3, indicating a period with three times
the original unit-cell length in real space.
We also perform analytical approaches withthe perturbation theory to obtain an intuitive
view of magnetic excitations. A comparison
between numerical and analytical results indicates the presence of a reconstructed quasiparticle originating from spontaneously broken
translational symmetry, which is realized asa collective mode of the spin trimer called atrimeron [1].

References[1] K. Sasaki , T. Sugimoto, T. Tohyama, and
S. Sota: Phys. Rev. B 101 (2020) 144407.
[2] S. Sota and T. Tohyama: Phys. Rev. B
82 (2010) 195130.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Conversion and storage of energy−fuel cells andsecondary batteries: Research and development offundamental technologies of battery simulators.
Susumu OKAZAKI
Department of Materials Chmistry, Nagoya University
Furo-cho, Chikusa-ku, Nagoya 464-8603

The goal of our project is to develop thebasic technology of the whole battery simulator. One of the key techniques is molecularlevel design of polymer membranes controllingtransportation of protons and ions across themembrane with proper stiffness resistant tomechanical deformation under external stress.
Such membranes are widely applicable to thefuel cells used in the industrial products.
We previously performed fully atomistic
molecular dynamics (MD) calculations of hydrated perfluorosulfonic acid (PFSA) ionomers
composed of a hydrophobic polytetrafluoroethylene backbone with hydrophilic side
chains terminated by sulfonic acid, as a modelof proton exchange polymer electrolyte membrane of fuel cells[1, 2, 3]. On the system
B and C, we further performed a series of
MD calculations of different equivalent weightPFSA membranes containing H2 molecules atdifferent water uptakes[4] (examples are shownin Figs. 1 (A)–(C)). They explored atomistic
detail of H2 permeation through the membranes. The local semicrystalline structure of
the PFSA polymer and the morphology of thewater clusters in the membrane were found toaffect H2 permeation.
Moreover, new algorithms relating to thefast multipole method which enable to treat
two dimensional periodic boundary conditions(slab geometry)[5] and rectangular unit cellwith an anisotropic cell-partitioning[6] weredeveloped. They make it possible to perform

370

Figure 1: Schematic images of hydrated equivalent weight PFSA membranes with (A) 6, (B)16, and (C) 30 wt % of water uptakes[4].
MD calculations for more general calculation
systems by the software MODYLAS.
These results will contribute to the development of higher performance fuel−cells andsecondary batteries and to the realization of
the entire battery simulator in the near future.
References[1] A. T. Kuo, W. Shinoda, S. Okazaki : J.
Phys. Chem. C 120 (2016) 25832.
[2] A. T. Kuo, S. Okazaki, W. Shinoda : J.
Chem. Phys. 147 (2017) 094904.
[3] A. T. Kuo, K. Takeuchi, A. Tanaka, S.
Urata, S. Okazaki, and W. Shinoda :Polymer 146 (2018) 53.
[4] K. Takeuchi, A. Kuo, T. Hirai, T. Miyajima, S. Urata, S. Terazono, S. Okazaki,
and W. Shinoda: J. Phys. Chem. C, 123(2019) 20628.
[5] N. Yoshii, Y. Andoh, S. Okazaki: J. Comput. Chem., 41 (2020) 940.
[6] Y. Andoh, N. Yoshii, S. Okazaki: J. Comput. Chem., 41 (2020) 1353.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of Fragment-Based GW/BSE Method
and Application to Organic Optoelectronic Materials
Takatoshi Fujita
Institute for Molecular Science
Myodaiji, Okazaki, Aichi 444-8585

Accurate calculations of electronic states
are essential for computational studies of organic materials which are directed toward understanding of fundamental processes in organic electronic devices. Many fundamental
processes governing the device operation takeplace at the variety of interfaces, such as metalorganic and organic donor-acceptor interfaces.
Although developments of quantum chemistry
or ab initio program packages have enabled
one to routinely run a calculation for an isolated molecule or a molecular crystal, performing such a calculation for interface systems isstill a challenging issue.
We have recently developed the large-scale
GW method [1, 2] which can be applied
to large and disordered molecular systems.
Our implementation is based on the fragment molecular orbital (FMO) method, inwhich an entire system is ﬁrst divided into
many subsystems refereed as fragments, andtotal energy or physical properties are approximated from molecular orbital calculations
for fragment monomers, dimers, and optionally, trimmers. In the FMO-GW method,
the polarization function of an entire system
is approximated from molecular orbital localized within fragment monomer or dimers.
In addition, the ∆COHSEX approximation
is employed, in which dynamically-screened
Coulomb potential is explicitly evaluated for atarget fragment, while the statically-screened
Coulomb potential of entire system is evaluated at the static COHSEX level. Basedon these development, we have performed thelarge-scale GW calculation for systems whichcontain more than 1,000 atoms, such as theorganic semiconductor thin ﬁlm [1] and thedonor/acceptor interface [2]. In addition, we
have also developed the GW/Bethe-Salpeter
equation method which reasonably describes
excited states in polarizable molecular environments.
As applications of the FMO-GW, we have
explored the energy levels and charge-transfer
excited states in pentacene/C60 bilayer heterojunctions. In particular, we have investigated the dependence of interfacial morphologies on the electronic states and the eﬀects ofpolarization and delocalization eﬀects. Calculated energy levels and the excitation energies of charge-transfer states are in reasonableagreement with those estimated from ultraviolet photoelectron spectroscopy and from external quantum eﬃciency measurements. We
have found that the electrostatic contributionof polarization energies, which arises from pentacene quasrupole moments, governs dependence of interfacial morphologies on the electronic states.

References[1] T. Fujita, Y. Noguchi, Phys. Rev. B 98
(2018) 205140.
[2] T. Fujita, Y. Noguchi, T. Hoshi, J. Chem.
Phys. 151 (2019) 114109.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Data-driven materials design for new functional highentropy alloys
Tetsuya Fukushima
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

Recently, the constructions of materials
databases using first-principles calculations
have been actively carried out.
Combining such materials databases and data-mining
technique, one can not only analyze the mechanisms of physical phenomena, but also design new functional materials. Actually, there
are several large materials databases, such as
Materials Project, Open Quantum Materials
Database (OQMD), and Novel Materials Discovery (NOMAD), which researchers can freely
access. However, these inorganic materials
databases are only for compounds with stoichiometric compositions and do not contain
information about configurational disorderedsystems
In this year, in order to construct the materials databases for configurational disorderedsystems, we have developed an automatic highthroughput calculation method on the basis of
the Korringa-Kohn-Rostoker (KKR) Green’s
function method. There are several merits
in the KKR Green’s function method, compared to other first-principles approaches. The
most important advantage is the ability to perform the calculations of alloys and impurity
doped systems, combining with the coherent
potential approximation (CPA). Additionally,
since the Green’s function is directory calculated in this method, physical quantities, e.g.,magnetic exchange interactions and transport
properties, can be eﬃciently calculated by thelinear response theory.
Automatic high-throughput calculations by

372

first-principles approaches are not easy tasks,
because we need to appropriately control many
numerical parameters and self-consistent procedures. For example, in the KKR Green’s
function method, the energy integration of theGreen’s function is performed in the complex
energy plane to obtain the electron density.
This complex energy contour must cover thevalence bands and depends on systems. Our
python interface for the high-throughput calculations enable to determine the numericalparameters and to manage the self-consistentprocedures completely automatically. For theelectronic structure calculations, the AkaiKKR
program package is employed.
The automatic high-throughput calculations
have been demonstrated for quaternary highentropy alloys with BCC and FCC solid solution phases, where 4 principal elements havethe same atomic concentration and are randomly distributed in the crystals. The numberof the target elements are 38 as follows: Al, Si,
Sc, Ti, V, Cr, Mn, Fe, Co, Ni, Cu, Zn, Ga, Ge,
Y, Zr, Nb, Mo, Tc, Ru, Rh, Pd, Ag, Cd, In,
Sn, Hf, Ta, W, Re, Os, Ir, Pt, Au, Hg, Tl, Pb
and Bi. We randomly choose the 4 elementsfrom the above target elements and constructa quaternary high entropy alloy. Since boththe BCC and FCC cases are considered, thetotal number of the systems is 147,630. All
calculations are done by the ISSP supercomputer, system B.
We succeeded in automatically converging
99.99% of the systems, i.e., 147614/147630.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1 shows a part of our high-throughput
calculations, in which the magnetic moments
and Curie temperatures for the quaternaryhigh entropy alloys with the BCC phase areplotted. The Curie temperatures are calculated by the magnetic exchange exchangeinteractions and mean-field approximation.
Such database is quite useful for the design of
new functional materials. For example, in thecases of high-performance soft magnets, thehigh magnet moments and Curie temperatures
are needed. Using the database, we can screen
the candidate systems immediately. Here, it isconcluded that FeCoXY, FeCoNiY, and MnFeCoY systems are good candidates for the highperformance soft magnets

Figure 1: Automatic high-throughput calculations for quaternary high entropy alloys with
the BCC phase.

References[1] T. Fukushima, H. Shinya, A. Masago, K.
Sato and H. Katayama-Yoshida: Appl.
Phys. Exp. 12 (2019) 063006.
[2] S. Yamada, S. Kobayashi, A. Masago, L.
S. R. Kumara, H. Tajiri, T. Fukushima,
S. Abo, Y. Sakuraba, K. Hono, T. Oguchi,

373

and K. Hamaya: Phys. Rev. B 100 (2019)195137.
[3] A. Masago, H. Shinya, T. Fukushima, K.
Sato, and H. Katayama-Yoshida: AIP
Advances 10 (2020) 025216.
[4] T. Nunokawa, Y. Fujiwara, Y. Miyata,
N. Fujimura, T. Sakurai, H. Ohta, A.
Masago, H. Shinya, T. Fukushima, K.
Sato, and H. Katayama-Yoshida: J. Appl.
Phys. 127 (2020) 083901.

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electron Theory on Secondary-Battery Materials
Hiroki KOTAKA1 , Motoyuki HAMAGUCHI2 , Huu Duc LUONG2 ,Hiroyoshi MOMIDA1,2 , Tamio OGUCHI1,2
1
ESICB, Kyoto University, Katsuragoryo, Kyoto, Kyoto 615-8245
2
ISIR, Osaka University, Mihogaoka, Ibaraki, Osaka 567-0047

Microscopic mechanism of charging anddischarging reactions in several battery systems is studied by first-principles calculations to explore novel secondary battery materials. In this year, we further extended
our previous studies on Na/NaFeSO4 F and
Li/Li2+2x Mn1−x Ti1−x O4 systems.
Recently NaFeSO4 F has been expected to
be a candidate cathode material for the
next-generation Na secondary batteries. In
this first-principles study [1], the structural stability and voltage-capacity profiles of
Na/NaFeSO4 F system are investigated. Calculated total energy of NaFeSO4 F is comparedwith those of NaF and FeSO4 and found to beslightly stable to the phase separation. X-ray
absorption spectroscopy (XAS) spectra at theK-edges of Fe, Na, and F for NaFeSO4 F andFeSO4 F in the fully discharged and charged
states and of NaF and FeSO4 are computedwith the Fermi golden rule within the electric
dipole and quadrupole approximation. The
XAS spectra at Fe K-edge reveal that the discharged state in NaFeSO4 F and the charged
state in FeSO4 F are dominated by Fe2+ (d6 )and Fe3+ (d5 ), respectively. It is also foundthat the XAS spectra near K-edge of F in addition to Fe provide crucial information concerning the local structure in the relevant phases
existing during the reaction processes.
Li-excess cation-disordered rock-salt oxides
Li2+2x Mn1−x Ti1−x O4 have recently attracted
much interests as high-capacity cathodes associated with two-electron reactions. In these oxides, cations are disordered on the octahedral

sites coordinated by six oxygen ions and theoctahedra are expected to be stable during discharging and charging reactions. To clarify themechanism of the reactions, cathode propertiesof the oxides with the Li-excess of 0≤x≤0.3
are investigated by using first-principles calculations [2]. To evaluate the structure stability and reaction equations of the cathodematerials for each x, formation enthalpies of
Li2+2x−y Mn1−x Ti1−x O4 are calculated as afunction of Li-removal amounts y considering
several Li configurations. To model the oxides
with disordered cations and several Li concentrations x and y, supercells including 80 atomsof rock-salt lattice are assumed with the special quasi-random structure method. Basedon the estimated reaction equations, voltagecapacity profiles are obtained for each x andcompared with experiments. By analyzing theelectronic structures, roles of cation and anion
redox reactions depending on y as well as x
are discussed in detail. We discuss energy stability of O2 -release from the cathode during
charging/discharging processes by calculating
vacancy formation energies of O and Li. The
best x values in terms of voltages, capacities,
and stability against the O2 -releases are proposed.

References[1] H, Momida et al., J. Phys. Soc. Jpn. 88,
124709 (2019).
[2] M. Hamaguchi, et al., Electrochimica Acta
330, 135286 (2020).

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Ab initio studies toward functional nanomaterials
based on abundant elements
Tetsuya TAKETSUGU
Faculty of Science, Hokkaido University
N10W8, Sapporo, Hokkaido 060-0810

Ab initio studies on various nano materials
are important to understand and design new
functional materials with abundant elements
for reducing costs and dependences on precious
metals used in many important aspects in ourdaily lives and therefore toward sustainable society. Heterogeneous catalysts rely mostly on
the expensive and rare metals such as Pt, Rh,
Pd, or Ru in automotive gas exhausts control,
water gas shifts, fuel cells, as well as combustive decomposition of ammonia. Platinum andpalladium are also used for hydrogen based energy strategies. Due to their high cost andlimited amounts, to reduce or even replacethese metals is emergent issues in industry.
To that end, we perform density functional
theory (DFT) computations under the periodic boundary conditions together with projector augmented wave method with VASP using ISSP supercomputers to gain chemical insights to understand the chemical mechanisms
in conventional catalysts as well as to designnovel catalysts with abundant elements.
We have developed a surface adsorption
model calculation database toward applicationto activity prediction of heterogeneous catalysts [1], where band calculations with SIESTA
are performed for various pure and alloy metal
surfaces adsorbed with molecules and atoms
relevant to important catalysis such as water gas shift. As a new functional nanomaterial, we have studied structural and electronic properties of borophene, an artificial
two-dimensional materials, whose structuraland electronic properties are not typical for
their bulk counterparts [2]. Scanning tunneling microscopy and density functional theory
calculations show that this structure forms asa single phase on iridium substrate in a wide
range of experimental conditions and maybe
then decoupled from the substrate via intercalation. We foresee that the adjacent borophene
sites with opposite electron doping might exhibit catalytic activity or facilitate highly regular adsorption of large molecules, metal clusters, and other objects interesting for catalysis,
sensors, and nanotechnology.
The excited states dynamics and spectroscopy are also important for the study on
functional nanomaterials. For spectroscopy,
the roles of silver nanocluster and plasmonic
nanocavity for surface- and tip-enhanced Raman spectroscopies, respectively, are investigated [3,4]. We are further studying electronic excitations of small molecule excitedby spatially nonuniform electric field, namely
the near-field, by using the real-time timedependent density functional theory codessuch as SALMON.

References [1] M. Kobayashi, H. Onoda,
Y. Kuroda, and T. Taketsugu, J. Comput.
Chem. Jap., 18, 251-253 (2019). [2] N.
A. Vinogradov, et al, ACS Nano, 13, 1451114518 (2019). [3] T. Tsuneda, T. Iwasa, andT. Taketsugu, J. Chem. Phys., 151, 094102(2019). [4] R. B. Jaculbia et al., Nature Nanotechnology, 15, 105-110 (2020).

375

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of high-performance permanent
magnets by large-scale simulation and data-driven
approach
Takashi MIYAKE
CD-FMat, AIST
Umezono, Tsukuba, Ibaraki 305-8568

We have studied magnetic properties andstability of rare-earth magnet compounds using fist-principles calculation combined withmachine-learning techniques. The RFe12 -type
compounds having the ThMn12 structure haveattracted attention in recent years, because
high saturation magnetization can be expectedfrom their high iron concentration. NdFe12 Nx
and Sm(Fe,Co)12 films have successfully synthesized a few years ago, and it was reported experimentally that these compounds
have higher saturation magnetization, higher
anisotropy field and higher Curie temperaturethan Nd2 Fe14 B which is the main phase of theneodymium magnet. However, they are thermodynamically unstable, and partial substitution of Fe sites are necessary to stabilize a bulk
phase. The choice of rare-earth element also
aﬀects stability [1].
We calculated the magnetization, Curie
temperature and formation energy of(R1−α Zα )(Fe(1−β)(1−γ) Coβ(1−γ) Tiγ )12 (R=Nd,
Sm, Y, Z=Zr, Dy) based on density functional theory using Akai-KKR code. Nonstoichiometric composition is treated by thecoherent potential approximation. Intersite
magnetic exchange couplings are calculatedby Liechtenstein’s method, from which theCurie temperature is evaluated by solving thederived Heisenberg model in the mean-fieldapproximation.
To reduce the systematic
error in the formation energy obtained by the
KKR-CPA, data integration method (Fig.1)

is adopted, where the formation energies of
stoichiometric systems calculated by QMAS
are used to reduce the systematic error.
In order to determine the optimal composition eﬃciently, we adopt Bayesian optimization. We performed 1000 independent runs toevaluate the success rate statistically. Figure
2 shows the success rate of finding top 10 systems out of 3630 chemical compositions within
50 trials. The target variables are saturation
magnetization, Curie temperature and formation energy. The success rate is over 95 % if
we appropriately chose the descriptor, which
is much higher than that by the random sampling (12.9%).

References[1] Yosuke Harashima, Taro Fukazawa, andTakashi Miyake: Scripta Materialia 179(2020) 12.
[2] Taro Fukazawa, Yosuke Harashima,
Zhufeng Hou and Takashi Miyake: Phys.
Rev. Mater. 3 (2019) 053807.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: Data integration method, where systematic errors contained in a large number ofdata for non-stoichiometric compositions arecorrected by a small number of more accurate
date for stoichiometric compositions.
[2].

100

Success rate [%]

80

µ 0M
TC
ΔE

60

40

20

0
RS BO #1 #2#3#4(without β nor γ)

#5

#6

#7

#8

#9

#10 #11(with β and γ)

β

γ

β, γ

(β, γ only)

Figure 2: Success rate of finding the systemwith the top 10 values of magnetization, Curie
temperature and formation energy out of 3630
candidates within 50 trials [2].

377

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Multiscale simulations on complex multiphase flows
Youhei Morii, Takahiro Murashima, and Toshihiro Kawakatsu
Department of Physics, Graduate School of Science, Tohoku University, Sendai 980-8578
Wedeveloped

techniques(MSS)

multiscale

simulation

it (See Fig.1).

[1]

multiscale

drives the macroscopic flow is calculated using

andasimulation platform for complex fluids (MSSP)The instantaneous stress that

this microscopic simulator.

[2,3], under the support from Post-K project

We applied this technique to a viscoelastic

and HPCI. These MSS and MSSP are aimed topolymeric fluid flowing around a cylindricalapply for complex flow phenomena such as

obstacle that generates Karmann’s vortex street.

multiphase flows and viscoelastic flows whose

Figure 2 shows a comparison between (a) aconstitutive equations are not a priori known.

Newtonian fluid and (b) a Maxwellian fluid

In such systems, a simple model constitutivethat contains set of dumbbells as a model of

equation is not in general available, andpolymer solution. One can confirm the effecttherefore one must obtain the stress tensor fromof viscoelasticity coming from the polymer

the flow history of the fluid. As such a flow iscomponent on the Karman’s vortex street.

often non-Markovian, Lagrangian description isquite suitable to trace the flow history.
Smoothed particle hydrodynamics (SPH) is atypical simulation technique of fluid flows
based on Largangian description. Our MSSP is

Fig.2 Karman vortex street for (a) abased on this SPH method, where each SPH

Newtonian fluid and (b) a Maxwellian

particle contains a microscopic simulator inside

fluid.

References[1] T. Murashima, S. Urata, S. Li, Eur. Phys. J.
B, 92, 211 (2019).
[2] 森井洋平, 川勝年洋, 第 68 回高分子討論会, 福井大学 文京キャンパス, 2019/9/25.
[3] Youhei Morii, Toshihiro Kawakatsu, 10th

Fig.1 A schematic illustration of MSSP.

International

Conference

ConsortiumonofComputational

the

Asian

Materials

Science (ACCMS-10), Hong Kong, 2019/7/24.

378

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Order-disorder transition in the superhigh-pressure phase of
Mg2SiO4
Koichiro UMEMOTO
Earth-Life Science Institute,Tokyo Institute of Technology, 2-12-1 Meguro-ku, Ookayama, Tokyo 152-8550
transitions

MgSiO3 bridgmanite with the orthorhombic

andthermodynamic

quantities

perovskite structure is a major constituent ofcalculated for these phases have been alreadythe lower mantle of the Earth. It takes the post-usedperovskite (PPV) structure near the core-mantle

dynamics of super-Earths [5].

innumerical

modelingofmantleboundary pressure (~125 GPa). The PPV phase

In this study, we predicted order-disorderis the final form of MgSiO3 in the Earth.

transition in the cation sublattice of tetragonal

However, at much higher pressures in “super-

Mg2GeO4 by first principles [4]. Mg2GeO4 is a

Earths” which are exoplanets expected to be

candidate of low-pressure analog of Mg2SiO4.

terrestrial with masses much larger than the

The dissociation of MgGeO3 PPV into pyrite-

Earth, MgSiO3 PPV should undergo “post-PPV”

type GeO2 and I-42d-type Mg2GeO4 wastransitions. So far, first principles studies havepredicted to occur at ~170 GPa [5]. Therefore,predictedof

Mg2GeO4 is a useful system to study the post-

MgSiO3 PPV: MgSiO3 PPV → I-42d-type

PPV transitions experimentally. In Mg2GeO4

Mg2SiO4 + P21/c-type MgSi2O5 → Mg2SiO4 +and Mg2SiO4, local oxygen arrangements

Fe2P-type SiO2 → CsCl-type MgO + SiO2 [1,2].

around Mg and Ge atoms are very close to each

When MgSiO3 coexists with NaCl-type MgOother. Therefore, configuration entropy isor pyrite-type SiO2, they were predicted to

expected to induce the order-disorder transition

recombine into Mg2SiO4 or MgSi2O5 [3].

at high temperature.

thethree-stage

dissociation

post-PPVThe order-disorder transition temperaturetransitions are extremely high, >~500 GPa, and(Tc) is given by the peak temperature of thehave been still difficult to be achieved

heat capacity which is calculated from theexperimentally. These predictions were based

partition function with respect to cationon the lowest-enthalpy phases under ultrahighconfigurations. For Mg2GeO4, we constructed apressures. Temperature effects by phonon weresupercell consisting of 56 atoms and generated

taken into account by using the quasi-harmonic

cation configurations until the convergence ofapproximation

Tc was achieved. Then we predicted that theTransitionpressuresof(QHA).

these

These

post-PPV379

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

order-disorder transition should occur at ~3000

Institute for Solid State Physics. This

K and 200 GPa; this pressure-temperature

research was supported by MEXT as

condition is now achievable by the diamond-“Exploratory

anvil-cell experiments. We found that Tc

computer” (Challenge of Basic Science –increases with pressure. Across the transition,

Exploring

the symmetry of Mg2GeO4 increases from

Physics and Multi-Scale Simulations)

Challenge

Extremesonthrough

Post-K

Multi-

tetragonal (I-42d) in the ordered phase to cubic(I-43d) in disordered one. In fact, the crystal
structure of the disordered cubic phase isReferences

identical to that of Th3P4. We also clarified that

[1] S. Q. Wu, et al.: J. Phys.: Condens. Matterthe effect of phonon on this transition is very

26 (2014) 035402.

small within the QHA.

[2] H. Niu et al.: Sci. Rep. 5 (2015) 18347.

Since Mg2GeO4 is the low-pressure analog[3] K. Umemoto et al.: Earth Planet. Sci. Lett.

of Mg2SiO4, the order-disorder transition

478 (2017) 40.

predicted in this study is expected to occur also[4] K. Umemoto and R. M. Wentzcovitch: inin Mg2SiO4 and will play an important role inpreparation.

modeling interiors of super-Earths.

[5] A. P. van den Berg, et al.: Icarus 317 (2019)
412.

The first principles calculations in this study
were performed using the Quantum-Espresso[6] K. Umemoto and R. M. Wentzcovitch: Phys.

packageRev. Mat. 3 (2019) 123601.

(https://www.quantum-espresso.org)

on the supercomputer (system B) at the380

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Chain-Increment Method for Approaching the Chemical
Potential of a Polymer with All-Atom Model
Kazuo YAMADA and Nobuyuki MATUBAYASIDivision of Chemical Engineering, Graduate School of Engineering Science,
Osaka University, Toyonaka, Osaka 560-8531
We have computed the free energy of thepolymer as a sum of ∆𝜇#$%&' over the monomers

dissolution of the polymer in polymer binary

in the tagged polymer. In the present report, we

systems [1] using all-atom molecular dynamics

focus on the computation of the incremental free

simulations. An atomistic computation of freeenergy in polymer-melt systems [1].

energy is a challenging task, however, when a

The polymer species treated are polyethylene

polymer molecule is treated simultaneously as a(PE),whole. This is because a polymer is highly

methacrylate) (PMMA), and polyvinylidene

flexible and structurally diverse due to large

difluoride (PVDF) in their linear forms. All-

number of intramolecular degrees of freedom.

atom molecular dynamics simulations and free-

Given the fundamental and practical importanceenergy calculations have been implemented onof the chemical-potential calculation of polymer,

the supercomputer system at ISSP. The free

therefore, an elaborate scheme needs to beenergy of chain increment is shown in Fig. 1 at

established which exploits a specific nature of

the number of monomer units of 100. The

the polymeric structure.

incremental free energy ∆𝜇#$%&' is obtained forpolypropylene(PP),

poly(methyl

We develop a chain-increment method toeach monomer by using the scheme in [1], and it

approach the chemical potential of a polymer

is found that the incremental free energy stays

withall-atom model. The intermolecularconstant within 0.1 kcal/mol except at terminals.

interaction of a polymer of interest with the

The standard deviation is within 0.2 kcal/mol insurrounding

introduced

the inner part of the polymer, and the averaged

sequentially for the monomers, and the free

free energy of chain increment is insensitive toenergy for turning on the interaction is treatedthe chain length. All-atom computation is thus

withinenergy-feasible for the free-energy analysis of a polymer

representation theory of solutions. In our method,

system at the degree of polymerization of

we compute the free energy of chain increment

several tens or more. It is also seen that the∆𝜇#$%&' along the monomers in the tagged

preference order of ∆𝜇#$%&' agrees with that ofpolymer as well as the total free energy Dµ of thethe average interaction energy <u>i of thethemolecules

framework

is

of

the

381

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

PE

PP

PMMA

PVDF

PE

PMMA

0

∆µ (kcal/mol)∆µincr(kcal/mol)
i

-1
-2
-3
-4

-100
-50

-200
-300

-100

-5

-400
25

-6
0

<u>i (kcal/mol)

0

20

40

60

80

50

100

25

50

100

degree of polymerization N

100

-5

Fig 2: Total solvation free energy Dµ against the-10

degree of polymerization N at 25, 50, and 100 for
PE and PMMA. Dµ is estimated from ∆𝜇#$%&' at i =-15

1, 5, 10, … (N–10), (N–5), and N. The dashed lineis the least-square fit to the form of Dµ ∝ N, and

-20
0

20

40

60

80

100

the slope is −1.0 and −3.6 kcal/mol for PE andmonomer index i

Fig 1: Incremental free energy and the average

PMMA, respectively.

interaction energy against the index i of theincremented monomer in the tagged polymer. The

degree of polymerization of several tens or more.

degree of polymerization is 100 in this figure, andAtomistic computation of the chemical∆𝜇#$%&' and <u>i are plotted against the monomer

potential is of much computational demand for aindex at i = 1, 5, 10, 15, …, 90, 95, and 100. The

polymer when the interaction with the solvent ishorizontal, dashed line is the averaged value ofturned on simultaneously throughout the whole∆𝜇#$%&' or <u>i over i = 5, 10, 15, …, 90, and 95.

polymer. The method of chain increment is analternative

schemethat

introducestheinteractions sequentially along the polymer

incremented monomer with the surroundings.
We further compute the total solvation freechain. This work formulates an all-atom method

energy ∆𝜇 as a function of the degree of thefor chain increment by combining molecularpolymerization N for PE and PMMA, by using

simulation with the energy-representation theory

the incremental free energy of solvation ∆𝜇#$%&' atof solutions, and it is demonstrated that the freei = 1, 5, 10, … (N–10), (N–5), and N. In Fig. 2,

energy of chain increment can be obtained at aa good linearity of Dµ to N is observed. The free

precision of a few tenths of kcal/mol.

energetics of a long polymer is thus determined

Referencesby the chain-increment contribution ∆𝜇#$%&' , and[1] K. Yamada and N. Matubayasi: Macromol.

Figs. 1 and 2 demonstrate that ∆𝜇#$%&' can be

53 (2020) 775-788.

assessed from an all-atom simulation with the382Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Study on thermodynamic properties and NOx redox
reactions of ternary alloy nanoclusters by O(N)density functional calculations
Shih-Hsuan Hung and Taisuke Ozaki
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

We perform first-principles calculations andMonte Carlo sampling to investigate the structures of ternary PdRuM (M=Pt, Rh, or Ir)nanoparticles (NPs) with respect to three different spherical shapes. The calculation is carried out using OpenMX (Open source package
for Material eXplorer) software package.

1

Introduction

Metallic nanoparticles (NPs) are a promising
functional material in many aspects, such asenergy conservation, catalyst, and elements
storage. [1] To achieve better performance ofparticular functions, many experiments synthesize modified NPs to adjust their properties
physically and chemically. Bimetallic PdRu
NPs have been reported for providing better
catalytic reactions, but the drawback is suffered from the loss of metal element duringcatalytic cycles. [1, 2] Therefore, PdRuPt,
PdRuRh, and PdRuIr NPs or alloy have beenstudied and demonstrate their promising ability of NO reaction. [4, 3] Therefore, we would
like to investigation these NPs and provide
deeper insight in atomistic aspect.

2

ResultTo compare different morphology influencing different composition ternary NP, we select three different spherical shapes for theNPs. There are hexagonal close-packed (hcp),

truncated-octahedral (fcc), and icosahedral(fcc) shapes with 57, 55, and 55 atoms, respectively. To achieve higher coverage of energy survey, each nanoparticle is sampled 30
times using Monte Carlo sampling method,
thus there is 270 sampling in total. The statistical characteristic implies the position trendof individual atom for respective nanoparticles (detail is in published paper). By following the trend, we manually construct the bareternary NPs and find the most stable one. Figure 1 shows the most stable ternary NPs in
our calculation. The calculation shows thatthe atomic arrangements depend on the surface formation energy of individual elements.
In other words, the element possesses smaller
surface formation energy dominating the surface sites. The species have greater surface formation energy immerse in the NPs as bulk-likestate. Figure 1 demonstrates Ru atoms are always as a core in NPs due to its larger surface formation energy (γ = 1.31 eV/atom) offcc (111) surface. In addition, there are twoparticular shells are found in the investigation.
One configuration is binary solid solution alloy
and the other one represents that two elements
segregate from each other on the shell. The
reason of these two particular arrangements is
because the NPs tend to minimize its surface
strain, compared to lattice constant of Pd fcc
bulk (3.79 Å). For the NPs with solid solution shell, the Pd-M bond length decreases by
3.8 % in average. Meanwhile, the bond reduc-383

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: The most energetically stable
ternary PdRuM NPs in the calculations. The
unit of Ef is eV/atom.
tion of 3.0 % in average has been found for theconfigurations with segregation shell. In addition, the Ir-Ir bond length shows a significant
reduction of 6.2 %. By modeling the single
layer hexagonal as shell structure, the calculation shows a good agreement with our NPs
calculation. The reduced bond length of alloy
decreases the total calculated energy.
Oxidized NPs is an other problematic issueof catalyst. Due to the oxidation formationenergy variance, the elements of the NPs may
migrate from site to site. The oxygen adsorption on surface calculation demonstrates thatthe preference of oxygen adsorption (eV/atom)
on fcc hollow site is found to be Ru (-3.65)→ Rh (-2.78) → Ir (-2.47) → Pd (-2.06) →Pt (-1.84). Besides the single oxygen adsorption on cleaved surface, we examine the oxygen
molecule adsorption on pure Pd NPs. The calculation demonstrate taht the oxidation energy
is as a function of O-O distances. The increasing O-O distance up tp 5.0 Å decreases theoxidation formation energy. Figure 2 demonstrates the most stable oxidized ternary NPs
and their oxidation formation energy what we
can find. The result shows that the Ru atoms
migrate outward to the surfaces of NPs to beoxide. Pt, Pd and Pd atoms penetrate inwards
as a core of the ternary PdRuPt, PdRuRh, and
PdRuIr NPs, respectively. By calculating theNPs formation energy with respect to chemical
potential of oxygen molecule, the free energy
indicates hcp ternary NP is thermodynami-

Figure 2: The most energetically stable structures of high oxygen coverage on hcp, tOh, andIh ternary NPs.
cally unstable under oxygen-rich condition.

3

Conclusion and Discussion

In summary, we have provide deeper insight
into the most stable structures with three different morphologies and two oxidation statuses. The investigation shows the atoms areorganized in specific arrangement instead ofsolid solution alloy. In addition, the oxidation
condition can facilitate the atomic migrationin the ternary NPs. Although the scale of thestudy is not satisfying to interpret real situation, it can be a pilot investigation for real
scale NPs calculation and provide some possible configurations in advance.
References[1] Kusada Kohei et al.: J. Am. Chem. Soc.
136 (2014) 1864–1871[2] Wu Dongshuang et al.: Phys. Chem.
Chem. Phys. 14 (2012) 8051–8057[3] Sarker Md Samiul et al.: J. Mater. Res.
29 (2014) 856–864[4] Shang Changshuai et al.: Nano Res. 11
2018 4348–4355

384

3.6

Software Advancement Projects,

GPGPU Implementation, andWorkshop Support

385

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Development of ab-initio configuration sampling toolkit(abICS) for combining first-principles calculations withextended ensemble methods
Shusuke KASAMATSU1, Yuichi MOTOYAMA2, Kazuyoshi YOSHIMI2,
Yoshiyuki YAMAMOTO2, Osamu SUGINO2, Taisuke OZAKI2
1

Faculty of Science, Academic Assembly, Yamagata University,
Yamagata 990-85602

Institute for Solid State Physics, University of Tokyo, Kashiwa 277-8581

In functional materials, varying types ofonefficientparallelalgorithms

forconfigurational disorder are often employed tothermodynamic sampling. Figure 1 shows our

obtaincomputationalfavorable

properties

for

a

given

scheme.

There

are

Nrep

application. The ability to simulate such

Metropolis samplers running in parallel atdisorder as a function of temperature should be

different temperatures. Each of the samplers

immenselywithspawns parallel DFT processes (we used VASP

experiment. It would also enable prediction and[1]) to perform local structural relaxation anddesign of properties in materials with realisticenergy calculation at every Metropolis step.

levels of disorder. To achieve this, a natural

The temperatures are swapped according to theway may be to combine first-principles

replica exchange algorithm [2] to speed up thecalculations with the Metropolis Monte Carlosampling. We successfully demonstrated thatalgorithm. However, this is quite costly insufficient sampling can be performed onterms of computational power, so many

meaningfully large supercells by calculating theworkers have opted to first derive lightweight

degree of disorder in MgAl2O4 [3].

helpfulforcomparingmodels from first-principles calculations, thenuse that model for Monte Carlo sampling. The
problem is that deriving lightweight andreliable models becomes increasingly difficult
with increasing complexity of the system(various dopants, charged defects, interfaces,etc.).
Figure 1 Our scheme for parallel
configuration sampling. Reproduced from Ref.
[3].

In last year’s ISSP joint-use project, SK
proposed to bypass such fitting and instead rely

386

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoAs this year’s Software Advancement

files to abICS input.

Project, we proposed to develop an easy-to-use

We believe that abICS will be immenselyinterface for this computational scheme. The

useful for making efficient use of next-

resultab-Initio

generation supercomputers due to its multi-

Configuration Sampling toolkit, or abICS forlayered parallelism. We are also aiming to bringshort. It is written in Python 3 and is registered

togetherat PyPI (Python Package Index; pypi.org). It

simulation, and statistical physics using abICS

can thus be installed in most environments

as a hub. Because of modular coding practices

rathereasilythroughthecommandemployed in our project, it should be relatively“pip

install-–userabics”.

Now,

easy to implement interfaces for other solvers,

abICS can sample using the replica exchangeor to implement new sampling schemes. Please

Monte Carlo algorithm, and we are planning tohave a look at our homepage [8] and do not

add support for other extended ensemble

refrain from contacting us if you are interested

methods soon. The parameters for the samplingin using or extending this software.

has

been

releasedasinformation

science,materials

are controlled by an input file in TOML format,
which

is

a

minimalandReferences

easy-to-read

configuration format that is being used in many[1] https://vasp.at/software projects [4]. The parameters for the[2] K. Hukushima and K. Nemoto: J. Phys. Soc.

DFT calculations such as k-point sampling,

Jpn. 65 (1996) 1604.

basis set specification, convergence parameters,[3] S. Kasamatsu and O. Sugino: J. Phys.:etc. are controlled by input formats of theCondens. Matter 31 (2019) 085901.

specified solver. As the solver, abICS supports[4] https://github.com/toml-lang/toml

the use of DFT codes VASP, Quantum Espresso[5] https://www.quantum-espresso.org/[5], and OpenMX [6] as of May 2020. It also

[6] http://www.openmx-square.org/

has experimental support for aenet [7], which[7] http://ann.atomistic.net/

uses neural network potentials. Preprocessing[8] https://www.pasums.issp.u-

scripts are provided for converting structure

tokyo.ac.jp/abics/en

387

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

GPU acceleration for solving Bethe-Salpeter equation−1e iνn ) = [χe−1χ(q,0 (q, iνn ) − Γ(iνn )] ,Time [sec]The Bethe-Salpeter equation (BSE) provides two-particle responses in interacting
many-body systems. In the context of dynamical mean-field theory (DMFT), for example,
the momentum-dependent dynamical susceptibility χ(q, iνn ) is obtained by solving the BSE.
The BSE is symbolically written as

1600

60

Time (24 threads + 1 GPU)
1400
(24 threads + 0 GPU)
Speedup Rate
1200

50
40

1000
800

30

600

20

400
10

200

(1)

0

0
100

where the bold symbols indicate matrices of2 N 2 N . Here, N
size M = Nsp
sp is the numorb ω
ber of spin components, Norb is the number oforbitals, and Nω is the number of the fermionicMatsubara frequencies. Solving Eq. (1) requires computations of matrix multiplications
and the inverse of a matrix. Therefore, thecomputational cost is O(M 3 ).
The matrix size M for typical models isshown in Table 1. Here, the value of Nω isfixed at 20, but a larger value is necessary toaddress low-temperature properties. Namely,
M in Table 1 should be regarded as a minimum estimation. We see that d-orbital systems require M = 500 without spin-orbit coupling (SOC) and M = 2,000 with SOC. For
the f -orbital, we need M ≈ 4,000.
Table 1: The matrix size M for typical models.
Model
Nsp Norb NωM
1 orbital
1
1 20
20
2 orbital
1
2 20
80
1
3 20
180
3 orbital
5 orbital
1
5 20
500
2
5 20 2,000
5 orbital (SOC)
7 orbital (SOC)
2
7 20 3,920

Speedup Rate

Junya Otsuki1 and Kazuyoshi Yoshimi2
1
Research Institute for Interdisciplinary Science, Okayama University, Okayama 700-85302
Institute for Solid State Physics, University of Tokyo, Chiba 277-8581

1000

2000
Matrix Size

4000

Figure 1: Computation time for solving theBSE (left axis) and the speedup rate achievedby the use of GPU (right axis).
Figure 1 shows a benchmark. We used 1
node (24 thread) of System B in ISSP supercomputer center. Without GPU, the computational time grows in proportion to M 3 as
expected (filled squares). Use of GPU suppresses the growth of the time (filled circles).
A significant speedup is achieved for M & 100:
The speedup rate (the time without GPU divided by the time with GPU) is 13 and 52
for M = 1,000 and 4,000, respectively. Thisbenchmark indicates that the GPU acceleration is highly beneficial for d and f orbitals
especially on the existence of SOC.
As a future work, our BSE code will be integrated into the open-source DMFT software
DCore developed under the support of ISSP [1].
Acknowledgment: This work was supported by support service of program portability to GPGPU.
Reference:[1] https://github.com/issp-center-dev/DCore

388

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Report of CCMS hands-on sessions in the 2019 fiscal year
Takahiro Misawa
Institute for Solid State Physics, University of Tokyo
Kashiwa-no-ha, Kashiwa, Chiba 277-8581

In the 2019 fiscal year, center for computational materials science (CCMS) in institutefor solid state physics (ISSP) held two handson sessions by using supercomputer (sekirei) of
ISSP. A list of the hands-on sessions is shownin Table 1. In this report, we briefly summarize the hands-on sessions in the order of date.
DSQSS [1] is an open-source software package for solving quantum many-body problems using the quantum Monte Carlo methodthat sample the Feynman path integral using the worm update.
Development of
DSQSS was supported by “Project for advancement of software usability in materials
science”(PASUMS) [2] in the 2018 fiscal year.
In the hands-on session, Naoki Kawashima andco-developers explained the basics of the quantum Monte Carlo method and gave a tutorialof DSQSS [3].
DCore [4] is a tool for performing quantum
many-body simulations based on the dynamical mean-filed theory (DMFT). Developmentof DCore was also supported by PASUMUS in
the 2017 fiscal year. In the hands-on session,
Hiroshi Shinaoka and co-developers explained
the basics of the DMFT and gave a tutorial of
DCore [5].

DateSoftware

Main lecturer

Jun. 6
Dec. 26

DSQSS
DCore

N. Kawashima
H. Shinaoka

Table 1: List of software packages used in
CCMS hands-on sessions.

389

References[1] https://ma.issp.u-tokyo.ac.jp/en/app/180[2] https://www.pasums.issp.u-tokyo.ac.jp[3] https://ccms.issp.u-tokyo.ac.jp/event/1942[4] https://ma.issp.u-tokyo.ac.jp/en/app/1004[5] https://ccms.issp.u-tokyo.ac.jp/event/2486

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Supercomputer course of Computational Materials Design(CMD®) workshop
Masaaki GESHI1, Yoshitada MORIKAWA2, Tomoya ONO3
1

Institute for NanoScience Design,

Osaka University, 1-2 Machikaneyama, Toyonaka, Osaka 560-0043
2

Department of Precision Engineering, Graduate School of Engineering,Osaka University, 2-1 Yamadaoka, Suita, Osaka 565-0871

3

Department of Electrical and Electronic Engineering, Graduate School of Engineering,
Kobe University, 1-1 Rokkodaicho, Nada, Kobe 657-8501
The 35rd Computational Materials Designmaterials, atomic diffusion on solid surfaces, dry(CMD®) workshop (CMD35) has been held

reforming of methane, chemical reactions infrom September 2nd to September 6th and thesolid oxide fuel cell, and so on. The participants

36th CMD® workshop (CMD36) has been done

performed the calculations and examined thefrom February 17th to February 21st at Graduate

results.

SchoolofEngineering

Science,Osaka

In CMD36 two participants took the

University. In this workshop we have thesupercomputersupercomputer course to train up humansupercomputer of ISSP. They got a tutorial on

resources to advance researches by using system

RSPACE developed by T. Ono. After giving the

B supercomputer of ISSP, the University of

introductory lecture of large-scale computing by

Tokyo.

M. Geshi and describing the calculation method

course

and

used

the

In CMD35 eight participants took theof electronic states and electron conduction

supercomputer course and got a tutorial on

property using RSPACE, exercises published in

STATE-Senri developed by Y. Morikawa. Afterthe manual were carried out by Y. Egami. Then,giving the introductory lecture of large-scale

electronic state calculations were carried out forcomputing by M. Geshi and explaining how toseveral molecules, and the electronic density

use the supercomputer of ISSP and explaining

distribution was visualized. Finally, the atomic

how to use STATE-Senri, calculation models on

structure optimization of the defects in GaAs

each research subject of the participants werebulks was carried out, and the calculation of

built and their calculations were carried out.

carrier scattering property by the defects wasSpecific subjects include oxidation of solid

investigated.

surfaces, chemical reactions on two-dimensional

390

4

PUBLICATION LIST

391

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Example:LASTNAME, Firstname [ project class; # points (B), # points (C) ] (Page #)— Project title
1. First paper
Names of Authors, etc.
2. Second paper...

2 ISSP Joint Research Projects
AKAGI, Kazuto [ C class; 5000 (B), 0 (C) ] (104)— Elucidation of diﬀusion process of ionic species in organic solvent
AKAGI, Yutaka [ B class; 900 (B), 100 (C) ] ()— Novel Topological Excitation in Magnet
AKAI, Hisazumi [ B class; 1800 (B), 100 (C) ] (146, 147)
— Data accumulation of magnetic properties of rare earth mixed crystal— Data accumulation of magnetic properties of rare earth mixed crystal magnetic materials
1. Calculating Curie temperatures for rare-earth permanent magnets: Ab initio inspection of localized magnetic moments in d-electron ferromagnetism
M.Matsumoto and H.Akai : Phys. Rev. B 101, 1444402 (2020).
2. Curie temperature of Sm2 Fe17 and Nd2 Fe14 B: a ﬁrst-principles study
T. Fukazawa, H.Akai, Y. Harashima, and T. Miyake : IEEE Trans. Magn. 55,2101305 (2019).
3. Ab initio Study of High-ﬁeld NMR Shift of 59 Co in the Ferromagnetic Heusler Alloy Co2 TiGa
H.Nishihara, H.Akai, K.Sato, T.Kanomata, M.Geshi, T.Sakon, and T.Wada : J. Phys. Soc. Jpn.
88, 034712 (2019).
4. First-principles study of spin-wave dispersion in Sm(Fe1−x Cox )12
T. Fukazawa, H.Akai, Y. Harashima, and T. Miyake : J. Magn. Magn. Mater. 469, 296 (2019).
AKASHI, Ryosuke [ C class; 5000 (B), 850 (C) ] (89)— Ab initio study on the metallization and superconductivity in metallic superhydrides
1. Superconductivity of LaH10 and LaH16 polyhydrides
I. A. Kruglov, D. V. Semenok, H. Song, R. Szczȩániak, I. A. Wrona, R. Akashi, M. M. D. Esfahani,
D. Duan, T. Cui, A. G. Kvashnin, and A. R. Oganov: Phys. Rev. B 101 (2020) 024508.
2. Archetypical push the band critical point mechanism for peaking of the density of states inthree-dimensional crystals: Theory and case study of cubic H3 S
Phys. Rev. B 101 (2020) 075126.
AOYAMA, Kazushi [ B class; 1500 (B), 190 (C) ] (301)— Eﬀects of a magnetic ﬁeld on spin-lattice-coupled orders in breathing pyrochlore antiferromagnets— Transport properties of the antiferromagnetic classical XXZ model in two dimensions
1. Eﬀects of magnetic anisotropy on spin and thermal transport in classical antiferromagnets on thesquare lattice
K. Aoyama and H. Kawamura: Phys. Rev. B 100 (2019) 144416.
2. Spin Current as a Probe of the Z2 -Vortex Topological Transition in the Classical Heisenberg
Antiferromagnet on the Triangular Lattice392

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoK. Aoyama and H. Kawamura: Phys. Rev. Lett. 124 (2020) 047202.
ARAI, Munehito [ C class; 9000 (B), 0 (C) ] (252)— Computational rational design of novel proteins for industrial and pharmaceutical applications— Protein design toward the development of anti-allergy drugs
ARAI, Toyoko [ C class; 2000 (B), 600 (C) ] (135)— DFT calculation of atomic displacement captured by energy dissipation channel of noncontact atomic
force microscope
ARIMA, Kenta [ B class; 700 (B), 90 (C) ] (178)— Simulation of STM images of graphene sheet after chemical reduction
ASANO, Yuta [ E class; 30000 (B), 4600 (C) ] (241)— Karman-Vortex Cavitation in a Complex Fluid— Molecular Dynamics Simulation of Cavitating Flow in a Complex Fluid
1. Eﬀects of cavitation on Kármán vortex behind circular-cylinder arrays: A molecular dynamics
study
Y. Aasno, H. Watanabe, and H. Noguchi: J. Chem. Phys. 152 (2020) 034501.
2. 分子動力学計算による複雑流体中のカルマン渦の解析
浅野 優太, 渡辺 宙志, 野口 博司: 分子シミュレーション研究会会誌 アンサンブル 22, 157 (2020).
DEKURA, Haruhiko [ B class; 800 (B), 0 (C) ] (173)— First-principles calculation of the higher-order phonon-phonon scattering strength
EGAMI, Yoshiyuki [ C class; 2500 (B), 800 (C) ] (119)— First-principles study on controlling of electronic structures and electron-transport properties of 2-D
materials— First-principles study on controlling of electronic structures and electron-transport properties ofatomic layered materials
1. Eﬃcient calculation of the self-energy matrices for electron-transport simulations
Y. Egami, S. Tsukamoto and T. Ono: Phys. Rev. B. 100 (2019) 075413.
2. Eﬃcient calculation of the Green s function in scattering region for electron-transport simulations
Y. Egami, S. Tsukamoto and T. Ono: submitted to Phys. Rev. Lett.
FUCHIZAKI, Kazuhiro [ C class; 4500 (B), 200 (C) ] (283)— Kinetics of phase transition and polyamorphism
1. Predicting the Melting Curve of MgO: An Essential Update
K. Fuchizaki: J. Phys. Soc. Jpn. 88 (2019) 065003.
FUJII, Keisuke [ B class; 400 (B), 0 (C) ] (351)— Quantum simulation for quantum many body systems using noisy-intermediate-scale quantum computers
FUJIMOTO, Yoshitaka [ C class; 1500 (B), 0 (C) ] (155)— First-principles investigation of electronic properties of carbon nanotubes and graphene
1. STM visualization of carbon impurities in sandwich structures consisting of hexagonal boron
nitride and graphene
T. Haga, Y. Fujimoto, and S. Saito: Jpn. J. Appl. Phys. 58, SIIB03 (2019).
2. Electronic structures and scanning tunneling microscopy images of heterostructures consisting ofgraphene and carbon-doped hexagonal boron nitride layers
T. Haga, Y. Fujimoto, and S. Saito: Phys. Rev. B 100, 125403 (2019).
3. Atomic structures and scanning tunneling microscopy of nitrogen-doped carbon nanotubes
Y. Fujimoto and S. Saito: IOP Conf. Ser.: Mater. Sci. Eng. 744, 012032 (2020).
4. First-Principles Materials Design for Graphene-based Sensor Devices393

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Y. Fujimoto: Sustainable Materials for Next Generation Energy Devices (Elsevier 2020),Accepted.
FUJISHIRO, Hiroki [ C class; 1500 (B), 0 (C) ] (153)— Strained Band-Structure Engineering for Antimonide-Based Terahertz Transistors
FUKUDA, Jun-ichi [ B class; 1500 (B), 0 (C) ] (312)— Calculation of ordered structures and their optical properties of soft materials
FUKUDA, Masahiro [ B class; 800 (B), 100 (C) ] (169)— Local physical quantities analysis based on the quantum ﬁeld theory in material surface
FUKUDA, Tuneo [ B class; 700 (B), 0 (C) ] (181)— First Principles Calculation of 2-Dimensional Silicides Formed on Nickel Surfaces
1. Formation of two-dimensional silicide on the Ni(100) surface
T. Fukuda, I. Kishida and K. Umezawa: Jpn. J. Appl. Phys., in press.
FUKUI, Ken-ichi [ C class; 1500 (B), 0 (C) ] (311)— Analysis on Structuring and Dynamics of Ionic Liquid Forming Electric Double Layer as a Local
Interfacial Field
1. Correlation between Mobility and Hydrogen Bonding Network of Water at Electriﬁed-Graphite
Electrode Using Molecular Dynamics Simulatio
M. Imai, Y. Yokota, I. Tanabe, K. Inagaki, Y. Morikawa, K. Fukui : Phys. Chem. Chem. Phys.22(2020) 1767
2. Ionic-Liquid-Originated Carrier Trapping Dynamics at the Interface in Electric Double-Layer Organic FET Revealed by Operando Interfacial Analyses
D. Okaue, I. Tanabe, S. Ono, K. Sakamoto, T. Sato, A. Imanishi, Y. Morikawa, J. Takeya, K.
Fukui: J. Phys. Chem. C, 124 (2020) 2543’
FUKUMOTO, Yoshiyuki [ B class; 1300 (B), 0 (C) ] (317)— Eﬀects of Dzyaloshinskii–Moriya interactions and structural distortions on magnetic susceptibilitiesof spherical-kagome spin-systems— Eﬀects of Dzyaloshinskii-Moriya interactions and exchange randomness on low-temperature speciﬁcheats of spherical-kagome spin-systems
GOHDA, Yoshihiro [ C class; 4500 (B), 700 (C) ] (99)
— First-principles calculations of multiferroic interfaces
1. First-principles study on surface stability and interface magnetic properties of SmFe12
Y. Ainai, T. Shiozawa, Y. Tatetsu, and Y. Gohda: Appl. Phys. Express 13, 045502 (2020).
2. First-principles study of crystalline Nd-Fe alloys
Y. Ainai, Y. Tatetsu, A. Terasawa, and Y. Gohda: Appl. Phys. Express 13, 017006 (2020).
3. Enhancement of magnetoelectric coupling by insertion of Co atomic layer into Fe3 Si/BaTiO3 (001)interfaces identiﬁed by ﬁrst-principles calculations
Y. Hamazaki and Y. Gohda: J. Appl. Phys. 126, 233902 (2019).
4. Great Diﬀerences between Low-Temperature Grown Co2 FeSi and Co2 MnSi Films on SingleCrystalline Oxides
K. Kudo, Y. Hamazaki, S. Yamada, S. Abo, Y. Gohda, and K. Hamaya: ACS Appl. Electron.
Mater. 1, 2371 (2019).
5. Eﬃcient Algorithm Based on Liechtenstein Method for Computing Exchange Coupling Constants
Using Localized Basis Set
A. Terasawa, M. Matsumoto, T. Ozaki, and Y. Gohda: J. Phys. Soc. Jpn. 88, 114706 (2019).
HAGIWARA, Satoshi [ B class; 800 (B), 0 (C) ] ()— Real-time propagated simulation for electron-positron scattering at the surface394

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

HAMADA, Ikutaro [ C class; 5500 (B), 800 (C) ] (82)
— van der Waals density functional study of molecules adsorbed on metal surfaces
HAMAGUCHI, Satoshi [ C class; 4000 (B), 650 (C) ] ()— Analyses of Surface Reactions in Atomic Layer Etching Processes
HAMAMOTO, Yuji [ C class; 2000 (B), 0 (C) ] (141)— van der Waals density functional study of image potential states at organic-metal interfaces
HARADA, KENJI [ C class; 2000 (B), 500 (C) ] (292)— Application of numerical renormalization group method in condensed-matter physics
1. Entropy Governed by the Absorbing State of Directed Percolation
K. Harada and N. Kawashima: Phys. Rev. Lett. 123 (2019) 090601.
HARASHIMA, Yosuke [ C class; 1500 (B), 0 (C) ] (151)— First principles study on leaking current at a dislocation in doped semiconductors
1. Screw dislocation that converts p-type GaN to n-type: Microscopic study on the Mg condensationand the leakage current in p-n diodes
T. Nakano, Y. Harashima, K. Chokawa, K. Shiraishi, A. Oshiyama, Y. Kangawa, S. Usami, N.
Mayama, K. Toda, A. Tanaka, Y. Honda, and H. Amano: arXiv, 2004.06876 (2020).
HARUYAMA, Jun [ C class; 5500 (B), 800 (C) ] (80)
— Electrochemical reaction analysis using density functional calculation + implicit solvation model
HASHIMOTO, Tamotsu [ C class; 1500 (B), 450 (C) ] (300)— Molecular dynamics simulation of ferroelectrics using a shell model V
1. Structure of Amorphous BaTiO3 by Molecular Dynamics Simulations Using a Shell Model
T. Hashimoto and H. Moriwake: Physica B: Condens. Matter 579 (2020) 411799.
HASHMI, Arqum [ C class; 1000 (B), 0 (C) ] (168)— 2D materials based symmetric and non-symmetric magnetoresistive junctions
1. Graphene-based Symmetric and Non-Symmetric Magnetoresistive Junctions
A. Hashmi, K. Nakanishi, T. Ono: J. Phys. Soc. Jpn. 89, 034708 (2020).
HATSUGAI, Yasuhiro [ C class; 4000 (B), 700 (C) ] (281)— Universality of bulk-edge correspondence by numerical methods
1. Sequential quantum phase transitions in J1 − J2 Heisenberg chains with integer spins (S > 1):
Quantized Berry phase and valence
Shota Fubasami, Tomonari Mizoguchi and Yasuhiro Hatsugai: Phys. Rev. B 100, 014438 (2019)
2. Many-Body Chern Number without Integration
Koji Kudo, Haruki Watanabe, Toshikaze Kariyado, and Yasuhiro Hatsugai: Phys. Rev. Lett.
122, 146601 (2019)
3. Higher-order Topological Mott Insulators
Koji Kudo, Tsuneya Yoshida, and Yasuhiro Hatsugai : Phys. Rev. Lett. 123, 196402 (2019)
4. Non-Hermitian fractional quantum Hall states
Tsuneya Yoshida, Koji Kudo, and Yasuhiro Hatsugai: Scientiﬁc Reports 9, 16895 (2019)
5. Exceptional rings protected by emergent symmetry for mechanical systems
Tsuneya Yoshida and Yasuhiro Hatsugai: Phys. Rev. B 100, 054109 (2019)
6. Phase diagram of a disordered higher-order topological insulator: A machine learning study
H. Araki, T. Mizoguchi, and Y. Hatsugai: Phys. Rev. B 99, 085406 (2019)
7. ZQ Berry Phase for Higher-Order Symmetry-Protected Topological Phases
Hiromu Araki, Tomonari Mizoguchi and Yasuhiro Hatsugai: Phys. Rev. Research 2, 012009(R)(2020)
8. Higher-order topological phases in a spring-mass model on a breathing kagome lattice
Hiromasa Wakao, Tsuneya Yoshida, Hiromu Araki, Tomonari Mizoguchi, and Yasuhiro Hatsugai:

395Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Phys. Rev. 101, 094107 (2020)
Exceptional band touching for strongly correlated systems in equilibrium
Tsuneya Yoshida, Robert Peters, Norio Kawakami, Yasuhiro Hatsugai: arXiv:2002.11265
10. Mirror skin eﬀect and its electric circuit simulation
Tsuneya Yoshida, Tomonari Mizoguchi, and Yasuhiro Hatsugai: arXiv:1912.12022
11. Non-Analytic Adiabatic Principle for Anyons
Koji Kudo and Yasuhiro Hatsugai : arXiv:2004.00859.

9.

HATTORI, Ken [ C class; 1500 (B), 450 (C) ] (143)— Atomic structure and electronic states for silicide ﬁlms
HAYAMI, Satoru [ C class; 5500 (B), 0 (C) ] (221)— Search for new types of skyrmion crystals based on point group symmetry
1. Magnetic Vortex induced by Nonmagnetic Impurity in Ferromagnets: Magnetic Multipole andToroidal around the Vacancy
S. Hayami, H.Kusunose, and Y. Motome: J. Phys. Soc. Jpn. 88, 063702 (2019).
2. Double-Q Chiral Stripe in the d-p Model with Strong Spin-Charge Coupling
R. Yambe and S. Hayami: J. Phys. Soc. Jpn. 89, 013702 (2020).
3. Electric Toroidal Quadrupoles in Spin-Orbit-Coupled Metal Cd2 Re2 O7
S. Hayami, Y. Yanagi, H. Kusunose, and Y. Motome: Phys. Rev. Lett. 122, 147602 (2019).
4. Atomic-Scale Magnetic Toroidal Dipole under Odd-Parity Hybridization
M. Yatsushiro and S. Hayami: J. Phys. Soc. Jpn. 88, 054708 (2019).
5. Multipole expansion for magnetic structures: A generation scheme for symmetry-adapted orthonormal basis set in crystallographic point group
M.-T. Suzuki, T. Nomoto, R. Arita, Y. Yanagi, S. Hayami, and H. Kusunose: Phys. Rev. B 99,
174407 (2019).
6. Momentum-Dependent Spin Splitting by Collinear Antiferromagnetic Ordering
M. Naka, S. Hayami, H. Kusunose, Y. Yanagi, Y. Motome, and H. Seo: Nat. Commun. 10, 4305
(2019).
7. Momentum-Dependent Spin Splitting by Collinear Antiferromagnetic Ordering
S. Hayami, Y. Yanagi, and H. Kusunose: J. Phys. Soc. Jpn. 88, 123702 (2019).
8. Odd-Parity Multipoles by Staggered Magnetic Dipole and Electric Quadrupole Orderings in CeCoSi
M. Yatsushiro and S. Hayami: J. Phys. Soc. Jpn. 89, 013705 (2020).
9. Dimension transcendence and anomalous charge transport in magnets with moving multiple-Q
spin textures
Y. Su, S. Hayami, and S.-Z. Lin: Phys. Rev. Research 2, 013160 (2020).
HIDA, Kazuo [ B class; 700 (B), 90 (C) ] (338)— Numerical Study of One Dimensional Frustrated Quantum Spin Systems
1. Ground State Phases of Distorted S=1 Diamond Chains
K. Hida: J. Phys. Soc. Jpn. 88, 074705 (2019)
2. Exact Thermodynamic Properties of Mixed Diamond Chains with Strong Single-Site Anisotropy
R. Iwazaki and K. Hida: J. Phys. Soc. Jpn. 88, 095001 (2019)
3. Ground-State Phases of Alternating-Bond S=1 Diamond Chains
K. Hida: J. Phys. Soc. Jpn. 89, 024709 (2020)
HIGUCHI, Yuji [ C class; 9500 (B), 1650 (C) ] (244)— Brittle structure of crystalline polymers by large-scale coarse-grained molecular dynamics simulation— Creep fracture process of crystalline polymers by large-scale molecular dynamics simulation
1. Stress Transmitters at the Molecular Level in the Deformation and Fracture Processes of theLamellar Structure of Polyethylene via Coarse-Grained Molecular Dynamics Simulations
Y. Higuchi: Macromolecules 52 (2019) 6201.

396

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoHINOKIHARA, Taichi [ C class; 500 (B), 0 (C) ] (349)— Magnetization reversal process in classical spin systems
1. Time Quantiﬁed Monte Carlo method for Long-range Interacting Systems
Taichi Hinokihara,Yuta Okuyama, Munetaka Sasaki, and Seiji Miyashita: Journal of Computational Physics, in review
HINUMA, Yoyo [ B class; 600 (B), 0 (C) ] (188)— Calculation of multication oxide surface properties for catalyst informatics
1. Band alignment at surfaces and heterointerfaces of Al2O3, Ga2O3, In2O3, and related group-III
oxide polymorphs: A ﬁrst-principles study
Y. Hinuma, T. Gake, and F. Oba: Phys. Rev. Mater., 3 (2019) 084605.
HIRATSUKA, Masaki [ B class; 800 (B), 100 (C) ] ()— Eﬀect of van der Waals interaction on vibrational spectra from ab initio molecular dynamics simulation
HIYAMA, Miyabi [ B class; 600 (B), 80 (C) ] (186)— Analysis of absorption spectra for caged compounds in aqueous solution
1. Theoretical study of the wavelength selection for the photocleavage of coumarin-caged D-luciferin
J. Usukura, M. Hiyama, M. Kurata, Y. Hazama, X-P. Qiu, F. M. Winnik, H. Akiyama, and N.
Koga: Photochem. Photobiol. (2020) in press.
2. Photoabsorption Spectra of Aqueous Oxyluciferin Anions Elucidated by Explicit Quantum Solvent
Y.Noguchi, M. Hiyama, M. Shiga, H. Akiyama, and O. Sugino: J. Chem.Theo. Comput.,15 (2019)
5474.
HOSHI, Takeo [ C class; 6500 (B), 900 (C) ] (76)
— Uniﬁcation of massively parallel quantum material simulation and data-driven science
1. Kω –Open-source library for the shifted Krylov subspace method
Takeo Hoshi, Mitsuaki Kawamura, Kazuyoshi Yoshimi, Yuichi Motoyama, Takahiro Misawa,
Youhei Yamaji, Synge Todo, Naoki Kawashima, Tomohiro Sogabe: arXiv:2001.08707
2. Two-stage data-analysis method for total-reﬂection high-energy positron diﬀraction (TRHEPD)
Kazuyuki Tanaka, Izumi. Mochizuki, Takashi Hanada, Ayahiko Ichimiya, Toshio Hyodo, andTakeo Hoshi: Submitted; Preprint:https://arxiv.org/abs/2002.12165
3. Development of data-analysis software for total-reﬂection high-energy positron diﬀraction (TRHEPD)
Kazuyuki Tanaka, Takeo Hoshi, Izumi Mochizuki, Takashi Hanada, Ayahiko Ichimiya, Toshio Hyodo: Acta. Phys. Pol. A 137, 188-192 (2020).
4. An a posteriori veriﬁcation method for generalized Hermitian eigenvalue problems in large-scale
electronic state calculations
Takeo Hoshi, Takeshi Ogita, Katsuhisa Ozaki, Takeshi Terao: J. Comp. Appl. Math. 376,
112830/1-13 (2020).
5. Charge-Transfer Excited States in the Donor/Acceptor Interface from Large-Scale GW Calculations
Takatoshi Fujita, Yoshifumi Noguchi, Takeo Hoshi: J. Chem. Phys. 151, 114109/1-8 (2019).
6. EigenKernel - A middleware for parallel generalized eigenvalue solvers to attain high scalability
and usability
Kazuyuki Tanaka, Hiroto Imachi, Tomoya Fukumoto, Akiyoshi Kuwata, Yuki Harada, Takeshi
Fukaya, Yusaku Yamamoto, Takeo Hoshi: Japan J. Indust. Appl. Math 36, 719-742 (2019).
7. Numerical aspect of large-scale electronic state calculation for ﬂexible device material
Takeo Hoshi, Hiroto Imachi, Akiyoshi Kuwata, Kohsuke Kakuda, Takatoshi Fujita, Hiroyuki Matsui: Japan J. Indust. Appl. Math 36, 685-698 (2019).
8. Recent progress in large-scale electronic state calculations and data-driven sciences
Takeo Hoshi and Satoshi Ito: Chap. 14 of Handbook of Silicon Based MEMS Materials andTechnologies 3rd Ed., Elsevier (2020).
9. Numerical methods for large scale electronic state calculation on supercomputer
Takeo Hoshi, Yusaku Yamamoto, Tomohiro Sogabe, Kohei Shimamura, Fuyuki Shimojo, Aiichiro

397

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Nakano, Rajiv Kalia, Priya Vashishta: Chap. 15 of 21st Century Nanoscience - A Handbook:
Nanophysics Sourcebook (Volume One), CRC Press (2019).
HOSHINO, Shintaro [ B class; 900 (B), 0 (C) ] (230)— Dynamical mean-ﬁeld theory + quantum Monte Carlo approach to strongly correlated electron systems
with multi-orbitals
1. Nickelate superconductors: Multiorbital nature and spin freezing
P. Werner and S. Hoshino, Phys. Rev. B 101, 041104(R) (2020).
2. Magnetic Field Induced Phase Transition in Superconducting State of Non-Kramers Doublet
Kondo Lattice Systems with Semi-Metallic Conduction Bands
S. Iimura, M. Hirayama, and S. Hoshino: JPS Conf. Proc. 30, 011048 (2020).
3. Fermi-surface anisotropy eﬀects on full-gap superconductivity in non-Kramers doublets coupled
to compensated metals
S. Iimura, M. Hirayama, and S. Hoshino: JPS Conf. Proc. 29, 011003 (2020).
HOTTA, Chisa [ B class; 600 (B), 0 (C) ] (347)— Numerical studies on some new phases of the transverse Ising model
1. Spin-orbital glass transition in a model of frustrated pyrochlore magnet without quenched disorder
Kouta Mitsumoto, Chisa Hotta, and Hajime Yoshino: Phys. Rev. Lett. 124 (2020) 087201.
2. Multiple quadrupolar or nematic phases driven by the Heisenberg interactions in a spin-1 dimer
system forming a bilayer
Katsuhiro Tanaka, Chisa Hotta: Phys. Rev. B 101 (2020) 094422.
3. Discovering momentum-dependent magnon spin texture in insulating antiferromagnets: Role ofthe Kitaev interaction
Masataka Kawano, Chisa Hotta: Phys. Rev. B 100 (2019) 174402.
HOTTA, Takashi [ C class; 7500 (B), 0 (C) ] (215, 217)
— Research of Two-Channel Kondo Eﬀect in Transuranium Systems— Two-Channel Kondo Eﬀect Emerging in a Multiorbital Anderson Model Hybridized with Γ7 and Γ8
Conduction Bands
1. Two-Channel Kondo Eﬀect Emerging from Np and Pu Ions
Dai Matsui and Takashi Hotta, JPS Conf. Proc. 30, 011125 (2020).
HU, Shiqian [ C class; 2500 (B), 650 (C) ] (125)— manipulation of the cross-plane thermal conductivity on the 2D hetero-junction materials
HUKUSHIMA, Koji [ C class; 3500 (B), 0 (C) ] (287)— Development of data-driven science to materials science
1. Adjusting the descriptor for a crystal structure search using Bayesian optimization
Nobuya Sato, Tomoki Yamashita, Tamio Oguchi, Koji Hukushima, and Takashi Miyake: Phys.
Rev. Materials 4, (2020) 033801.
IDO, Kota [ C class; 5000 (B), 750 (C) ] (262)— Numerical studies on magnetization process of the Kitaev spin liquid
1. Correlation eﬀects on the magnetization process of the Kitaev model
K. Ido, and T. Misawa: Phys. Rev. B 101 (2020) 045121.
2. Charge dynamics of correlated electrons: Variational description with inclusion of composite
fermions
K. Ido, M. Imada, and T. Misawa: Phys. Rev. B 101 (2020) 075124.
IGARASHI, Ryo [ C class; 1000 (B), 500 (C) ] ()— Full diagonalization using low-rank approximation to Hamiltonian matrices and its application toquantum spin models

398

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

IKEDA, Hiroaki [ B class; 400 (B), 0 (C) ] (195)— Development and application of the ﬁrst-principles approach
IKUHARA, Yuichi [ C class; 4500 (B), 0 (C) ] (111)— Ab initio calculations of atomic and electronic structures for functional oxide materials— Study of atomic and electronic structure of hetero interface by ﬁrst-principles molecular dynamics
simulations
1. Strong metalmetal interaction and bonding nature in metal/oxide interfaces with large mismatches
H. Li, M. Saito, C. Chen, K. Inoue, K. Akagi, Y. Ikuhara: Acta Mater. 179 (2019) 237.
IMADA, Masatoshi [ E class; 34000 (B), 4950 (C) ] (197)— Development of methodology for analysis of nonequilibrium superconductivity in strongly correlated
systems via integration of electronic state theory and time-resolved experimental data
— Mechanism of quantum spin liquid and high-Tc superconductivity studied by excitation spectra andnonequilibrium dynamics calculation by variational Monte Carlo methods
1. Charge dynamics of correlated electrons: Variational description with inclusion of composite
fermions
Kota Ido, Masatoshi Imada, Takahiro Misawa: Phys. Rev. B 101 (2020) 075124.
2. Ab initio study of superconductivity and inhomogeneity in a Hg-based cuprate superconductor
Takahiro Ohgoe, Motoaki Hirayama, Takahiro Misawa, Kota Ido, Youhei Yamaji, Masatoshi
Imada: Phys. Rev. B 101 (2020) 045124.
3. Eﬀective Hamiltonian for cuprate superconductors derived from multiscale ab initio scheme withlevel renormalization
Motoaki Hirayama, Takahiro Misawa, Takahiro Ohgoe, Youhei Yamaji, Masatoshi Imada: Phys.
Rev. B 99 (2019) 245155.
4. Ab initio derivation of an eﬀective Hamiltonian for the La2 CuO4 /La1 .55Sr0 .45CuO4 heterostructure
Terumasa Tadano, Yusuke Nomura, Masatoshi Imada: Phys. Rev. B 99 (2019) 155148.
INAGAKI, Kouji [ C class; 2000 (B), 600 (C) ] ()— Analysis and Design of reaction process and catalyst material for CARE machining
INAOKA, Takeshi [ B,C class; 1000 (B), 200 (C) ] (160)— Search and realization of novel electronic properties of solid surfaces and interfaces and of small
particles— Search and realization of novel electronic properties of solid surfaces and interfaces and of small
particles II
1. Finite-diﬀerence time-domain analysis of scanning tunneling microscope light emission from vibrating molecules
Y. Uehara, W. Iida, T. Inaoka, S. Iwaoka, H. Aoyagi, and S. Katano: to be submitted.
ISHIBASHI, Shoji [ C class; 4500 (B), 0 (C) ] (110)— Prediction of properties of organic ferroelectrics and piezoelectrics by ﬁrst-principles calculation
1. Coexistence of normal and inverse deuterium isotope eﬀects in a phase-transition sequence oforganic ferroelectrics
S. Horiuchi, S. Ishibashi, K. Kobayashi, and R. Kumai: RSC Adv. 9 (2019) 39662.
ISHIDA, Kunio [ B class; 1200 (B), 170 (C) ] (315)— Entanglement in remote electron-phonon systems created by photoirradiation— Ultrafast nonadiabatic dynamics of electron-phonon-photon system
1. Interplay of electron-phonon nonadiabaticity and Raman scattering in the wavepacket dynamics
of electron-phonon-photon systems
Kunio Ishida: Eur. Phys. J. D73, 117 (2019)
2. Coherent control of nonadiabatic dynamics of electron-phonon systems by quantized light ﬁeld
Kunio Ishida: Progress in Ultrafast Intense Laser Science XV, 10.1007/978-3-030-47098-2 6399

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

ISHIHARA, Sumio [ B class; 800 (B), 0 (C) ] (234)— Photoinduced dynamics and high harmonic generation in magnetism
1. Nonequilibrium susceptibility in photoinduced Floquet states
Atsushi Ono and Sumio Ishihara, Phys. Rev. B 100, 075127 (2019).
2. Optical Response in Excitonic Insulating State: Variational Cluster Approach
Hengyue Li, Junya Otsuki, Makoto Naka, Sumio Ishihara, Phys. Rev. B 101, 125117 (2020).
3. Photoinduced Ultrafast Phenomena in Correlated Electron Magnets
Sumio Ishihara, J. Phys. Soc. Jpn. 88, 023703 (2019).
ISHII, Fumiyuki [ C class; 8500 (B), 0 (C) ] (70)
— First-Principles Crystal Structure Prediction of Magnetic Thermoelectric Materials— First-principles study of electric-ﬁeld eﬀect on magnetic insulator
1. Realization of Spin-dependent Functionality by Covering a Metal Surface with a Single Layer ofMolecules
H. Isshiki, K. Kondou, S. Takizawa, K. Shimose, T. Kawabe, E. Minamitani, N. Yamaguchi, F.
Ishii, A. Shiotari, Y. Sugimoto, S. Miwa and Y. Otani: Nano Lett. 197 (2019) 7119.
2. First-principles Study of Spiral Spin Density Waves in Monolayer MnCl2 Using Generalized Bloch
Theorem
T.B. Prayitno and F. Ishii: J. Phys. Soc. Jpn. 88 (2019) 104705.
3. Intrinsic persistent spin helix state in two-dimensional group-IV monochalcogenide MX monolayers(M=Sn or Ge and X=S, Se, or Te)
M.A.U. Absor and F. Ishii: Phys. Rev. B. 100 (2019) 115104.
4. Photoinduced Rashba Spin-to-Charge Conversion via an Interfacial Unoccupied State
J. Puebla, F. Auvray, N. Yamaguchi, M. Xu, S.Z. Bisri, Y. Iwasa, F. Ishii, and Y. Otani: Phys.
Rev. Lett. 122 (2019) 256401.
5. Electric-ﬁeld-induced Z2 topological phase transition in strained single bilayer Bi(111)
H. Sawahata, Y. Yamaguchi, and F. Ishii: Appl. Phys. Express 12 (2019) 075009.
ISHIZUKA, Jun [ C class; 4500 (B), 750 (C) ] (223)— Multipole and anisotropic superconductivity from ﬁrst principles
1. Insulator-Metal Transition and Topological Superconductivity in UTe2 from a First-Principles
Calculation
Jun Ishizuka, Shuntaro Sumita, Akito Daido, and Youichi Yanase: Phys. Rev. Lett. 123, 217001(2019).
2. Observation of superconducting diode eﬀect
Fuyuki Ando, Yuta Miyasaka, Tian Li, Jun Ishizuka, Yoichi Shiota, Takahiro Moriyama, Yoichi
Yanase, and Teruo Ono: submitted to Nature.
ISOBE, Masaharu [ B class; 600 (B), 0 (C) ] (345)— Nonequilibrium phase transition and slow dynamics in the dense hard sphere systems
IYODA, Eiki [ C class; 1500 (B), 0 (C) ] (309)— Numerical analysis on the oﬀ-diagonal eigenstate thermalization hypothesis
1. Characterizing complexity of many-body quantum dynamics by higher-order eigenstate thermalization
K. Kaneko, E. Iyoda, and T. Sagawa: Phys. Rev. A, in press.
JESCHKE, Harald [ C class; 6500 (B), 0 (C) ] (257, 258)
— Doping dependence of electronic structure and superconductivity in FeSe intercalated by organic
molecules— Stability of the superconductor LaFe2 As2
1. Novel Fe-Based Superconductor LaFe2As2 in Comparison with Traditional Pnictides
I. I. Mazin, M. Shimizu, N. Takemori, and H. O. Jeschke: Phys. Rev. Lett. 123 (2019), 267001.
2. Unusual non-valence-skipping electronic state of Sn in AgSnSe2

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Y. Naijo, K. Hada, T. Furukawa, T. Itou, T. Ueno, K. Kobayashi, I. I. Mazin, H. O. Jeschke, andJ. Akimitsu: Phys. Rev. B 101 (2020), 075134.
JOUTSUKA, Tatsuya [ B class; 1300 (B), 0 (C) ] (158, 159)
— Ab Initio Calculation of High-Rate Deposition of Copper Film by Low-Pressure Chemical Vapor
Deposition with CuI on Ru Substrate— Molecular Science at Solid/Liquid Interfaces using Molecular Dynamics Simulation and Ab Initio
Calculation
1. Low-pressure chemical vapor deposition of Cu on Ru substrate using CuI: Ab initio calculations
T. Joutsuka, S. Yamauchi: Chem. Phys. Lett. 741 (2020) 137108.
JU, Shenghong [ C class; 5000 (B), 1200 (C) ] (83)
— Energy Transport in Hybrid Organic-Inorganic Thermoelectric Materials
KAGESHIMA, Hiroyuki [ C class; 500 (B), 0 (C) ] (189)— Study on structural elementary excitations at semiconductor surfaces and interfaces
1. First-principles Study of pressure and SiO-incorporation eﬀect on dynamical properties of silicon
oxide
H. Kageshima, Y. Yajima, K. Shiraishi, and T. Endoh: Jpn. J. Appl. Phys. 58 (2019) 111004(11pages).
KARIYADO, Toshikaze [ B class; 1000 (B), 0 (C) ] (331)— Manipulation of electronic states with nanostructures: model construction and its application
1. Flat band in twisted bilayer Bravais lattices
T. Kariyado and A. Vishwanath, Phys. Rev. Research 1 (2019) 033076.
KASAMATSU, Shusuke [ C class; 11000 (B), 1750 (C) ] (57, 386)
— Designing doping schemes for BaZrO3 -based ion conductors— First-principles conﬁgurational sampling of highly-doped ionic conductors
1. Insights Into Defect Arrangements in Y-Doped BaZrO3 From Large-Scale First-Principles Thermodynamic Sampling: Association, Repulsion, Percolation, and Trapping
Chemrxiv. Preprint.
KATO, Takeo [ D class; 10000 (B), 1000 (C) ] (210)— Variational Monte Carlo calculation of two-dimensional Wigner crystal under lattice commensurability
KATO, Yusuke [ C class; 5000 (B), 0 (C) ] (272)— Functional Renormalization Group Study of Quantum Spin Liquids
KAWAKAMI, Norio [ C class; 9500 (B), 1700 (C) ] (206)— Study of magnetism and superconductivity in strongly correlated quantum systems using approaches
including non-equilibrium methods— Study of magnetism topology and transport phenomena in strongly correlated quantum systems
1. Spin-caloritronic transport in hexagonal graphene nanoﬂakes
Thi. Thu Phung, Robert Peters, Andreas Honecker, Guy Trambly de Laissardiere, and Javad
Vahedi: arXiv:2003.01139.
2. Equivalence of the eﬀective non-hermitian Hamiltonians in the context of open quantum systems
and strongly-correlated electron systems
Yoshihiro Michishita and Robert Peters: arXiv:2001.09045.
3. Hubbard model on the honeycomb lattice: From static and dynamical mean-ﬁeld theories tolattice quantum Monte Carlo simulations
Marcin Raczkowski, Robert Peters, Thi. Thu Phng, Nayuta Takemori, Fakher F. Assaad, Andreas
Honecker, and Javad Vahedi: Phys. Rev. B 101 (2020) 125103.
4. Relationship between exceptional points and the Kondo eﬀect in f -electron materials

401Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

5.
6.
7.

Yoshihiro Michishita, Tsuneya Yoshida, and Robert Peters: Phys. Rev. B 101 (2020) 085122.
Chiral-symmetry protected exceptional torus in correlated nodal-line semimetals
Kazuhiro Kimura, Tsuneya Yoshida, and Norio Kawakami: Phys. Rev. B 100 (2019) 115124.
Quantum oscillations in strongly correlated topological Kondo insulators
Robert Peters, Tsuneya Yoshida, and Norio Kawakami: Phys. Rev. B 100 (2019) 085104.
Impact of the Rashba Spin Orbit Coupling on f-electron Materials
Yoshihiro Michishita and Robert Peters: Phys. Rev. B 99 (2019) 155141.

KAWAMURA, Hikaru [ C class; 11000 (B), 0 (C) ] (249)— Novel order in frustrated magnets
1. Spin ordering induced by lattice distortions in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
K. Aoyama and H. Kawamura, Phys. Rev., B 99, 1444062-(1-14) (2019)
2. Ripple state in the frustrated honeycomb-lattice antiferromagnet
T. Shimokawa and H. Kawamura, Phys. Rev. Letters 123, 057202(1-6) (2019)
3. Nature of the randomness-induced quantum spin liquids in two dimensions
H. Kawamura and K. Uematsu, J. Phys. Condens. Matter 31, 504003(1-18) (2019)
4. Randomness-induced quantum spin liquid behavior in the s=1/2 random-bond Heisenberg antiferromagnet on the pyrochlore lattice
K. Uematsu and H. Kawamura, Phys. Rev. Letters 123, 087201-(1-6) (2019)
5. Eﬀects of magnetic anisotropy on spin and thermal transport in classical antiferromagnets on
the square lattice
K. Aoyama and H. Kawamura, Phys. Rev. B 100, 144416-(1-19) (2019)
6. Multiple-q states of the J1-J2 classical honeycomb-lattice Heisenberg antiferromagnet under amagnetic ﬁeld
T. Shimokawa and H. Kawamura, Phys. Rev. B 100, 224404-(1-15) (2019)
7. Monte Carlo study of the critical properties of noncollinear Heisenberg magnets: O(3) × O(2)universality class
Y. Nagano, K. Uematsu, and H. Kawamura, Phys. Rev. B 100, 224430(1-15) (2019)
8. Monte Carlo studies of the spin-chirality decoupling in the three-dimensional Heisenberg spin glass
T. Ogawa, K. Uematsu, and H. Kawamura, Phys. Rev. B 101, 014434(1-16) (2020)
9. Spin Current as a Probe of the Z2-Vortex Topological Transition in the Classical Heisenberg
Antiferromagnet on the Triangular Lattice
K. Aoyama and H. Kawamura, Phys. Rev. Letters 124, 047202-(1-6) (2020)
KAWAMURA, Mitsuaki [ B class; 700 (B), 90 (C) ] (176)— Benchmark of density functional theory for superconductors
1. Benchmark of density functional theory for superconductors in elemental materials
M. Kawamura, Y. Hizume, and T. Ozaki Phys. Rev. B 101, (2020) 134511.
KAWASHIMA, Naoki [ E class; 39000 (B), 5450 (C) ] (239)— Tensor-Ring Decomposition Based on HOSVD and Its Appication— Variational calculation of Kitaev and related models with tensor-network representation
1. Tensor network wavefunction of S = 1 Kitaev spin liquids
Hyun-Yong Lee, Naoki Kawashima, and Yong Baek Kim:arXiv:1911.07714
2. Boundary conformal spectrum and surface critical behavior of classical spin systems:A tensor
network renormalization study
Shumpei Iino, Satoshi Morita, and Naoki Kawashima: Phys. Rev. B 101, 155418 (2020)
3. Magnetic ﬁeld induced quantum phases in a tensor network study of Kitaev magnets
Hyun-Yong Lee, Ryui Kaneko, Li Ern Chern, Tsuyoshi Okubo, Youhei Yamaji, Naoki Kawashima
and Yong Baek Kim: Nature Communications 11, 1639 (2020)
4. Abelian and non-Abelian chiral spin liquids in a compact tensor network
Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, Naoki Kawashima: Phys. Rev. B 101, 035140(2020)
5. Thermal-transport studies of kagom antiferromagnets

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6.
7.
8.

9.

Minoru Yamashita, Masatoshi Akazawa, Masaaki Shimozawa, Takasada Shibauchi, Yuji Matsuda,
Hajime Ishikawa, Takeshi Yajima, Zenji Hiroi, Migaku Oda, Hiroyuki Yoshida, Hyun-Yong Lee,
Jung Hoon Han and Naoki Kawashima: J. Phys: Condens. Matter 32, 074001(11pp) (2019)
Entropy Governed by the Absorbing State of Directed Percolation
Kenji Harada and Naoki Kawashima: Phys. Rev. Lett. 123, 090601 (2019)
Boundary Tensor Renormalization Group
Shumpei Iino, Satoshi Morita, and Naoki Kawashima: Phys. Rev. B 100, 035449 (2019)
Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, and Naoki Kawashima: Phys. Rev. Lett. 123,
087203 (2019)
Tensor-Ring Decomposition with Index-Splitting
Hyun-Yong Lee and Naoki Kawashima: J. Phys. Soc. Jpn. 89, 054003 (2020)

KITA, Takafumi [ C class; 1000 (B), 0 (C) ] ()— studying the enhancement of the thermal Hall angle in d-wave superconductors
KITAO, Akio [ C class; 5000 (B), 0 (C) ] (270)— Eﬃcient sampling simulation of the soft modes signiﬁcantly contribute to protein properties
1. Kinetic selection and relaxation of the Intrinsically Disordered Region of a Protein upon Binding.
D.P. Tran and A Kitao: J. Chem. Theory Comput, in press (2020) doi: 10.1021/acs.jctc.9b01203.
2. High pressure inhibits signaling protein binding to the ﬂagellar motor and bacterial chemotaxis
through enhanced hydration.
H. Hata, Y. Nishihara, M. Nishiyama, Y. Sowa, I. Kawagishi, A. Kitao: Sci. rep. 10 (2020) 2351.
3. Molecular dynamics simulation of proteins under high pressure: Structure, function and thermodynamics.
H. Hata, M. Nishiyama, A. Kitao: Biochimica et Biophysica Acta 1864 (2020) 7.
4. evERdock BAI: Machine-learning-guided selection of protein-protein complex structure.
K. Terayama, A. Shinobu, K. Tsuda, K. Takemura, and A. Kitao: J. Chem. Phys. 151 (2019)
215104.
5. Impact of key residues within chloroplast thioredoxin-f on recognition for reduction and oxidationof target proteins.
Y. Yokochi et. al.: J. Biol. Chem. 294 (2019) 17437.
6. Phagocytosis is mediated by two-dimensional assemblies of the F-BAR protein GAS7.
K. Hanawa-Suetsugu et. al.: Nat. Commun. 10 (2019) 10.
7. Enhancing Biomolecular Sampling with Reinforcement Learning: A Tree Search Molecular Dynamics Simulation Method.
K. Shin, D.P. Tran, K. Takemura, A. Kitao, K. Terayama, and K. Tsuda: ACS omega 4 (2019)13853.
8. Cancellation between auto-and mutual correlation contributions of protein/water dynamics interahertz time-domain spectra.
Y. Joti and A. Kitao: Biophys. Physicobiol. 16 (2019) 240.
9. More eﬃcient screening of protein-protein complex model structures for reducing the number ofcandidates.
K. Takemura and A. Kitao: Biophys. Physicobiol. 16 (2019) 295.
KOBAYASHI, Akito [ B class; 1500 (B), 200 (C) ] (228)— Spin-Charge Separation in Charge Order Phase of Organic Dirac Electron System α-(BEDT-TTF)2 I3
1. Domain wall conductivity with strong Coulomb interaction of two-dimensional massive Dirac
electrons in the organic conductor α-(BEDT-TTF)2I3
D. Ohki, Y. Omori, and A. Kobayashi, Phys. Rev. B 100, 075206 (2019).
KOBAYASHI, Katsuyoshi [ B class; 400 (B), 50 (C) ] (190)— Theoretical study on electronic properties of new nanoscale surfaces and interfaces403

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

KOBAYASHI, Nobuhiko [ C class; 4000 (B), 650 (C) ] (108)— First-principles study of quantum transport in nanostructures
1. Second highest occupied molecular orbital eﬀects on the valence band structure of organic semiconductors
Y. Kuroda, H. Ishii, S. Yoshino, N. Kobayashi, Jpn. J. Appl. Phys. 58 SIIB27 (2019).
2. Carrier transport calculations of organic semiconductors with static and dynamic disorder
H. Ishii , N. Kobayashi, and K. Hirose, Jpn. J. Appl. Physics 58, 110501 (2019).
3. Electronic Band Structure of TiN/MgO−4 × 4 and 5 × 5 Nanostructures
K. Kobayashi, H. Takaki, M. Shimono, N. Kobayashi, and K. Hirose, Jpn. J. Appl. Phys. 58
SBBH06 (2019).
4. Seebeck coeﬃcients in CuFeS2 thin ﬁlms by ﬁrst-principles calculations
H. Takaki, K. Kobayashi, M. Shimono, N. Kobayashi, K. Hirose, N. Tsujii, and T. Mori Jpn. J.
Appl. Phys. 58 SIIB01 (2019).
5. Magnetism-mediated thermoelectric performance of the Cr-doped bismuth telluride tetradymite
J. B. Vaney, S. A. Yamini, H. Takaki, K. Kobayashi, N. Kobayashi, T. Mori, Mater. Today Phys.
8 (2019) 100090.
6. Sub-molecular structural relaxation at a physisorbed interface with monolayer organic singlecrystal semiconductors
A. Yamamura, H.Fujii, H. Ogasawara, D. Nordlund, O. Takahashi, Y. Kishi, H. Ishii, N. Kobayashi,
N. Niitsu, B. Blulle, T. Okamoto, Y. Wakabayashi, S. Watanabe, and J. Takeya, Commun. Phys.
3 20 (2020)
7. Charge mobility calculation of organic semiconductors without use of experimental single-crystal
data
H. Ishii, S. Obata, N. Niitsu, S. Watanabe, H. Goto, K. Hirose, N. Kobayashi, T. Okamoto, and
J. Takeya, Sci Rep 10, 2524 (2020)
KOBAYASHI, Riki [ B class; 300 (B), 0 (C) ] (357)— Screening of substitutable non-magnetic element in rare-earth inter-metallic compounds
KOGA, Akihisa [ C class; 9500 (B), 650 (C) ] (211, 212)
— Magnetic and transport properties in double-exchange systems with quasiperiodicity— Numerical analysis for nonequilibrium dynamics in correlated electron systems with orbital degrees of
freedom
1. Majorana-mediated spin transport without spin polarization in Kitaev quantum spin liquids
T. Minakawa, Y. Murakami, A. Koga and J. Nasu: submitted to PRL.
2. Spin transport in the Quantum Spin Liquid State in the S = 1 Kitaev model: role of the fractionalized quasiparticles
A. Koga, T. Minakawa, Y. Murakami and J. Nasu: J. Phys. Soc. Jpn. 89 (2020) 033701.
3. Excitonic condensation reﬂecting electronic states in two-band Penrose-Hubbard model
K. Inayoshi, Y. Murakami and A. Koga: submitted to JPSJ.
KOMATSU, Hisato [ B class; 1100 (B), 150 (C) ] (321, 323)
— Competiton between dipolar and Dzyaloshinskii-Moriya interactions on the magnetic thin ﬁlms
— Competiton between dipolar and short-range interactions on the magnetic thin ﬁlms
1. Anisotropy-temperature phase diagram for the two-dimensional dipolar Heisenberg model withand without magnetic ﬁeld
H. Komatsu, Y. Nonomura, and M. Nishino, Phys. Rev. B 100, 094407 (2019).
KOMATSU, Yu [ C class; 2500 (B), 500 (C) ] (291)— Constructing the electronic structure database for the molecular design of pigments utilizing nearinfrared light
KOTA, Yohei [ B class; 400 (B), 0 (C) ] (193)— Analysis of magnetic properties in Cr and Mn alloys— Analysis of strain eﬀect on magnetism in chromium metals

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1.

Perpendicularly magnetized Cu2 Sb type (Mn-Cr)AlGe ﬁlms onto amorphous SiO2
T. Kubota, Y. Kota, K. Ito, R. Y. Umetsu, M. Sun, M. Mizuguchi, and K. Takanashi: Appl.
Phys. Express 12 (2019) 103002.

KOU, Sonju [ B class; 400 (B), 0 (C) ] (191)— Development of First-principles calculations method of Seebeck coeﬃcient in the framework of linear
response theory
KOURA, Akihide [ C class; 1000 (B), 0 (C) ] (167)— First principles study on static structure of glass materials
1. Guidelines for creating artiﬁcial neural network empirical interatomic potential from ﬁrst-principles
molecular dynamics data under speciﬁc conditions and its application to α-Ag2 Se
K. Shimamura, S. Fukushima, A. Koura, F. Shimojo, M. Misawa, R. K. Kalia, A. Nakano, P.
Vashishta et al.: J. Chem. Phys. 151, (2019) 124303.
2. GGA+U Molecular Dynamics Study of Structural and Dynamic Properties of Superionic Conductor Ag2 Se
S. Fukushima, M. Misawa, A. Koura, and F. Shimojo: J. Phys. Soc. Jpn. 88, (2019) 115002.
3. Thermodynamic Integration by Neural Network Potentials Based on First-principles Dynamic
Calculations
S. Fukushima, E. Ushijima, H. Kumazoe, A. Koura, F. Shimojo, K. Shimamura, M. Misawa, R.
K. Kalia, A. Nakano, and P. Vashishta: Phys. Rev. B 100, (2019) 214108.
4. コンピュータシミュレーションによる永久高密度化ガラスの構造計算
高良明英, 若林大佑, 下條冬樹: NEW GLASS 35, (2020) 12.
5. Intermediate range structure of amorphous Cu2 GeTe3 : ab initio molecular dynamics study
A. Koura, and F. Shimojo: J. Phys.: Condens. Matter 32, (2020) 244001.
6. Molecular-Dynamics Study of Thermal Conductivity of Silver Chalcogenides
S. Fukushima, A. Koura, and F. Shimojo: submitted to Phys. Status Solidi B
7. Pressure Dependence of Static Structure of Liquid V2 O5 : ab initio Molecular Dynamics Study
A. Koura, and F. Shimojo: submitted to Phys. Status Solidi B
KUMAZOE, Hiroyuki [ C class; 1000 (B), 250 (C) ] (320)— Establishment of new analysis method for extend X-ray absorption ﬁne structure with sparse modeling
KUNISADA, Yuji [ C class; 8000 (B), 0 (C) ] (72)
— Reduction of Rare Metals in Formic Acid Decomposition Catalysts and Oxygen Storage Materials
1. グラフェン上での金属原子吸着状態の理論的研究
長谷川瞬，國貞雄治，坂口紀史: 表面と真空 62 (2019) 344.
2. Extraordinarily Large Kinetic Isotope Eﬀect on Alkene Hydrogenation over Rh-based Intermetallic
Compounds
S. Furukawa, P. Yi, Y. Kunisada, K. Shimizu: Science and Technology of Advanced Materials 20(2019) 805.
3. Co-appearance of superconductivity and ferromagnetism in a Ca2 RuO4 nanoﬁlm crystal
SH. Nobukane, K. Yanagihara, Y. Kunisada, Y. Ogasawara, K. Nomura, Y. Asano, S. Tanda:
Scientiﬁc Reports 10 (2020) 3462.
KUROKI, Kazuhiko [ C class; 10500 (B), 1600 (C) ] (204)— Study on electron correlation and possible superconductivity in mixed-anion systems— Study on the possibility of superconductivity in ladder-type electronic structures constructed frommultiple anions
1. Comparative ﬁrst-principles study of antiperovskite oxides and nitrides as thermoelectric material:
multiple dirac cones, low-dimensional band dispersion, and high valley degeneracy
M. Ochi, K. Kuroki: Phys. Rev. Applied. 12 (2019) 034009.
2. Strongly enhanced superconductivity due to ﬁnite energy spin ﬂuctuations induced by an incipientband : a FLEX study on the bilayer Hubbard model with vertical and diagonal interlayer hoppings
K. Matsumoto, D. Ogura, and K. Kuroki: J. Phys. Soc. Jpn. 89 (2020) 044709.

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3.

Many-variable variational Monte-Carlo study of superconductivity in two-band Hubbard models
with an incipient band
D. Kato and K. Kuroki: Phys. Rev. Research, in press (2020) (arXiv:1912.11983)

KUSAKABE, Koichi [ C class; 2000 (B), 300 (C) ] (140)— Transport and reaction properties of nanographene
1. Spin-current control by induced electric-polarization reversal in Ni/hBN/Ni: A cross-correlationmaterial
H. Harfah, Y. Wicaksono, M.A. Majidi, and K. Kusakabe: ACS Appl. Elect. Materials, in press.
2. Interplanar stiﬀness in defect-free monocrystalline graphite
K. Kusakabe, A. Wake, A. Nagakubo, K. Murashima, M. Murakami, K. Adachi, H. Ogi: Phys.
Rev. Materials 4 (2020) 043603.
3. アルカン脱水素触媒，及びこれを用いる水素製造方法
草部浩一，高井和之，西川正浩，劉明, 特願 2019-135780.
4. Counting the Zero Modes and Magnetic Moment by Topology of a Phenalenyl-Tessellation Moleculewith Vacancies
N. Morishita, K. Kusakabe: J. Phys. Soc. Jpn. 88 (2019) 124707.
MAKINO, Takayuki [ B class; 1500 (B), 210 (C) ] (149)— Ab-initio calculation of phonon density-of-states spectra in cuprous oxides— Calculation of electron-phonon interaction in delafossite-type cuprates— Electronic structure calculation in strongly-correlated electron oxides under presence of static electric
ﬁeld
1. Temperature dependence of dielectric functions in Yb2O3 and Lu2O3 epitaxial thin ﬁlms on
sapphire (0001)
T. Makino et al.: Jpn. J. Appl. Phys. (2020) .
MASUDA, Keisuke [ B class; 600 (B), 90 (C) ] (184)— First-principles study of magnetoresistance ratios and magnetic anisotropy in magnetic tunnel junctions
1. Mechanism of strong enhancement of anomalous Nernst eﬀect in Fe by Ga substitution
H. Nakayama, K. Masuda, J. Wang, A. Miura, K. Uchida, M. Murata, and Yuya Sakuraba: Phys.
Rev. Materials 3 (2019) 114412.
2. Observation of anomalous Ettingshausen eﬀect and large transverse thermoelectric conductivity
in permanent magnets
A. Miura, H. Sepehri-Amin, K. Masuda, H. Tsuchiura, Y. Miura, R. Iguchi, Y. Sakuraba, J.
Shiomi, K. Hono, and K. Uchida: Appl. Phys. Lett. 115 (2019) 222403.
3. Contributions of magnetic structure and nitrogen to perpendicular magnetocrystalline anisotropy
in antiperovskite ϵ − Mn4 N
S. Isogami, K. Masuda, and Y. Miura: Phys. Rev. Materials 4 (2020) 014406.
4. Strain-induced enhancement of the Seebeck eﬀect in magnetic tunneling junctions via interface
resonant tunneling: Abinitio study
K. Yamamoto, K. Masuda, K. Uchida, and Y. Miura: Phys. Rev. B 101 (2020) 094430.
5. Interface-driven giant tunnel magnetoresistance in (111)-oriented junctions
K. Masuda, H. Itoh, and Y. Miura: Phys. Rev. B 101 (2020) 144404.
MATSUDA, Yasuhiro [ B,C class; 3700 (B), 640 (C) ] (227)— Estimation of the density of states using Maximum entropy method and Sparse modeling— Study on the high-ﬁeld-induced phases of low dimensional frustrated quantum spin system
MATSUKAWA, Hiroshi [ C class; 1500 (B), 400 (C) ] ()— Physics of Friction

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MATSUMOTO, Munehisa [ C,D class; 17000 (B), 1350 (C) ] (49, 51)— Ab initio optimization of the champion rare earth magnet compound (Nd R)2(Fe Co)14B (R=rare
earth)— Multiscale data assimilation between ab initio theory at ﬁnite temperatures and experiments for rareearth permanent magnets— Self-consistent analysis between miroscopic electronic structure calculations and macroscopic data
analysis for experimental measurements
1. Calculating Curie temperatures for rare-earth permanent magnets: Ab initio inspection of localized magnetic moments in d-electron ferromagnetism
Munehisa Matsumoto and Hisazumi Akai: Phys. Rev. B 101 (2020) 144402.
2. Magnetism trends in doped Ce-Cu intermetallics in the vicinity of quantum criticality: realistic
Kondo lattice models based on dynamical mean-ﬁeld theory
Munehisa Matsumoto: Phys. Rev. Materials 4 (2020) 054401.
3. (Sm,Zr)Fe12 − x Mx (M=Zr,Ti,Co) for permanent-magnet applications: Ab initio material design
integrated with experimental characterization
Munehisa Matsumoto, Takafumi Hawai, and Kanta Ono: Phys. Rev. Applied 13 (2020) 064028.
MATSUNAKA, Daisuke [ B class; 700 (B), 0 (C) ] (183)— First-principles Study of Defects of Magnesium Alloys
1. Molecular Dynamics Study of Inﬂuences of Non-Glide Stress on Slips in Magnesium
So Yoshikawa, Daisuke Matsunaka: ,Materials Transactions 61 (2019) 127-135.
2. Molecular Dynamics Simulation on Defect Nucleation from Pre-existing I1 Stacking Fault in Magnesium
S. Yoshikawa and D. Matsunaka: Computational Materials Science, 179 (2020) 109644.
MATSUSHITA, Katsuyoshi [ C class; 0 (B), 800 (C) ] (333)— Adhesion Inducing Cell Dynamics in Tissue— Numerical Study of Cell Guiding Mechanism in Cellular Tissue
1. Crowding-Boosting Polarity and Motion Order of Cells
K Matsushita, K Horibe, N Kamamoto, S Yabunaka, K Fujimoto Proceedings of the Symposiumon Simulation of Traﬃc Flow 25, 21
2. Curved surface geometry-induced topological change of an excitable planar wavefront
K Horibe, K Hironaka, K Matsushita, K Fujimoto Chaos: An Interdisciplinary Journal of Nonlinear Science 29 (9), 093120
3. Cell Motion Alignment as a Polarity Memory Eﬀect
Matsushita, K Horibe, N Kamamoto, K Fujimoto Journal of the Physical Society of Japan 88(10), 103801
MATSUSHITA, Yu-ichiro [ C class; 11500 (B), 1800 (C) ] (56)
— Identiﬁcation of interface-state defects in power semiconductors: Approach from ab-initio calculations— Relation between defect structures and electronic properties in power semiconductors: Approach fromab-initio calculations
1. Native point defects and carbon clusters in 4H-SiC: A hybrid functional study
T. Kobayashi, K. Harada, Y. Kumagai, F. Oba, and Y. Matsushita: J. Appl. Phys. 125 (2019)125701.
2. Energetics and electronic structure of native point defects in α-Ga2 O3
T. Kobayashi, T. Gake, Y. Kumagai, F. Oba, and Y. Matsushita: Appl. Phys. Expr. 12 (2019)091001.
3. Structure and energetics of carbon-related defects in SiC(0001)/SiO2 systems revealed by ﬁrstprinciples calculations: Defects in SiC, SiO2 , and just at their interface
T. Kobayashi and Y. Matsushita: J. Appl. Phys. 126 (2019) 145302.
4. Carbon dangling-bond center (carbon Pb center) at 4H-SiC(0001)/SiO2 interface
T. Umeda, T. Kobayashi, M. Sometani, H. Yano, Y. Matsushita, and S. Harada: Appl. Phys.
Lett. 116 (2020) 071604.

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MAYUMI, Koichi [ B class; 1400 (B), 180 (C) ] (303, 305)
— Study on Dynamic Mechanical Properties of Slide-Ring Gels using Coarse-Grained MD Simulations— Study on Microscopic Dynamics of Polyrotaxanes using Full-Atomistic MD Simulations
1. Sliding Dynamics of Ring on Polymer in Rotaxane: A Coarse-Grained Molecular Dynamics Simulation Study
Y. Yasuda, M. Toda, K. Mayumi, H. Yokoyama, H. Morita, K. Ito: Macromolecules, 2019, 52,
3787.
2. Molecular Dynamics of Polyrotaxane in Solution Investigated by Quasi-Elastic Neutron Scatteringand Molecular Dynamics Simulation: Sliding Motion of Rings on Polymer
Y. Yasuda, Y. Hidaka, K. Mayumi, H. Yokoyama, T. Yamada, K. Fujimoto, S. Okazaki, H.
Yokoyama, K. Ito: J. Am. Chem. Soc., 2019, 141, 9655.
MINAMITANI, Emi [ C class; 6500 (B), 450 (C) ] (79)
— Ab-initio analysis of electron-phonon interaction
1. Simulating lattice thermal conductivity in semiconducting materials using high-dimensional neuralnetwork potential
E. Minamitani, M. Ogura, S. Watanabe:Appl. Phys. Express, 12 (2019) 095001
MISAWA, Masaaki [ B class; 400 (B), 0 (C) ] ()— First-principles study on the structures and electronic properties of silicates under high pressure
MISAWA, Takahiro [ E class; 19500 (B), 2750 (C) ] ()— Numerical analysis of quantum transport phenomena in topological materials
MIURA, Yoshio [ B class; 800 (B), 100 (C) ] ()— A ﬁrst-principles calculation on ﬁnite temperature eﬀects of half-metallic ferromagnets
MIZUGUCHI, Tomoko [ C class; 1000 (B), 0 (C) ] (329)— Molecular dynamics simulations of water conﬁned in carbon structures with the reactive force ﬁeld
1. Hydrogen bond analysis of conﬁned water in mesoporous silica using the reactive force ﬁeld
T. Mizuguchi, K. Hagita, S. Fujiwara and T. Yamada: Mol. Sim. 45 (2019) 1437.
2. Icosahedral order in liquid and glassy phases of cyclohexane
T. Mizuguchi, S. Tatsumi and S. Fujiwara: Mol. Sim. in press.
MIZUKAMI, Wataru [ C class; 2500 (B), 150 (C) ] (134)— Exploration of surface reactions on model real catalyst II
1. Orbital optimized unitary coupled cluster theory for quantum computer
W. Mizukami, K. Mitarai, Y.O. Nakagawa, T. Yamamoto, T. Yan, Y.y. Ohnishi: arXiv:1910:11526(2019)MOMIDA, Hiroyoshi [ C class; 4000 (B), 650 (C) ] (106)— Electrode properties of novel lithium-ion secondary battery materials: First-principles calculations
1. First-Principles Study of Na-Ion Battery Performance and Reaction Mechanism of Tin Sulﬁde as
Negative ElectrodeH. Kotaka, H. Momida, A. Kitajou, S. Okada and T. Oguchi: Chem. Rec. 19, 811 (2019).
2. Spectral Dependence of the Third-Order Optical Susceptibility of Au Nanostructures: Experiments and First-Principles Calculations
B. Zhang, R. Sato, H. Momida, T. Ohno, M. Chundak, M. Naito, M. Yoshitake and Y. Takeda:
Phys. Rev. B 100, 035446 (2019).
3. Amorphous xNaF-FeSO4 Systems (1 ≤ x ≤ 2) with Excellent Cathode Properties for Sodium-Ion
Batteries
A. Kitajou, H. Momida, T. Yamashita, T. Oguchi and S. Okada: ACS Appl. Energy Mater. 2,5968 (2019).
4. First-Principles Study of X-Ray Absorption Spectra in NaFeSO4 F for Exploring Na-Ion Battery
Reactions408

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5.

H. Momida, A. Kitajou, S. Okada and T. Oguchi: J. Phys. Soc. Jpn. 88, 124709 (2019).
Signiﬁcant Role of Oxygen Redox Reaction with O2 -Release in Li-Excess Cation-Disordered RockSalt Cathodes Li2+2x Mn1−x Ti1−x O4 : First-Principles Calculations
M. Hamaguchi, H. Momida and T. Oguchi: Electrochim. Acta 330, 135286 (2020).

MORIKAWA, Yoshitada [ C class; 5000 (B), 750 (C) ] (95)
— First-principles Theoretical Study of Chemical Reactions in Heterogeneous Catalysts
1. Van der Waals Density Functional Study of Formic Acid Adsorption and Decomposition on
Cu(111)S. E. M. Putra, F. Muttaqien, Y. Hamamoto, K. Inagaki, I. Hamada, and Y. Morikawa: J. Chem.
Phys. 150 (2019) 154707.
2. Vibration-driven reaction of CO2 on Cu surfaces via EleyRideal-type mechanism
J. Quan, F. Muttaqien, T. Kondo, T. Kozarashi, T. Mogi, T. Imabayashi, Y. Hamamoto, K.
Inagaki, I. Hamada, Y. Morikawa, and J. Nakamura: Nature Chem. 11 (2019) 722.
3. Development of Co supported on Co‐ Al spinel catalysts from exsolution of amorphous Co‐ Aloxides for carbon dioxide reforming of methane
Y. J. Wong, M. K. Koh, N. F. Khairudin, S. Ichikawa, Y. Morikawa, and A. R. Mohamed: Chem.
Cat. Chem. 11 (2019) 5593.
4. First-principles theoretical study on carrier doping eﬀects induced by Zn vacancies in Mn-dopedin ZnSnAs2
H. Kizaki and Y. Morikawa: Jpn. J. Appl. Phys. 58 (2019) 110601.
5. Analyses of three-dimensional atomic arrangements of impurities doped in Si relating to electricalactivity by spectro-photoelectron holography
K. Tsutsui and Y. Morikawa: Jpn. J. Appl. Phys. 59 (2020) 010503.
6. Insight into Trimeric Formation of Nitric Oxide on Cu(111): A Density Functional Theory Study
T. N. Pham, Y. Hamamoto, K. Inagaki, D. N. Son, I. Hamada, and Y. Morikawa: J. Phys. Chem.
C 124 (2020) 2968.
7. Atomic and Molecular Adsorption on Single Platinum Atom at the Graphene Edge: A Density
Functional Theory Study
S. A. Wella, Y. Hamamoto, F. Iskandar, Suprijadi, Y. Morikawa, and I. Hamada: J. Chem. Phys.
152 (2020) 104707.
MORITA, Satoshi [ B class; 800 (B), 100 (C) ] (25)
— Improvement of higher-order tensor renormalization group method and its applications
MOTOME, Yukitoshi [ C class; 13500 (B), 1900 (C) ] (202)— Theoretical study of novel quantum properties induced by strong spin-orbit coupling— Theoretical study of quantum properties induced by spin-orbit coupling and electron correlation
1. Magnetic Vortex Induced by Nonmagnetic Impurity in Ferromagnets: Magnetic Multipole andToroidal around the Vacancy
S. Hayami, H. Kusunose, and Y. Motome, J. Phys. Soc. Jpn. 88, 063702 (2019).
2. Antiferromagnetic Kitaev interaction in f-electron based honeycomb magnets
S.-H. Jang, R. Sano, Y. Kato, and Y. Motome, Phys. Rev. B 99, 241106(R) (2019).
3. Nonequilibrium Majorana dynamics by quenching a magnetic ﬁeld in Kitaev spin liquids
J. Nasu and Y. Motome, Phys. Rev. Research 1, 033007 (2019).
4. Hunting Majorana Fermions in Kitaev Magnets
Y. Motome and J. Nasu, J. Phys. Soc. Jpn. 89, 012002 (2020).
5. Chiral spin liquids with crystalline Z2 gauge order in a three-dimensional Kitaev model
P. A. Mishchenko, Y. Kato, K. O’Brien, T. A. Bojesen, T. Eschmann, M. Hermanns, S. Trebst,
and Y. Motome, Phys. Rev. B 101, 045118 (2020).
6. The range of non-Kitaev terms and fractional particles in α-RuCl3
Y. Wang, G. B. Osterhoudt, Y. Tian, P. Lampen-Kelley, A. Banerjee, T. Goldstein, J. Yan, J.
Knolle, H. Ji, J. Cava, J. Nasu, Y. Motome, S. Nagler, D. Mandrus, and K. S. Burch, npj Quant.
Mat. 5, 14 (2020).
7. Majorana-magnon crossover by a magnetic ﬁeld in the Kitaev model: Continuous-time quantum409

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8.
9.

Monte Carlo study
J. Yoshitake, J. Nasu, Y. Kato, and Y. Motome, Phys. Rev. B 101, 100408(R) (2020).
Antiferromagnetic Kitaev interactions in polar spin-orbit Mott insulators
Y. Sugita, Y. Kato, and Y. Motome, Phys. Rev. B 101, 100410(R) (2020).
Spin-current diode with a monoaxial chiral magnet
S.-H. Jang, R. Sano, Y. Kato, and Y. Motome, preprint (arXiv:1912.03422), submitted to Phys.
Rev. Materials

MURAGUCHI, Masakazu [ B class; 600 (B), 80 (C) ] (185)— Study on carrier dynamics in nano scale semiconductor devices with machine learning
MURAI, Naoki [ B class; 900 (B), 100 (C) ] (327)— Lattice dynamics investigation of a charge-density-wave phase in transition metal chalcogenides
MURASHIMA, Takahiro [ E class; 8500 (B), 2100 (C) ] (250)— Multiscale analysis of polymeric ﬂuids and solids
1. Coupling Finite Element Method with Large Scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) for Hierarchical Multiscale Simulations
T. Murashima, S. Urata, S. Li: Euro. Phys. J. B 92 (2019) 211.
2. ミクロスケールとマクロスケールのシミュレーション連成による高分子材料系のマルチスケールシ
ミュレーション
村島隆浩: CICSJ Bulletin (日本化学情報化学部会誌) 37 (2019) 87.
3. Multiscale Modeling of Plasticity in Amorphous & Polymeric Materials
S. Li, S. Urata, T. Murashima: IACM Express. 46 (2020) 10.
NADA, Hiroki [ C class; 0 (B), 750 (C) ] (340)— Construction of A New Method for Analysis of Crystallization Mechanism from Amorphous Precursor
Using Molecular Dynamics Simulation Method and Unsupervised Machine Learning
1. Shock Growth of Ice Crystals Near Equilibrium Melting Pressure Under Dynamic Compression
Y.-J. Kim, Y.-H. Lee, S. Lee, H. Nada and G. W. Lee: Proc. Natl. Acad. Sci. U.S.A., 116 (2019)8679.
2. Anisotropy in Stable Conformations of Hydroxylate Ions Between the 001 and 110 Planes of TiO2
Rutile Crystals for Glycolate, Lactate, and 2-Hydroxybutyrate Ions Studied by Metadynamics
MethodH. Nada, M. Kobayashi and M. Kakihana: ACS Omega, 4 (2019) 11014.
3. Transport Mechanisms of Water Molecules and Ions in Sub-Nano Channels of Nanostructured
Water Treatment Liquid-Crystalline Membranes: A Molecular Dynamics Simulation Study
H. Nada, T. Sakamoto, M. Henmi, T. Ogawa, M. Kimura and T. Kato: Environ. Sci.: Water Res.
& Technol., 6 (2020) 604.
4. Pathways for the Formation of Ice Polymorphs from Water Predicted by a Metadynamics Method
H. Nada: Sci. Rep., 10 (2020) 4708.
NAKAGAWA, Naoko [ C class; 3500 (B), 600 (C) ] (286)— Macroscopic properties characterized by an extended thermodynamic functions to nonequilibrium
1. Global thermodynamics for heat conduction systems
N. Nakagawa and S.-i. Sasa: J. Stat. Phys. 177 (2019) 825.
2. Multiplicative Langevin Equation to Reproduce Long-time Properties of Nonequilibrium Brownian
MotionAtsumasa Seya, Tatsuya Aoyagi, Masato Itami, Yohei Nakayama and Naoko Nakagawa: J. Stat.
Mech. 2020 (2020) 013201
NAKAHARA, Akio [ B class; 700 (B), 90 (C) ] (337)— Transition in the memory eﬀect of paste

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NAKAMURA, Kazuma [ C,D class; 8500 (B), 0 (C) ] (66, 68)— Ab initio calculation for thermodynamic phase diagram— Ab initio calculations for Sr2IrO4 and Ca5Ir3O12— Ab initio phonon calculation for Ca5Ir3O12
1. GW calculation of plasmon excitations in the quasi-one-dimensional organic compound (TMTSF)2PF6
Kazuma Nakamura, Shiro Sakai, Ryotaro Arita, and Kazuhiko Kuroki: Physical Review B 88
(2013) 125128.
2. Eﬀect of Electron-Phonon Interactions on Orbital Fluctuations in Iron-Based Superconductors
Yusuke Nomura, Kazuma Nakamura, and Ryotaro Arita: Phys. Rev. Lett. 112 (2014) 027002.
3. Ab initio GW plus cumulant calculation for isolated band systems: Application to organic conductor (TMTSF)2PF6 and transition-metal oxide
Kazuma Nakamura, Yoshiro Nohara, Yoshihide Yoshimoto, and Yusuke Nomura: Phys. Rev. B
93 (2016) 085124.
4. Large enhancement of superconducting transition temperature in single-element superconducting
rhenium by shear strain
M. Mito, H. Matsui, K. Tsuruta, T. Yamaguchi, K. Nakamura, H. Deguchi, N. Shirakawa, H.
Adachi, T. Yamasaki, H. Iwaoka, Y. Ikoma, and Z. Horita: Scientiﬁc reports 6, (2016) 36337.
5. Uniaxial strain eﬀects on superconducting transition in Re-doped Hg-1223 cuprate superconductors
M. Mito, K. Ogata, H. Goto, K. Tsuruta, K. Nakamura, H. Deguchi, T. Horide, K. Matsumoto,T. Tajiri, H. Hara, T. Ozaki, H. Takeya, and Y. Takano: Phys. Rev. B 95, (2017) 064503.
6. Nonlinear Conductivity of Geometrically Frustrated Iridate Ca5Ir3O12
K. Matsuhira, K. Nakamura, Y. Yasukuni, Y. Yoshimoto, D. Hirai, Z. Hiroi: J. Phys. Soc. Jpn.
87, (2018) 013703.
7. Hydrostatic pressure eﬀects on superconducting transition of nanostructured niobium highly
strained by high-pressure torsion
M. Mito, Y. Kitamura, T. Tajiri, K. Nakamura, R. Shiraishi, K. Ogata, H. Deguchi, T. Yamaguchi,
N. Takeshita, T. Nishizaki, K. Edalati, Z. Horita: J. Appl. Phys. 125, (2019) 125901.
8. Hydrostatic Compression Eﬀects on Fifth-Group Element Superconductors V, Nb, and Ta Subjected to High-Pressure Torsion
M. Mito, S. Shigeoka, H. Kondo, N. Noumi, Y. Kitamura, K. Irie, K. Nakamura, S. Takagi, H.
Deguchi, T. Tajiri, M. Ishizuka, T. Nishizaki, K. Edalati, Z. Horita: Mater. Trans. (Overview),
60, (2019) 1472-1483.
9. Anisotropic compression eﬀects on nanocrystalline crystals of nickel oxide
M. Mito, T. Tajiri, S. Saisho, H. Deguch, A. Kohno, K. Nakamura: Journal of Magnetism andMagnetic Materials 489, (2019) 165407.
10. Harmonic voltage response to AC current in the nonlinear conductivity of iridium oxide Ca5Ir3O12
H. Hanate, K. Nakamura, K. Matsuhira: J. Magn. Magn. Mater. 498, (2020) 166203.
11. Formation of a two-dimensional single-component correlated electron system and band engineeringin the nickelate superconductor NdNiO2
Y. Nomura, M. Hirayama, T. Tadano, Y. Yoshimoto, K. Nakamura, R. Arita: Phys. Rev. B 100,
(2019) 205138(1-11). [Editors’ Suggestion]
12. Raman Scattering Investigation of Structural Transition in Ca5Ir3O12
T. Hasegawa, W. Yoshida, K. Nakamura, N. Ogita, K. Matsuhira: J. Phys. Soc. Jpn 89 (2020)
054602/1-11.
13. Study of Phonon Dispersion of Iridium Oxide Ca5Ir3O12 with Strong Spin?Orbit Interaction
H. Hanate, T. Hasegawa, S. Tsutsui, K. Nakamura, Y. Yoshimoto, N. Kishigami, S. Haneta, K.
Matsuhira1: J. Phys. Soc. Jpn 89 (2020) 053601/1-5.
NAKANO, Hiroki [ C class; 4000 (B), 1050 (C) ] (268)— Numerical study on low-energy states of quantum spin systems
1. Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior
H. Nakano, N. Todoroki, and T. Sakai: J. Phys. Soc. Jpn. 88 (2019) 114702.
2. From kagome strip to kagome lattice: Realizations of frustrated S = 1/2 antiferromagnets in
Ti(III) ﬂuorides

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3.

H. O. Jeschke, H. Nakano, and T. Sakai: Phys. Rev. B 99 (2019) 140410(R).
Two magnetization plateaus in the kagome ﬂuoride Cs2 LiTi3 F12
R. Shirakami, H. Ueda, H. O. Jeschke, H. Nakano, S. Kobayashi , A. Matsuo, T. Sakai, N.
Katayama, H. Sawa, K. Kindo, C. Michioka, and K. Yoshimura: Phys. Rev. B 100 (2019)174401.

NAKAYAMA, Takashi [ C class; 5000 (B), 800 (C) ] (92)
— First-principles study on physics of gap-state control at metal/semiconductor interfaces
1. Eﬀect of electric ﬁeld on formation energies of point defects around metal/SiC and metal/GaN
interfaces: First-principles study
R. Nagasawa, T. Nakayama: Jpn. J. Appl. Phys. 58 (2019) 091006.
2. Origin of Fermi-level depinning at TiN/Ge(001) interfaces: ﬁrst-principles study
T. Nishimoto, T. Nakayama: Jpn. J. Appl. Phys. 58 (2019) 061007.
3. Origin of Fermi-level depinning at metal/Ge interfaces: ﬁrst-principles study on eﬀect of segregation
T. Nishimoto, T. Nakayama: Jpn. J. Appl. Phys. 58 (2019) SIIB11.
4. Resonance-enhanced tunneling current through Si-p/n junction with additional dopants; theoretical study
S. Cho, S. Iizuka, T. Nakayama: Jpn. J. Appl. Phys. 58 (2019) 061004.
5. Theoretical studies on the switching mechanism of VMCO memories
T. Nakanishi, K. Chokawa, M. Araidai, T. Nakayama, K. Shiraishi: Microelectronic Engineering
215 (2019) 110997.
NASU, Joji [ C class; 3500 (B), 1500 (C) ] (226)— Magnetic state of Kitaev spin liquid under time-dependent ﬁeld
— Time evolution by magnetic-ﬁeld quench in Kitaev spin liquid
1. Low temperature properties in the Bilayer Kitaev model
H. Tomishige, J. Nasu, A. Koga: Phys. Rev. B 99, 174424 (2019).
2. Ferromagnetic instability for the single-band Hubbard model in the strong-coupling regime
Y. Kamogawa, J. Nasu, and A. Koga: Phys. Rev. B 99, 235107 (2019).
3. Residual Entropy and Spin Fractionalizations in the Mixed-Spin Kitaev Model
A. Koga and J. Nasu: Phys. Rev. B 100, 100404(R) (2019).
4. Nonequilibrium Majorana Dynamics by Quenching a Magnetic Field in Kitaev Spin Liquids
J. Nasu, and Y. Motome: Phys. Rev. Research 1, 033007 (2019).
5. Hunting Majorana Fermions in Kitaev Magnets
Y. Motome and J. Nasu: J. Phys. Soc. Jpn. 89, 012002 (2020).
6. Two-step gap opening across the quantum critical point in the Kitaev honeycomb magnet α-RuCl3
Y. Nagai, T. Jinno, Y. Yoshitake, J. Nasu, Y. Motome, M. Itoh, and Y. Shimizu: Phys. Rev. B
101, 020414(R) (2020).
7. Spin Transport in the Quantum Spin Liquid State in the S = 1 Kitaev Model: Role of the
Fractionalized Quasiparticles
A. Koga, T. Minakawa, Y. Murakami, and J. Nasu: J. Phys. Soc. Jpn. 89, 033701 (2020).
8. The range of non-Kitaev terms and fractional particles in α-RuCl3
Y. Wang, G. B. Osterhoudt, Y. Tian, P. Lampen-Kelley, A. Banerjee, T. Goldstein, J. Yan, J.
Knolle, H. Ji, R. J. Cava, J. Nasu, Y. Motome, S. Nagler, D. Mandrus, and K. S. Burch: npj
Quantum Materials 5, 14 (2020).
9. Majorana-Magnon Crossover by a Magnetic Field in the Kitaev Model: Continuous-Time Quantum Monte Carlo Study
J. Yoshitake, J. Nasu, Y. Kato, and Y. Motome: Phys. Rev. B 101, 100408(R) (2020).
NISHIDATE, Kazume [ C class; 3000 (B), 0 (C) ] (131)— Computational physics and chemistry approach to develop the artiﬁcial photosynthesis and fuel cell
catalysts
1. Electronic Properties and Crystal Structures of Double-Perovskites, Ba2 BiIII BiV O6 , Ba2 PrBiO6 ,and Ba2 PrSbO6 : First-principles study

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K. Nishidate et al.: submitted.
NISHIGUCHI, Kazutaka [ B class; 700 (B), 0 (C) ] (342)— Theoretical study for superconductivity in superstructured strongly correlated materials with twoparticle self-consistent approach
1. Possible Superconductivity Induced by a Large Spin-Orbit Coupling in Carrier Doped Iridium
Oxide Insulators: A Weak Coupling Approach
Kazutaka Nishiguchi, Tomonori Shirakawa, Hiroshi Watanabe, Ryotaro Arita, and Seiji Yunoki:
J. Phys. Soc. Jpn. 88 (2019) 094701
NISHINO, Masamichi [ B class; 700 (B), 90 (C) ] (336)— Elucidation of coercivity mechanism by statistical physical approaches
1. Nontrivial temperature dependence of ferromagnetic resonance frequency for spin reorientationtransitions
M. Nishino, and S. Miyashita: Phys. Rev. B 100 (2019) 020403(R).
2. Multistep spin-crossover transitions induced by the interplay between short- and long-range interactions with frustration on a triangular lattice
M. Nishino, C. Enachescu, and S. Miyashita:Phys. Rev. B 100 (2019) 134414
3. Anisotropy-temperature phase diagram for the two-dimensional dipolar Heisenberg model withand without magnetic ﬁeld
H. Komatsu, Y. Nonomura, and M. Nishino: Phys. Rev. B 100, (2019) 094407
NOGUCHI, Hiroshi [ C class; 11000 (B), 1800 (C) ] (243)— structure formation of biomembrane
1. Shape transition from elliptical to cylindrical membrane tubes induced by chiral crescent-shaped
protein rods
H. Noguchi: Sci. Rep. 9, 11721 (2019).
2. Cup-to-vesicle transition of a ﬂuid membrane with spontaneous curvature
H. Noguchi: J. Chem. Phys. 51, 094903 (2019).
3. Detachment of ﬂuid membrane from substrate and vesiculation
H. Noguchi: Soft Matter 15, 8741 (2019).
4. Curvature induction and sensing of the F-BAR protein Pacsin1 on lipid membranes via molecular
dynamics simulations
M. I. Mahmood, H. Noguchi, and K. Okazaki: Sci. Rep. 9, 14557 (2019).
5. Eﬀects of Cavitation on Karman Vortex Behind Circular-Cylinder Arrays: A Molecular Dynamics
Study
Y. Asano, H. Watanabe, and H. Noguchi: J. Chem. Phys. 152, 034501 (2020).
6. 分子動力学計算による複雑流体中のカルマン渦の解析
浅野 優太, 渡辺 宙志, 野口 博司: 分子シミュレーション研究会会誌 アンサンブル 22, 157 (2020).
NOGUCHI, Yoshifumi [ C class; 3500 (B), 600 (C) ] (112)— GW method without GPP model
1. Photoabsorption Spectra of Aqueous Oxyluciferin Anions Elucidated by Explicit Quantum Solvent
Y. Noguchi, M. Hiyama, M. Shiga, H. Akiyama, and O. Sugino: J. Chem. Theory Compt., 15(2019) 5474.
NOMURA, Yusuke [ C class; 9500 (B), 1600 (C) ] (207, 209)
— Study on frustrated magnetism using machine learning— Study on metal-insulator transition in nickel oxides
1. Strong-coupling formula for momentum-dependent susceptibilities in dynamical mean-ﬁeld theory
Junya Otsuki, Kazuyoshi Yoshimi, Hiroshi Shinaoka, and Yusuke Nomura: Phys. Rev. B 99
(2019) 165134.
2. Ab initio derivation of an eﬀective Hamiltonian for the La2CuO4/La1.55Sr0.45CuO4 heterostructure
Terumasa Tadano, Yusuke Nomura, and Masatoshi Imada: Phys. Rev. B 99 (2019) 155148.

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3.

4.
5.

Formation of a two-dimensional single-component correlated electron system and band engineering in the nickelate superconductor NdNiO2Yusuke Nomura, Motoaki Hirayama, Terumasa Tadano, Yoshihide Yoshimoto, Kazuma Nakamura, and Ryotaro Arita: Phys. Rev. B 100 (2019) 205138.
Wannier90 as a community code: new features and applications
Giovanni Pizzi et. al.: J. Phys.: Condens. Matter 32 (2020) 165902.
Materials design of dynamically stable d9 layered nickelates
Motoaki Hirayama, Terumasa Tadano, Yusuke Nomura, and Ryotaro Arita: Phys. Rev. B 101(2020) 075107.

NONOMURA, Yoshihiko [ B,C class; 2700 (B), 490 (C) ] (288, 289)
— Generalization of temperature scaling in early-time nonequilibrium relaxation— Uniﬁed understanding of early-time nonequilibrium relaxation in Monte Carlo simulations
NOZAWA, Kazuki [ C class; 1000 (B), 100 (C) ] (162)— Atomic and electronic structures of intermetallic compound catalysts
OBATA, Masao [ B,C class; 1800 (B), 100 (C) ] (145)— Analysis on atomic and magnetic structure in magnetic molecular complex crystal and interface andinvestigation of external electric and magnetic ﬁeld eﬀect
1. Noncollinear magnetic structure with spin-dependent van der Waals density functional approach:β-phase solid oxygen
M. Christivana, M. Obata, and T. Oda: J. Phys. Soc. Jpn. 88 (2019) 104601
2. Density Functional Approach under External Magnetic Field
A. R. Rio, I. Pardede,A. M. Gani, M. Christivana, M. Obata, T. Oda: J. Phys. Soc. Jpn. 89,(2020) 035002
ODA, Tatsuki [ E class; 25500 (B), 2650 (C) ] (47)
— Analyses on electronic structure and magnetic property in high-performance spintronics and magnetic
materials
1. Noncollinear magnetic structure with spin-dependent van der Waals density functional approach:β-phase solid oxygen
Mega Christivana, Masao Obata, and Tatsuki Oda: Journal of the Physical Society of Japan, 88(2019) 104601.
2. Large nonvolatile control of interfacial magnetic anisotropy in CoPt by a ferroelectric ZnO-basedtunneling barrier
Muftah Al-Mahdawi, Mohamed Belmoubarik, Masao Obata, Daiki Yoshikawa, Hideyuki Sato,
Tomohiro Nozaki, Tatsuki Oda, Masashi Sahashi: Phys. Rev. B,100 (2019) 054423.
3. Anatomy of large perpendicular magnetic anisotropy in free-standing Co/Ni (111) multilayer,
Journal of Magnetism and Magnetic Materials
Indra Pardede, Daiki Yoshikawa, Tomosato Kanagawa, Nurul Ikhsan, Itsuki Murata, Masao
Obata, Tatsuki Oda: Journal of Magnetism and Magnetic Materials 500(2020)166357.
4. Density functional approach under external magnetic ﬁeld
Afrioni Roma Rio, Indra Pardede, Achmad Maulana Gani, Mega Christivana, Masao Obata, andTatsuki Oda: Journal of the Physical Society of Japan, 89,(2020) 035002.
5. Finite electric-ﬁeld approach to evaluate the vertex correction for the screened Coulomb interactionin the quasiparticle self-consistent GW method
Hirofumi Sakakibara, Takao Kotani, Masao Obata, and Tatsuki Oda: submitted to PhysicalReview B.
OHGOE, Takahiro [ C class; 4500 (B), 700 (C) ] (225)— Development and applications of continuous-time quantum Monte Carlo method in the thermodynamic
limit

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OHMURA, Satoshi [ B,C class; 3200 (B), 0 (C) ] (122, 123)
— Ab initio molecular dynamics study of stability of artiﬁcial retina molecule— Ab initio molecular dynamics study of structural properties and immiscibility in liquid Fe-Si-O mixtures under high pressure
1. Selective Reduction Mechanism of Graphene Oxide Driven by the Photon Mode versus the Thermal Mode
M. Hada, K. Miyata, S. Ohmura, Y. Arashida, K. Ichiyanagi, I. Katayama, T. Suzuki, W. Chen,
S. Mizote, T. Sawa, T. Yokoya, T. Seki, J. Matsuo, T. Tokunaga, C. Itoh, K. Tsuruta, R. Fukaya,
S. Nozawa, S. Adachi, J. Takeda, K. Onda, S. Koshihara, Y. Hayashi, Y. Nishina: ACS NANO.
13 2019) 10103.
2. 共有結合にとらわれた原子が液体中でどのように動くのか――共有結合性液体の高圧物性
大村訓史, 下條冬樹, 土屋卓久: 日本物理学会誌, 74 (2019) 621.
3. Structures of liquid iron-light-element mixtures under high pressure
S. Ohmura, T. Tsuchiya, and F. Shimojo: Physica Status Solidi B. in press
OHNISHI, Masato [ C class; 4500 (B), 700 (C) ] (98)
— Analysis of Thermoelectric Properties of Clathrate Compounds with Ab Initio Calculations
1. Enhancing thermal boundary conductance of graphite- metal interface by triazine-based molecularbonding
Aun Ota, Masato Ohnishi, Hisayoshi Oshima, Hisayoshi, Takuma Shiga, Takashi Kodama, Junichiro Shiomi :ACS Applied Materials & Interfaces, 11, 37295-37301 (2019).
2. Spectral control of thermal boundary conductance between copper and carbon crystals by selfassembled monolayers
Shih-Wei Hung, Shiqian Hu, Junichiro Shiomi: ACS Applied Electronic Materials, 1, 2594-2601(2019).
3. Disorder Limits the Coherent Phonon Transport in Two- Dimensional Phononic Crystal Structure
Shiqian Hu, Zhongwei Zhang, Pengfei Jiang, Weijun Ren, Cuiqian Yu, Junichiro Shiomi, Jie Chen:
Nanoscale, 11, 11839-11846 (2019).
OHSAWA, Kazuhito [ C class; 1000 (B), 0 (C) ] (165)— Study of interaction between radiation damage and interstitial atom
OHTO, Tatsuhiko [ C class; 9500 (B), 0 (C) ] (60, 61)— First-principles molecular dynamics simulation of electron-doped graphene/water interfaces— First-principles molecular dynamics simulation of the water/air interface using hybrid functionals
1. Hydrogen-Bonds and Molecular Orientations of Supramolecular Structure between Barbituric
Acid and Melamine Derivative at the Air/Water Interface Revealed by Heterodyne-Detected Vibrational Sum Frequency Generation Spectroscopy
Masanari Okuno, Shuhei Yamada, Tatsuhiko Ohto, Hirokazu Tada, Waka Nakanishi, Katsuhiko
Ariga, and Taka-aki Ishibashi: J. Phys. Chem. Lett. 11, 2422 (2020).
2. Mechanical switching of current-voltage characteristics in spiropyran single-molecule junctions
Takashi Tamaki, Keigo Minode, Yuichi Numai, Tatsuhiko Ohto, Ryo Yamada, Hiroshi Masai,
Hirokazu Tada, and Jun Terao: Nanoscale, in press.
3. Molecular Structure and Modeling of Water-Air and Ice-Air Interfaces Monitored by Sum-Frequency
Generation
Fujie Tang, Tatsuhiko Ohto, Shumei Sun, Jeremy Rouxel, Sho Imoto, Ellen H. G. Backus, Shaul
Mukamel, Mischa Bonn, and Yuki Nagata: Chem. Rev. in press.
4. Eﬀect of Graphene Encapsulation of NiMo Alloys on Oxygen Evolution Reaction
Samuel Jeong, Kailong Hu, Tatsuhiko Ohto, Yuki Nagata, Hideki Masuda, Jun-ichi Fujita, andYoshikazu Ito: ACS Catal. 10, 792 (2020).
5. Three Sites Molecular Orbital Controlled Single-Molecule Rectiﬁer based on Perpendicularly
Linked Porphyrin-Imide Dyads
Murni Handayani, Hirofumi Tanaka, Shinichi Katayose, Tatsuhiko Ohto, Zhijin Chen, Ryo Yamada, Hirokazu Tada, and Takuji Ogawa: Nanoscale, 11, 22724 (2019).
6. Eﬀects of cis-trans Conformation Between Thiophene Rings on Conductance of Oligothiophenes

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Tatsuhiko Ohto, Takuya Inoue, Helen Stewart, Yuichi Numai, Yoshio Aso, Yutaka Ie, Ryo Yamada,and Hirokazu Tada: J. Phys. Chem. Lett. 10, 5292 (2019).
7. Accessing the Accuracy of Density Functional Theory through Structure and Dynamics of theWater-Air Interface
Tatsuhiko Ohto, Mayank Dodia, Jianhang Xu, Sho Imoto, Fujie Tang, Frederik Zysk, Thomas D.
Kuhne, Yasuteru Shigeta, Mischa Bonn, Xifan Wu, and Yuki Nagata: J. Phys. Chem. Lett. 10,4914 (2019).
8. Impact of intermolecular vibrational coupling eﬀects on the sum-frequency generation spectra of
the water/air interface
Naveen Kumar Kaliannan, Andres Henao Aristizabal, Hendrik Wiebeler, Frederik Zysk, TatsuhikoOhto, Yuki Nagata, and Thomas D. Kuhne: Mol. Phys. in press.
9. Highly Planar and Completely Insulated Oligothiophenes: Eﬀects of π-Conjugation on Hopping
Charge Transport
Yutaka Ie, Yuji Okamoto, Takuya Inoue, Saori Tone, Takuji Seo, Yasushi Honda, Shoji Tanaka,
See Kei Lee, Tatsuhiko Ohto, Ryo Yamada, Hirokazu Tada, and Yoshio Aso: J. Phys. Chem.
Lett. 10, 3197 (2019).
10. Structure and Dynamics of Water at the Water?Air Interface Using First Principles Molecular
Dynamics Simulations II: Non-Local vs Empirical van der Waals Corrections
Mayank Dodia, Tatsuhiko Ohto, Sho Imoto, and Yuki Nagata: J. Chem. Theory Comput. 15,3836 (2019).
11. Chemical dopants on edge of holey graphene accelerate electrochemical hydrogen evolution reaction
Akichika Kumatani, Chiho Miura, Hirotaka Kuramochi, Tatsuhiko Ohto, Mitsuru Wakisaka, Yuki
Nagata, Hiroki Ida, Yasufumi Takahashi, Kailong Hu, Samuel Jeong, Jun-ichi Fujita, Tomokazu
Matsue, Yoshikazu Ito: Adv. Sci. 6, 1900119 (2019).
OHTSUKI, Tomi [ C class; 4500 (B), 750 (C) ] (267)— Wave function analyses in disordered electron systems
1. Ballistic transport in disordered Dirac and Weyl semimetals
K. Kobayashi, M. Wada, T. Ohtsuki: arXiv:2003.01929
2. Drawing Phase Diagrams of Random Quantum Systems by Deep Learning the Wave Functions
T. Ohtsuki, T. Mano: Journal of the Physical Society of Japan 89, 022001 (2020)
3. Critical behavior of Anderson transitions in three-dimensional orthogonal classes with particlehole symmetries
X. Luo, B. Xu, T. Ohtsuki, R. Shindou: Physical Review B 101, 020202(R), (2020)
4. Application of Convolutional Neural Network to Quantum Percolation in Topological Insulators
T. Mano, T. Ohtsuki: Journal of the Physical Society of Japan 88, 123704 (2019)
5. Multifractality and the distribution of the Kondo temperature at the Anderson transition
K. Slevin, S. Kettemann, T. Ohtsuki: The European Physical Journal B 92, 281, (2019)
OKAMOTO, Yuko [ C,E class; 2000 (B), 0 (C) ] (353)— Study on complex systems by generalized-ensemble algorithms— Study on phase transitions of Lennard-Jones ﬂuid systems by generalized-ensemble algorithms
1. Eﬃcient simulation protocol for determining the density of states: Combination of replica-exchange
Wang-Landau method and multicanonical replica-exchange method
T. Hayashi and Y. Okamoto: Phys. Rev. E 100 (2019) 043304.
2. Analysis of liquids, gases, and supercritical ﬂuids by a two-dimensional replica-exchange Monte
Carlo method in temperature and chemical potential space
D. Matsubara and Y. Okamoto: J. Chem. Phys. 152 (2020) 194108.
OKITSU, Kouhei [ C class; 1500 (B), 0 (C) ] (307)— Study on an X-ray n-beam method to solve protein crystal structure— Study on crystal structure analysis using the X-ray multiple-beam diﬀraction theory
1. Experimentally obtained and computer-simulated X-ray asymmetric eight-beam pinhole topographs
for a silicon crystal

416

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2.

3.

K. Okitsu, Y. Imai, Y. Yoda and Y. Ueji: Acta Cryst. A75 (2019) 474-482. https://doi.org/10.1107/S205327331900
Experimentally obtained and computer-simulated X-ray non-coplanar 18-beam pinhole topographs
for a silicon crystal
K. Okitsu, Y. Imai and Y. Yoda: Acta Cryst. A75 (2019) 483-488. https://doi.org/10.1107/S2053273319002936.
X 線多波 (n 波) 動力学理論とその数値解法および放射光実験による検証 (X-ray n-beam dynamical
diﬀraction theories, numerical method to solve them and experimental veriﬁcation)
沖津康平: 日本結晶学会誌 33 (2020) K. Okitsu: J. Jpn. Soc. Synchrotron Rad. Res. 33 (2020)
61-80 [Invited].

OKUBO, Tsuyoshi [ C class; 5500 (B), 800 (C) ] (259)— Novel phases and dynamics in frustrated spin systems
1. Anisotropic Tensor Renormalization GroupD. Adachi, T. Okubo and S. Todo: arXiv:1906.02007.
2. Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
H.-Y. Lee, R. Kaneko, T. Okubo and N. Kawashima: Phys. Rev. Lett. 123 (2019) 087203.
3. Multiple–q states of the J1 –J2 classical honeycomb-lattice Heisenberg antiferromagnet under magnetic ﬁelds
T. Shimokawa, T. Okubo and H. Kawamura: Phys. Rev. B 100 (2019) 224404.
4. Abelian and Non-Abelian Chiral Spin Liquids in a Compact Tensor Network Representation
H.-Y. Lee, R. Kaneko, T. Okubo and N. Kawashima: Phys. Rev. B 101 (2020) 035140.
5. Magnetic-ﬁeld Induced Quantum Phases in Tensor Network Study of Kitaev Magnets
H.-Y. Lee, R. Kaneko, L.-E. Chern, T. Okubo, Y. Yamaji, N. Kawashima, and Y.-B. Kim: Nat.
Commun. 11 (2020) 1639.
OKUMURA, Hisashi [ C class; 11000 (B), 0 (C) ] (248)— Aggregation process of full-length amyloid-beta peptides studied by molecular dynamics simulations
1. Conformational change of amyloid-β 40 in associated with binding to GM1-glycan cluster
Y. Tachi, Y. Okamoto, and H. Okumura: Sci. Rep. 9 (2019) 6853 (11 pages).
2. Dynamic views of the Fc region of immunoglobulin G provided by experimental and computational
observations
S. Yanaka, R. Yogo, R. Inoue, M. Sugiyama, S. G. Itoh, H. Okumura, Y. Miyanoiri, H. Yagi, T.
Satoh, T. Yamaguchi, and K. Kato: Antibodies 8 (2019) 39 (13pages).
3. Replica sub-permutation method for molecular dynamics and Monte Carlo simulations
M. Yamauchi and H. Okumura: J. Comput. Chem. 40 (2019) 2694-2711.
4. Structural characterization of HypX responsible for CO biosynthesis in the maturation of NiFehydrogenase
N. Muraki, K. Ishii, S. Uchiyama, S. G. Itoh, H. Okumura, S. Aono: Commun. Biol. 2 (2019)385 (12 pages).
5. Molecular dynamics simulations of amyloid-β(16-22) peptide aggregation at air-water interfaces
H. Okumura and S. G. Itoh: J. Chem. Phys. 151 (2020) 095101 (12 pages).
ONISHI, Hiroaki [ C class; 2000 (B), 0 (C) ] (299)— Spin multipole dynamics and spin transport in frustrated magnets
1. Magnetic excitations and transport properties in frustrated ferromagnetic chain
H. Onishi, J. Magn. Magn. Mater. 479, 88 (2019).
ONO, Shota [ B class; 1200 (B), 170 (C) ] (313, 314)
— Femtosecond luminescence dynamics of metals— Ultrafast relaxation of inhomogeneous electron distribution around the Dirac cone in graphene
1. Ultrafast photoluminescence in metals: Theory and its application to silver
S. Ono and T. Suemoto: submitted to Phys. Rev. B
ONO, Tomoya [ C class; 8500 (B), 750 (C) ] (62)
— Development of ﬁrst-principles electronic-structure and transport calculation code RSPACE and simulations for device

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1.

2.
3.
4.

Highly Reproducible Formation of a Polymer Single-Molecule Junction for a Well-Deﬁned Current
Signal
T. Harashima, Y. Hasegawa, S. Kaneko, M. Kiguchi, T. Ono, and T. Nishino: Angewandte Chem.
Int. Ed. 58 (2019) 9109.
Eﬃcient calculation of self-energy matrices for electron-transport simulations
Y. Egami, S. Tsukamoto, and T. Ono: Phys. Rev. B, 100 (2019) 075413.
Graphene-based Symmetric and Non-Symmetric Magnetoresistive Junctions
A. Hashmi, K. Nakanishi, and T. Ono: J. Phys. Soc. Jpn. 89 (2019) 034708.
DFT calculation for oxidation reaction of SiC(0001)
T. Ono: Materials Science Forum, Materials Science Forum 963 (2019) 208.a

ONO, Yoshiaki [ C class; 5000 (B), 750 (C) ] (219)— First-principles and quantum many-body calculations for electronic states and superconductivity inthe multi-band systems
1. First-Principles Study and Orbital-Fluctuation Eﬀect on the Superconductivity in Tungsten Bronze
Ax WO3
Takuya Sekikawa, Rai Watabe, Jun Ishizuka, Yoshihiro Nitta, Kazuhiro Sano and Yoshiaki Ōno:JPS Conf. Proc. 30, 011043 (2020)
2. RKKY Interaction and Quadrupole Order in PrT2 Al20 (T =Ti, V) Based on Eﬀective 196 Orbital
Model Extracted from First-Principles Calculation
Yuto Iizuka, Takemi Yamada, Katsurou Hanzawa and Yoshiaki Ōno: JPS Conf. Proc. 30, 011152(2020)
3. Dynamical Mean-Field Study of Excitonic Phase in the Spinless Two-Band Hubbard Model for
Electron-Hole System
Kento Sasaki, Takemi Yamada, Kaoru Domon and Yoshiaki Ōno: JPS Conf. Proc. 30, 011070(2020)
4. FFLO Superconductivity Mediated by Excitonic Fluctuation in Semimetallic Ta2 NiSe5
Takemi Yamada, Kaoru Domon and Yoshiaki Ōno: Journal of the Physical Society of Japan 88,
064701 (2019)OSHIKAWA, Masaki [ B class; 700 (B), 0 (C) ] (180)— A data-driven investigation of topological materials based on symmetry
OSHIYAMA, Atsushi [ E class; 43500 (B), 5550 (C) ] (44)
— Mechanisms of Semiconductor Interface Formation and its Electronic Properties based on Quantum
Theory1. Microscopic Identiﬁcation of Surface Steps on SiC by Density-Functional Calculations
K. Seino and A. Oshiyama: Proc. ICSRM2019
2. Energetics of the surface step and its morphology on the 3C-SiC(111) surface clariﬁed by thedensity-functional theory
K. Seino and A. Oshiyama: Appl. Phys. Exp. 13 (2020) 015506.
3. Density-Functional Calculations for Structures and Energetics of Atomic Steps and their Implication for Surface Morphology on Si-face SiC Polar Surfaces
K. Seino and A. Oshiyama: Phys. Rev. B (2020) to be published4. A two-dimensional liquid-like phase on Ga-rich GaN (0001) surfaces evidenced by ﬁrst principles
molecular dynamics
K. M. Bui, M. Boero, K. Shiraishi and A. Oshiyama: Jpn. J. Appl. Phys. 59 (2020) SGGK04.
5. Computational study of oxygen stability in vicinal m(10-10)-GaN growth by MOVPE
F. Shintaku, D. Yosho, Y. Kangawa, J.-I. Iwata, A. Oshiyama, K. Shiraishi, A. Tanaka aand H.
Amano: Appl. Phys. Exp. 13 (2020) 055507.
6. Oxygen incorporation kinetics in vicinal m(10-10)-GaN growth by MOVPE
D. Yosho, F. Shintaku, Y. Inatomi, Y. Kangawa, J.-I. Iwata, A. Oshiyama, K. Shiraishi, A. Tanaka
and H. Amano: Phys. Sta. Solidi - Rapid Res. Lett. (2020) 2000142.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoOTOMO, Junichiro [ C class; 1500 (B), 950 (C) ] (138)— Analysis of ion conduction in materials of proton-conducting solid electrolyte and application tocatalytic surface reaction with proton conductors
OZEKI, Yukiyasu [ C class; 8000 (B), 0 (C) ] (254)— Dynamical scaling analysis applied to studies on critical universality for topological phase transitions— Dynamical scaling analysis applied to studies on critical universality for topological phase transitions
II
1. Dynamical scaling analysis on critical universality class for fully frustrated XY models in two
dimensions
Y. Ozeki, Y. Yajima and Y. Nakamura: Phys. Rev B 101 (2020) 094437
RAEBIGER, Hannes [ C class; 6000 (B), 0 (C) ] (87)
— First principles calculation of quantum phase transitions
1. Supercomputer System at ISSP
S. Tsuneyuki: J. Phys. Soc. Jpn. 32 (1996) 41.
2. First principles methods for defects: state of the art and emerging methods
E. Ertekin and H. Raebiger: Characterisation and Control of Defects in Semiconductors, ed.
F. Tuomisto (IET, United Kingdom 2019) pp. 289–343; ISBN-10: 1-78561-655-2, ISBN-13: 9781-78561-655-6
3. Electronic mechanism for resistive Switching in metal/insulator/metal nanodevices
H. Raebiger, A. C. M. Padilha, A. R. Rocha, and G. M. Dalpian: Journal of Physics D: Applied
Physics, accepted (2020); DOI: 10.1088/1361-6463/ab7a58
4. Modulation of the optical absorption edge of ϵ- and κ-Ga2O3 due to Co impurities caused byband structure changes: Work function measurements and ﬁrst-principle calculations
K. Yamanaka, H. Raebiger, K. Mukai, and K. Shudo: Journal of Applied Physics 127 (2020)065701.
5. Carrier mediated ferromagnetism in Ga2 O3 :Cr
K. Ichihashi, H. Shinya, and H. Raebiger: Applied Physics Express 13 (2020) 021002.
SAITO, Mineo [ C class; 7500 (B), 0 (C) ] (75)
— First-principles study for widening the potential of spin-polarized positron experiments
1. First-principles calculation of anomalous muonium in silicon: origin of the negative Fermi contact
interaction constantMuhamad Nasruddin Manaf, Susumu Minami, Fumiyuki Ishii and Mineo Saito: J. J. Appl. Phys.
58 (2019) 081008.
SAKAGUCHI, Norihito [ C class; 7000 (B), 0 (C) ] (78)
— Reduction of Rare Metals in Fuel Cell Catalysts and Hydrogen Permeable Membrane
1. グラフェン上での金属原子吸着状態の理論的研究
長谷川瞬，國貞雄治，坂口紀史: 表面と真空 62 (2019) 344.
2. Extraordinarily Large Kinetic Isotope Eﬀect on Alkene Hydrogenation over Rh-based Intermetallic
Compounds
S. Furukawa, P. Yi, Y. Kunisada, K. Shimizu: Science and Technology of Advanced Materials 20(2019) 805.
3. Co-appearance of superconductivity and ferromagnetism in a Ca2 RuO4 nanoﬁlm crystal
SH. Nobukane, K. Yanagihara, Y. Kunisada, Y. Ogasawara, K. Nomura, Y. Asano, S. Tanda:
Scientiﬁc Reports 10 (2020) 3462.
SAKAI, Toru [ C class; 9500 (B), 1600 (C) ] (245, 247)
— Numerical Diagonalization Study on Spin Nematic Phase of Low-Dimensional Systems— Topological Magnetization Plateau of Quantum Antiferromagnetic Spin Chain with Anisotropies
1. Analysis of Rashba Eﬀect on Au(111) Model Surface
M. Fujiwara, N. Shima, K. Makoshi and T. Sakai: J. Phys. Soc. Jpn. 88 (2019), 034604.
2. From kagome strip to kagome lattice: Realizations of frustrated S=1/2 antiferromagnets in Ti(III)419

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ﬂuoridesH. O. Jeschke, H. Nakano and T. Sakai: Phys. Rev. B 99 (2019) 140410(R).
3. Magnetization plateau of the S=2 antiferromagnetic Heisenberg chain with anisotropies
T. Sakai, K. Okamoto and T. Tonegawa: Phys. Rev. B 100 (2019) 054407.
4. Two magnetization plateaus in the kagome ﬂuoride Ce2 LiTi3 F12
R. Shirakami, H. Ueda, H. O. Jeschke, H. Nakano, S. Kobayashi, A. Matsuo, T. Sakai, N.
Katayama, H. Sawa, K. Kindo, C. Michioka and K. Yoshimura: Phys. Rev. B 100 (2019)174401.
5. Properties of the H-T phase diagram of the 3-K phase in eutectic Sr2RuO4-Ru: Evidence forchiral superconductivity
H. Kaneyasu, Y. Enokida, T. Nomura, Y. Hasegawa, T. Sakai and M. Sigrist: Phys. Rev. B 100(2019) 21451.
6. Spin Nematic Phase of the Quantum Spin Nanotube
T. Sakai: JPS Conference Proceedings 29 (2020) 014004.
7. Field-Induced Spin Nematic Phase in the S=1 Anisotropic Spin Ladder
R. Yamanokuchi, K. Okamoto and T. Sakai: Proceedings of 2018 16th International Conference
on Megagauss Magnetic Field Generation and Related Topics (MEGAGAUSS) (2019) 8722674.
8. Haldane Gaps of Large-S Heisenberg Antiferromagnetic Chains and Asymptotic Behavior
H. Nakano, N. Todoroki and T. Sakai: J. Phys. Soc. Jpn. 88 (2019) 114702.
9. Spin Nematic Liquids of the S = 1 Spin Ladder in Magnetic Field
T. Sakai and K. Okamoto: JPS Conference Proceedings 30 (2020) 011083.
10. Ground-State Phase Diagram of an Anisotropic S = 1 Ferromagnetic-Antiferromagnetic BondAlternating Chain
K. Okamoto, T. Tonegawa, M. Kaburagi and T. Sakai: JPS Conference Proceedings 30 (2020)
011024.
11. Quantum Phase Transition of the Twisted Spin Tube
Y. Tachibana, Y. Ueno, T. Zenda, K. Okamoto and T. Sakai: JPS Conference Proceedings 30(2020) 011082.
12. Quantum Phase Transitions of the Distorted Diamond Spin Chain
T. Zenda, Y. Tachibana, Y. Ueno, K. Okamoto and T. Sakai: JPS Conference Proceedings 30(2020) 011084.
13. Magnetization Plateau of the Distorted Diamond Spin Chain
Y. Ueno, T. Zenda, Y. Tachibana, K. Okamoto and T. Sakai: JPS Conference Proceedings 30(2020) 011085.
14. Features of Chirality Generated by Paramagnetic Coupling to Magnetic Fields in the 3K-Phaseof Sr2 RuO4
H. Kaneyasu, Y. Enokida, T. Nomura, Y. Hasegawa, T. Sakai and M. Sigrist: JPS Conference
Proceedings 30 (2020) 011039.
SAKAKIBARA, Hirofumi [ B class; 800 (B), 0 (C) ] (171)— Developments of a derivation method of a low-energy models in ﬁrst-principles
1. Model-mapped random phase approximation to evaluate superconductivity in the ﬂuctuationexchange approximation from ﬁrst principles
H. Sakakibara, T. Kotani: Phys. Rev. B 99, 195141(2019).
2. Finite electric-ﬁeld approach to evaluate the vertex correction for the screened Coulomb interactionin the quasiparticle self-consistent GW method
H. Sakakibara, T. Kotani, M. Obata, T. Oda: Phy. Rev. B (2020) in press.
SAKURAGI, Shunsuke [ C class; 1000 (B), 0 (C) ] (163)— Controlling of magnetism in Pd(100) ultrathin ﬁlms by modiﬁcation of quantum-well states via adsorption of transition metals
1. Switching of magnetism via modifying phase shift of quantum-well states by tailoring the interface
electronic structure
S. Sakuragi, H. Kageshima, and T. Sato: Phys. Rev. B 101 (2020) 014410.

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SASAKI, Kazuo [ B class; 700 (B), 90 (C) ] (335)— Simulation analysis of collision of two ﬁlaments driven by protein molecular motors
SASAKI, Takehiko [ C class; 3000 (B), 200 (C) ] (120)— Reaction processes of polyalcohols in high temperature water by First Principles Calculations
SATO, Tetsuya [ C class; 1000 (B), 350 (C) ] (157)— Study of appearance of ferromagnetism by electric ﬁeld application to Pt thin ﬁlm
SHAO, Cheng [ C class; 2000 (B), 650 (C) ] (132)— Multiscale computational design of thermoelectric materials
SHIGA, Takuma [ B,C class; 2200 (B), 0 (C) ] (293, 295, 296)
— Clariﬁcation of thermal transport spectra in hierarchical structured organic bulk materials— Compherensive study on transition between heat conduction and radiative heat transfer— Heat conduction analysis for phononic crystal
SHIMADA, Toshihiro [ B class; 800 (B), 0 (C) ] (170)— First principle simulation on ultrahigh pressure synthesis of new material from organic molecules
1. Sugar-assisted Mechanochemical Exfoliation of Graphitic Carbon Nitride for Enhanced Visiblelight Photocatalytic Performance
Wei Liu, Takashi Yanase, Nobuhiro Iwasa, Hitoshi Koizumi, Shin Mukai, Shinichiro Iwamura,
Taro Nagahama, and Toshihiro Shimada: International J. of Hydrogen Enegry 44 (2020) 8444.
2. Porous Graphitic Carbon Nitride Nanoplates Obtained by A Combined Exfoliation Strategy for
Enhanced Visible Light Photocatalytic Activity
Wei Liu, Nobuhiro Iwasa, Shinichiro Fujita, Hitoshi Koizumi, Makoto Yamaguchi and Toshihiro
Shimada: Applied Surface Science 499 (2020) 143901.
3. Synthesis and Enhanced Room-temperature Ferromagnetic Properties of Carbon-doped Boron
Nitride Nanosheets
Wei Liu, Takashi Yanase, Taro Nagahama and Toshihiro Shimada: J. Alloys and Compounds 792(2019) 1206.
SHIMAMURA, Kohei [ C class; 2500 (B), 650 (C) ] (124)— Construction of neural network force ﬁeld for molecular dynamics simulation in multicomponent
system
1. Guidelines for Creating Artiﬁcial Neural Network Empirical Interatomic Potential from FirstPrinciples Molecular Dynamics Data under Speciﬁc Conditions and Its Application to α-Ag2 Se
K. Shimamura, S. Fukushima, A. Koura, F. Shimojo, M. Misawa, R. K. Kalia, A. Nakano, P.
Vashishta, T. Matsubara, and S. Tanaka: J. Chem. Phys. 151 (2019) 124303.
SHIMOJO, Fuyuki [ C class; 5000 (B), 0 (C) ] (103)— First-Principles Molecular-Dynamics Study of Structural and Electronic Properties of Covalent Liquids and Glasses under Pressure
1. Structural studies on ﬂuid sulfur at high temperatures and high pressures: II. Molecular structure
obtained by ab initio molecular dynamics simulations
S. Munejiri, F. Shimojo, K. Hoshino, and M. Inui: J. Non-Cryst. Solids 510, 15 (2019).
2. Structural change in liquid sulphur from chain polymeric liquid to atomic simple liquid under highpressure
S. Ohmura and F. Shimojo,: J. Phys.: Condens. Matter 31, 215101 (2019).
3. Guidelines for Creating Artiﬁcial Neural Network Empirical Interatomic Potential from FirstPrinciples Molecular Dynamics Data under Speciﬁc Conditions and Its Application to α-Ag2 Se
K. Shimamura, S. Fukushima, A. Koura, F. Shimojo, M. Misawa, R. K. Kalia, A. Nakano, P.
Vashishta, T. Matsubara, and S. Tanaka: J. Chem. Phys. 151, 124303 (2019).
4. GGA+U Molecular Dynamics Study of Structural and Dynamic Properties of Superionic Conductor Ag2 Se

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5.

S. Fukushima, M. Misawa, A. Koura and F. Shimojo: J. Phys. Soc. Jpn. 88, 115002 (2019).
Thermodynamic Integration by Neural Network Potentials Based on First-principles Dynamic
Calculations
S. Fukushima, E. Ushijima, H. Kumazoe, A. Koura, F. Shimojo, K. Shimamura, M. Misawa, R.
K. Kalia, A. Nakano, and P. Vashishta: Phys. Rev. B 100, 214108 (2019).

SHIMOKAWA, Tokuro [ C class; 4500 (B), 1250 (C) ] (261)— Thermal eﬀect on the quantum frustrated magnetism
SHINAOKA, Hiroshi [ B class; 800 (B), 0 (C) ] (232)— Exploring low-rank tensor representation of Matsubara Green’s functions
1. Sparse sampling and tensor network representation of two-particle Green’s functions
H. Shinaoka, D. Geﬀroy, M. Wallerberger, J. Otsuki, K. Yoshimi, E. Gull, J. Kuneš, SciPost Phys.
8, (2020) 012 .
SHINODA, Wataru [ E class; 24000 (B), 3000 (C) ] (355)— Molecular basis analysis of Soft Materials using All-Atom and Coarse-Grained Molecular Dynamics
Simulations
1. Free energy analysis of membrane pore formation process in the presence of multiple melittin
peptidesY. Miyazaki, S. Okazaki, and W. Shinodai: BBA - Biomembranes 1861 (2019) 1409-1419.
2. Cholesterol-Induced Conformational Change in the Sphingomyelin Headgroup
S. Hanashima, K. Murakami, M. Yura, Y. Yano, Y. Umegawa, H. Tsuchikawa, N. Matsumori, S.
Seo, W. Shinoda, and M. Murata: Biophys. J. 117 (2019) 307-318.
3. Hydrogen Permeation in Hydrated Perﬂuorosulfonic Acid Polymer Membranes: Eﬀect of Polymer
Crystallinity and Equivalent Weight
K. Takeuchi, A. Kuo, T. Hirai, T. Miyajima, S. Urata, S. Terazono, S. Okazaki, and W. Shinoda:
J. Phys. Chem. C 123, (2019) 20628-20638.
4. Average Conformation of Branched Chain Lipid PGP-Me That Accounts for the Thermal Stabilityand High-Salinity Resistance of Archaeal Membranes
M. Yamagami, H. Tsuchikawa, J. Cui, Y. Umegawa, Y. Miyazaki, S. Seo, W. Shinoda, and M.
Murata: Biochemistry 58, (2019) 3869-3879.
5. Eﬀects of Packing Density and Chain Length on the Surface Hydrophobicity of Thin Films Composed of Perﬂuoroalkyl Acrylate Chains: A Molecular Dynamics Study
H. O. S. Yadav, A. Kuo, S. Urata, and W. Shinoda: Langmuir 35, (2019) 14316-14323.
6. Large-scale molecular dynamics simulation of perﬂuorosulfonic acid T membranes: Remappingcoarse-grained to all-atomistic simulations
A. Kuo, Y. Miyazaki, C. Jang, T. Miyajima, S. Urata, S. O. Nielsen, S. Okazaki, and W. Shinoda:
Polymer 181, (2019) 121766.
7. Heteroaryldihydropyrimidines Alter Capsid Assembly By Adjusting the Binding Aﬃnity and Pattern of the Hepatitis B Virus Core Protein
H. Liu, S. Okazaki, and W. Shinoda: J. Chem. Inf. Model. 59, (2019) 5104-5110.
8. pSPICA: A Coarse-Grained Force Field for Lipid Membranes Based on a Polar Water Model
Y. Miyazaki, S. Okazaki, and W. Shinoda: J. Chem. Theory Comput. 16, (2020) 782-793.
SHINOHARA, Yasushi [ C class; 4000 (B), 0 (C) ] (113)— First-principles calculations for nonlinear light absorption of insulators
1. Asymmetric nonlinear optics of a polar chemical bondYuya Morimoto, Yasushi Shinohara, Mizuki Tani, Bo-Han Chen, Kenichi L. Ishikawa, Peter Baum:arXiv:1910.11821, submitted.
2. Detecting electron-phonon couplings during photo-induced phase transition
Takeshi Suzuki, Yasushi Shinohara, Yangfan Lu, Mari Watanabe, Jiadi Xu, Kenichi L. Ishikawa,
Hide Takagi, Minoru Nohara, Naoyuki Katayama, Hiroshi Sawa, Masami Fujisawa, Teruto Kanai,
Jiro Itatani, Takashi Mizokawa, Shik Shin, Kozo Okazaki: arXiv:2002.10037, submitted.
3. Strong-Field Electron Dynamics in Solids

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Kenichi L. Ishikawa, Yasushi Shinohara, Takeshi Sato, Tomohito Otobe: arXiv:2003.14090, appeared as a chapter in a book.
SHIOMI, Junichiro [ C class; 4500 (B), 750 (C) ] (265)— Screening for Thermal Functional Materials using Materials Informatics
1. Design of highly-selective radiative-cooling structure accelerated by materials informatics
Jiang Guo, Shenghong Ju, Junichiro Shiomi: Optics Letters, 45, 343-346(2020).
2. Enhancing thermal boundary conductance of graphite- metal interface by triazine-based molecularbonding
Aun Ota, Masato Ohnishi, Hisayoshi Oshima, Hisayoshi, Takuma Shiga, Takashi Kodama, Junichiro Shiomi: ACS Applied Materials & Interfaces, 11, 37295-37301 (2019).
3. Spectral control of thermal boundary conductance between copper and carbon crystals by selfassembled monolayers
Shih-Wei Hung, Shiqian Hu, Junichiro Shiomi: ACS Applied Electronic Materials, 1, 2594-2601(2019).
4. Scalable multi- nanostructured silicon for room-temperature thermoelectrics
Makoto Kashiwagi, Yuxuan Liao, Shenghong Ju, Asuka Miura, Shota Konishi, Takuma Shiga,
Takashi Kodama, and Junichiro Shiomi: ACS Applied Energy Materials, 2, 7083-7091 (2019).
5. Disorder Limits the Coherent Phonon Transport in Two- Dimensional Phononic Crystal Structure
Shiqian Hu, Zhongwei Zhang, Pengfei Jiang, Weijun Ren, Cuiqian Yu, Junichiro Shiomi, Jie Chen:
Nanoscale, 11, 11839-11846 (2019).
6. Monte Carlo tree search for materials design and discovery
Thaer Dieb, Shenghong Ju, Junichiro Shiomi, Koji Tsuda: MRS Communications, 9, 532-536(2019).
7. Anomalously low thermal conductivity in superhard cubic-Si3N4Jing Liu, Shenghong Ju, Norimasa Nishiyama, Junichiro Shiomi: Physical Review B, 100, 064303(2019).
8. Materials informatics for heat transfer: Recent progresses and perspectives
Shenghong Ju, Junichiro Shiomi: Nanoscale and Microscale Thermophysical Engineering, 23,
157172 (2019).
9. Quantifying phonon particle and wave transport in nanostructures–The unexpectedly strong particle eﬀect in silicon nanophononic metamaterial with cross junction, Materials Today Physics, 8,56-61 (2019). cooling structure accelerated by materials informatics
Dengke Ma, Anuj Arora, Shichen Deng, Junichiro Shiomi, Nuo Yang: Optics Letters, 45, 343-346(2020).
SHIRAI, Tatsuhiko [ B class; 700 (B), 0 (C) ] (341)— The analysis of the dynamical response to the optical bistability
1. Dynamical phase transition in Floquet optical bistable systems: An approach from ﬁnite-size
quantum systems
T. Shirai, S. Todo, and S. Miyashita: Phys. Rev. A 101 (2020) 013809.
2. Thermalization in open many-body systems based on eigenstate thermalization hypothesis
T. Shirai and T. Mori: Phys. Rev. E 101 (2020) 042116.
3. A guiding principle for embedding in simulated-annealing based Ising machines
T. Shirai, S. Tanaka and N. Togawa: Submitted to IEEE Transactions on Computers: Special
Issue of Quantum Computing
SHIRAISHI, Kenji [ C class; 5500 (B), 0 (C) ] (97)— Theoretical Design of Gate Dielectrics of Future GaN Power Devices
SHUDO, Ken-ichi [ C class; 500 (B), 50 (C) ] ()— Impurity eﬀects on electronic states of PbS nano-particles

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SUGINO, Osamu [ E class; 13000 (B), 2000 (C) ] (52)— Physics of electrode interfaces
1. Nuclear quantum eﬀect for hydrogen adsorption on Pt(111)
L. Yan, Y. Yamamoto, M. Shiga, and O. Sugino: Phys. Rev. B 101, 165414 (2020).
2. Scaling Relation of Oxygen Reduction Reaction Intermediates at Defective TiO2 Surfaces
Y. Yamamoto, S. Kasamatsu, and O. Sugino: J. Phys. Chem. C 123, 19486-19492 (2019).
SUWA, Hidemaro [ C class; 9500 (B), 0 (C) ] (251)— Dynamical spin structure factor of spin-orbit insulator— Dynamics of Slater-Mott crossover materials
SUZUKI, Takafumi [ C class; 4000 (B), 650 (C) ] (285)— Quantum spin liquids in extended Kitaev models on a honeycomb lattice
1. Quantized Δ S=2 Excitation Spectra by Conﬁnement in an S=1 Spin Chain
Takafumi Suzuki and Seiichiro Suga:J. Phys. Soc. Jpn. 88, 053702 (2019).
2. Temperature Dependence of Heat Capacity in the Kitaev-Heisenbeg Model on a Honeycomb Lattice
Takafumi Suzuki and Youhei Yamaji:J. Phys. Soc. Jpn. 88, 115001 (2019).
SUZUKI, Yuji [ C class; 6000 (B), 0 (C) ] (85)
— Development of High-performance Polymer Electret— Development of High-performance Polymer Electret Using Quantum Chemical Analysis
1. Solid State Quantum Chemical Investigation of a High-performance Fluorinated Amorphous Polymer Electret
S. Kim, K.Suzuki, and Y. Suzuki: Invited talk, IEEE 17th Int. Symp. Electrets (ISE17), Limerick,p.23 (2019)
2. Investigation of Charge Stability in Amorphous Fluorinated Polymer Using Quantum Chemical
Analysis
S. Kim, Y. Zhang, K.Suzuki, and Y. Suzuki: IEEE Conf. on Electr. Insul. Dielectr. Phenom.
(CEIDP), Richland, 8-1 (2019)
TADANO, Terumasa [ C class; 6000 (B), 1000 (C) ] (15)— Predicting and understanding structural phase transition of solids from ﬁnite-temperature phonon
calculations
1. First-principles study of phonon anharmonicity and negative thermal expansion in ScF3
Y. Oba, T. Tadano, R. Akashi and S. Tsuneyuki: Phys. Rev. Mater. 3 (2019) 033601.
2. Quantum crystal structure in the 250-kelvin superconducting lanthanum hydride
I. Errea, F. Belli, L. Monacelli, A. Sanna, T. Koretsune, T. Tadano, R. Bianco, M. Calandra, R.
Arita, F. Mauri and J. A. Flores-Livas: Nature 578 (2020) 66.
3. Materials design of dynamically stable d9 layered nickelates
M. Hirayama, T. Tadano, Y. Nomura and R. Arita: Phys. Rev. B 101 (2020) 075107.
4. Anharmonicity Explains Temperature Renormalization Eﬀects of the Band Gap in SrTiO3 .
Y. Wu, W. A. Saidi, J. K. Wuenschell, T. Tadano, P. Ohodnicki, B. Chorpening and Y. Duan: J.
Phys. Chem. Lett. 11 (2020) 2518.
5. Enargite Cu3 PS4 : A CuS-Based Thermoelectric Material with a Wurtzite-Derivative Structure
T. Tanimoto, K. Suekuni, T. Tanishita, H. Usui, T. Tadano, T. Kamei, H. Saito, H. Nishiate, C.
H. Lee, K. Kuroki and M. Ohtaki: Adv. Funct. Mater. 2020 (2020) 2000973.
TAKAHASHI, Osamu [ C,D class; 1000 (B), 750 (C) ] (148)— Electronic state of water and ethanol in aqueous solution— Electronic state of water under various environments
1. Si 1s−1 , 2s−1 and 2p−1 lifetime broadening of SiX4 (X = F, Cl, Br, CH3 ) molecules: SiF4 anomalous behaviour reassessed
R. Pttner, T. Marchenko, R. Guillemin, L. Journel, G. Goldsztejn, D. Colin, O. Takahashi, K.
Ueda, A. F. Lago, M. N. Piancastelli, and M. Simon: Phys. Chem. Chem. Phys., 21(17), 8827 -424

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2.

3.

8836 (2019)
Electronic States of Acetic Acid in a Binary Mixture of Acetic Acid and 1-Methylimidazole Dependon the Environment
N. Yoshimura, O. Takahashi, M. Oura, and Y. Horikawa: J. Phys. Chem. B 123 (6), 1332 1339(2019)
pH dependence of aqueous oxalic acid observed by X-ray absorption and emission spectroscopy
R. Yamamura, T. Suenaga, M. Oura, T. Tokushima, and O. Takahashi, Chem. Phys. Lett. 738,
136895 (2020).

TAKETSUGU, Tetsuya [ C class; 3500 (B), 600 (C) ] ()— Ab initio study on the structure and functions of nanomaterials
TAMURA, Ryo [ C class; 1000 (B), 250 (C) ] (318)Eﬀective model estimation using experimental results
1. Eﬃcient recommendation tool of materials by an executable ﬁle based on machine learning
K. Terayama, K. Tsuda, and R. Tamura: Japanese Journal of Applied Physics 58 (2019) 098001.
2. Quantum Phase Transition in Fully Connected Quantum WajnﬂaszPick Model
Y. Seki, S. Tanaka, and S. Kawabata: J. Phys. Soc. Jpn. 88 (2019) 054006.
3. Application of Ising Machines and a Software Development for Ising Machines
K. Tanahashi, S. Takayanagi, T. Motohashi, and S. Tanaka: J. Phys. Soc. Jpn. 88 (2019) 061010.
4. A Fully-Connected Ising Model Embedding Method and Its Evaluation for CMOS Annealing
Machines
D. Oku, K. Terada, M. Hayashi, M. Yamaoka, S. Tanaka, and N. Togawa: IEICE Transactions
on Information and Systems, E102.D (2019) 1696.
5. Designing metamaterials with quantum annealing and factorization machines
K. Kitai, J. Guo, S. Ju, S. Tanaka, K. Tsuda, J. Shiomi, and R. Tamura: Physical Review Research
2 (2019) 013319.
6. Data Integration for Accelerated Materials Design via Preference Learning
X. Sun, Z. Hou, M. Sumita, S. Ishihara, R. Tamura, and K. Tsuda: New Journal of Physics inpress.
7. A guiding principle for embedding in simulated-annealing based Ising machines
T. Shirai, S. Tanaka, and N. Togawa: submitted to IEEE Journal
8. Data-driven determination of a spin Hamiltonian of KCu4 P3 O12 with uncertainty
R. Tamura, K. Hukushima, A. Matsuo, K. Kindo, and M. Hase: submitted.
TANAKA, Hajime [ B,D class; 4900 (B), 0 (C) ] (273, 275, 277, 279)
— Coarsening mechanism of network-forming phase separation in colloidal suspensions
1. Inﬂuence of Hydrodynamic Interactions on Colloidal Crystallization
M. Tateno ,T. Yanagishima ,J. Russo and H. Tanaka: Phys. Rev. Lett. 123 (2019) 258002.
TANAKA, Shu [ C class; 500 (B), 100 (C) ] (344)— Study on Ising machines from a viewpoint of statistical mechanics
1. Quantum Phase Transition in Fully Connected Quantum WajnﬂaszPick Model
Y. Seki, S. Tanaka, and S. Kawabata: J. Phys. Soc. Jpn. 88 (2019) 054006.
2. Application of Ising Machines and a Software Development for Ising Machines
K. Tanahashi, S. Takayanagi, T. Motohashi, and S. Tanaka: J. Phys. Soc. Jpn. 88 (2019) 061010.
3. A Fully-Connected Ising Model Embedding Method and Its Evaluation for CMOS Annealing
Machines
D. Oku, K. Terada, M. Hayashi, M. Yamaoka, S. Tanaka, and N. Togawa: IEICE Transactions
on Information and Systems, E102.D (2019) 1696.
4. Eﬃcient recommendation tool of materials by an executable ﬁle based on machine learning
K. Terayama, K. Tsuda, and R. Tamura: Japanese Journal of Applied Physics 58 (2019) 098001.
5. Designing Metamaterials with Quantum Annealing and Factorization Machines
K. Kitai, J. Guo, S. Ju, S. Tanaka, K. Tsuda, J. Shiomi, and R. Tamura: Phys. Rev. Research 2(2020) 013319.

425

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

6.

7.
8.

Data Integration for Accelerated Materials Design via Preference Learning
X. Sun, Z. Hou, M. Sumita, S. Ishihara, R. Tamura, and K. Tsuda: New Journal of Physics inpress.
A guiding principle for embedding in simulated-annealing based Ising machines
T. Shirai, S. Tanaka, and N. Togawa: submitted to IEEE Journal.
Data-driven determination of a spin Hamiltonian of KCu4 P3 O12 with uncertainty
R. Tamura, K. Hukushima, A. Matsuo, K. Kindo, and M. Hase: submitted.

TATENO, Masaru [ C class; 5000 (B), 0 (C) ] ()— Multi-scale Hybrid Molecular Dynamics Simulations of Biological Catalysis
TATETSU, Yasutomi [ C class; 4000 (B), 750 (C) ] (105)— First-principles study on grain boundaries of permanent magnets
1. First-principles study on surface stability and interface magnetic properties of SmFe12
Y. Ainai, T. Shiozawa, Y. Tatetsu, and Y. Gohda: Appl. Phys. Exp. 13 (2020) 045502.
2. First-principles study of crystalline NdFe alloys
Y. Ainai, Y. Tatetsu, A. Terasawa, and Y. Gohda, Appl. Phys. Exp. 13 (2020) 017006.
TATEYAMA, Yoshitaka [ C class; 12500 (B), 900 (C) ] (54)
— DFT sampling analysis of interfaces and electrolytes in novel batteries— DFT-MD sampling analysis of interfaces and electrolytes in novel batteries
1. Li+ Transport Mechanism at Heterogeneous Cathode / Solid Electrolyte Interface in All-SolidState Battery via First-Principles Structure Prediction Scheme
B. Gao, R. Jalem, Y. Ma, Y. Tateyama, Chem. Mater. 32 (2020) 85.
2. Reaction Energy Benchmarks of Hydrocarbon Combustion by Gaussian Basis and Plane Wave
Basis Approaches
A. Ishikawa, Y. Tateyama, J. Comp. Chem. 40 (2019) 1866.
3. Electrochemical properties of ﬂuorinated boron-doped diamond electrodes via ﬂuorine-containing
plasma treatmen
C. Yamaguchi, K. Natsui, S. Iizuka, Y. Tateyama, Y. Einaga, Phys. Chem. Chem. Phys. 21(2019) 13788.
4. Theoretical picture of positive electrode / solid electrolyte interface in all-solid-state battery fromelectrochemistry and semiconductor physics viewpoints
Y. Tateyama, B. Gao, R. Jalem, J. Haruyama, Curr. Opin. Electrochem. 17 (2019) 149.
5. Surface-Dependent Stability of Interface between the Garnet Li7La3Zr2O12 and the Li Metal in
the All-Solid-State Battery from First-Principles Calculations
B. Gao, R. Jalem, Y. Tateyama, ACS Appl. Mater. Interfaces, 12 (2020) 16350.
6. Possible high-potential ilmenite type Na1MO3 (M = VNi) cathodes realized by dominant oxygen
redox reaction
M. H. N. Assadi, M. Okubo, A. Yamada, Y. Tateyama, Phys. Rev. Mater. 4 (2020) 015401.
7. Machine learning prediction of coordination energies for alkali group elements in battery electrolyte
solvents
A. Ishikawa, K. Sodeyama, Y. Igarashi, T. Nakayama, Y. Tateyama, M. Okada, Phys. Chem.
Chem. Phys. 21 (2019) 26339.
8. What Is the Active Site for the Oxidative Coupling of Methane Catalyzed by MgO? A MetadynamicsBiased Ab Initio Molecular Dynamics Study
A. Ishikawa, Y. Tateyama, J. Phys. Chem. C 124 (2020) 6054.
TERAO, Takamichi [ B class; 1200 (B), 160 (C) ] (316)— Molecular simulation of patchy particles
1. Numerical method to study three-dimensional metamaterial composites
T. Terao: Proceedings of 13th international congress on artiﬁcial materials for novel wave phenomena (2019) X426.

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of TokyoTERASAWA, Asako [ C class; 3000 (B), 550 (C) ] (115)— First principles calculations and analysis on relationship between exchange coupling constants andlocal structures for magnetic alloys and amorphous grain boundary phases in permanent magnets
1. Eﬃcient Algorithm Based on Liechtenstein Method for Computing Exchange Coupling Constants
Using Localized Basis Set
A. Terasawa, M. Matsumoto, T. Ozaki, and Y. Gohda: J. Phys. Soc. Jpn., vol. 88, no. 11, p.
114706, Oct. 2019, doi: 10.7566/JPSJ.88.114706.
TODO, Synge [ C class; 6000 (B), 850 (C) ] (256)— Entanglement Quantum Phase Transition and Quantum Dynamics in Quantum Many-body Systems
1. Machine learning for molecular dynamics with strongly correlated electrons
Hidemaro Suwa, Justin S. Smith, Nicholas Lubbers, Cristian D. Batista, Gia-Wei Chern, Kipton
Barros, Phys. Rev. B **99**, 161107 (5pp) (2019)
2. Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, Naoki Kawashima, Phys. Rev. Lett. 123, 087203(6pp) (2019)
3. Subspace-search variational quantum eigensolver for excited states
Ken M. Nakanishi, Kosuke Mitarai, Keisuke Fujii, Phys. Rev. Research 1, 033062 (7pp) (2019)
4. Characterization of localized eﬀective spins in gapped quantum spin chains
Hayate Nakano, Seiji Miyashita, Phys. Rev. B **100**, 195105 (11pp) (2019)
5. Multiple-q states of the J1 -J2 classical honeycomb-lattice Heisenberg antiferromagnet under magnetic ﬁelds
Tokuro Shimokawa, Tsuyoshi Okubo, Hikaru Kawamura, Phys. Rev. B 100, 224404 (15pp) (2019)6. Dynamical phase transition in Floquet optical bistable systems: An approach from ﬁnite-size
quantum systems
Tatsuhiko Shirai, Synge Todo, Seiji Miyashita, Phys. Rev. A 101, 013809 (7pp) (2020)
7. Abelian and Non-Abelian Chiral Spin Liquids in a Compact Tensor Network Representation
Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, Naoki Kawashima, Phys. Rev. B 101, 035140(9pp) (2020)
8. Spin-lattice coupling in a ferrimagnetic spinel: Exotic H − T phase diagram of MnCr2 S4 up to
110 T
A. Miyata, H. Suwa, T. Nomura, L. Prodan, V. Felea, Y. Skourski, J. Deisenhofer, H.-A. Krug
von Nidda, O. Portugall, S. Zherlitsyn, V. Tsurkan, J. Wosnitza, A. Loidl, Phys. Rev. B 101,
054432 (8pp) (2020)
TOHYAMA, Takami [ C class; 2500 (B), 550 (C) ] (290)— Finite-Temperature Properties and Spin Dynamics in Kagome Kitaev-Heisenberg Model
1. Finite-temperature properties of the Kitaev-Heisenberg models on kagome and triangular lattices
studied by improved ﬁnite-temperature Lanczos methods
K. Morita and T. Tohyama: Phys. Rev. Research 2, (2020) 013205.
2. Magnetic orders induced by RKKY interaction in Tsai-type quasicrystalline approximant Au-AlGd
H. Miyazaki, T. Sugimoto, K. Morita, and T. Tohyama: Phys. Rev. Materials 4, (2020) 024417.
3. Vanishing Wilson ratio as the hallmark of quantum spin-liquid models
P. Prelovsek, K. Morita, T. Tohyama, and J. Herbrych: Phys. Rev. esearch 2, (2020) 023024.
TOMITA, Yusuke [ C class; 5500 (B), 0 (C) ] (264)— Study of relaxor ferroelectrics by using a minimal model
TONEGAWA, Takashi [ B,C class; 2100 (B), 0 (C) ] (297)— Numerical Study of the One-Dimensional Quantum Spin Systems with Spatial Structures— Numerical Study of the One-Dimensional Quantum Spin Systems with Spatial Studies
1. Mgnetization Plateau of the S = 2 Antiferromagnetic Heisenberg Chain with Anisotropies
T. Sakai, K. Okamoto, and T. Tonegawa: Phys. Rev. B 100, 054407 (2019).
2. Ground-State Phase Diagram of an Anisotropic S = 1 Ferromagnetic-Antiferromagnetic Bond-427

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Alternating Chain
K. Okamoto, T. Tonegawa, M. Kaburagi, and T. Sakai: JPS Conf. Proc. 30, 011024 (2020).
TSUKAHARA, Noriyuki [ B class; 400 (B), 0 (C) ] ()— Theoretical study of spin detection in lanthanoid atoms and molecules by adsorption on superconducting substrate
TSUNEYUKI, Shinji [ C class; 7000 (B), 950 (C) ] (73)— Material exploration by advanced ﬁrst-principles simulation
1. Ab initio prediction of structural phase-transition temperature of SrTiO3 from ﬁnite-temperaturephonon calculation
T. Tadano and S. Tsuneyuki: J. Ceram. Soc. Jpn., 127 (2019) 404.
2. Search for common minima in joint optimization of multiple cost functions
D. Adachi, N. Tsujimoto, R. Akashi, S. Todo and S. Tsuneyuki: Comp. Phys. Commun. 241(2019) 92.
3. X 線回折実験とシミュレーションのデータ同化による結晶構造解析
藤堂 眞治, 常行 真司, 日本結晶学会誌 62 (2020) 51.
TSURUTA, Kenji [ C class; 2500 (B), 0 (C) ] (137)— Hybrid Ab-Initio/Machine-Learning Computation for Designing Dynamical Properties of Nano/Molecular
Structures
1. First-principles Study on Water Dissociation in Grain Boundary of MAPbI3 Perovskite
M.A.A. Asad, K. Sato, and K. Tsuruta: MRS Adv. 4 (2019) 1965.
2. Optimization of Molecular Characteristics via Machine Learning based on Continuous Representation of Molecules
K. Sato and K. Tsuruta: Mater. Sci. Forum, in press.
UCHIDA, Takashi [ B class; 500 (B), 90 (C) ] (348)— Magnetic structures of multiple-Q states in frustrated itinerant magnets
WAKABAYASHI, Daisuke [ B class; 700 (B), 0 (C) ] ()— Inhomogeneous structure of silica glass during the structural transformations under high pressure
WATANABE, Hiroshi [ B class; 900 (B), 100 (C) ] (326)— Molecular dynamics study of the properties of near-critical ﬂuids
WATANABE, Hiroshi [ B class; 700 (B), 0 (C) ] (236)— Calculation for ground and excited states in strongly-correlated electron systems by variational Monte
Carlo method
1. Mechanism of superconductivity and electron-hole doping asymmetry in κ-type molecular conductors
H. Watanabe, H. Seo, and S. Yunoki: Nat. Commun. 10 (2019) 3167.
WATANABE, Kazuyuki [ C class; 8000 (B), 700 (C) ] (64)
— First-Principles Study of Excited Electron Positron and Atom Dynamics and Optical and Thermoelectric Properties of Nanostructures
1. Angle-resolved photoemission spectroscopy in low-dimensional periodic structures: a real-timeﬁrst-principles simulation
K. Uchida, Y. Akimoto, K. Einaga, and K. Watanabe, Jpn. J. Appl. Phys. 58, 128001 (2019).
2. Excitons in two-dimensional atomic layer materials from time-dependent density functional theory: mono-layer and bi-layer hexagonal boron nitride and transition-metal dichalcogenides
Y. Suzuki and K. Watanabe, Phys. Chem. Chem. Phys. 22, 2908 (2020).
3. Simulation of a hydrogen atom in a laser ﬁeld using the time-dependent variational principle
K. Rowan, L. Schatzki, T. Zaklama, Y. Suzuki, K. Watanabe, and K. Varga, Phys. Rev. E 101,
023313 (2020).

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4.

Stationary-state electron scattering using a complex injecting potential
T. Yamaguchi, K. Uchida, K. Varga, and K. Watanabe, J. Phys. Soc. Jpn. 89,044002(2020).

WATANABE, Satoshi [ C class; 10500 (B), 1700 (C) ] (58)
— Analyses of atomic structures and atom dynamics at surfaces interfaces and defects
1. A Comparative Study on the Diﬀusion Behaviors of Metal and Oxygen Ions in Metal-Oxide Based
Resistance Switches via Ab Initio Molecular Dynamics Simulations
B. Xiao, X.-F. Yu, and S. Watanabe: ACS Appl. Electronic Mater. 1 (2019) 585.
2. Simulating lattice thermal conductivity in semiconducting materials using high-dimensional neuralnetwork potential
E Minamitani, M Ogura, and S Watanabe: Appl. Phys. Express 12 (2019) 095001.
3. Low-Energy-Consumption Three-Valued Memory Device Inspired by Solid-State Batteries
Y. Watanabe, S. Kobayashi, I. Sugiyama, K. Nishio, W. Liu, S. Watanabe, R. Shimizu, and T.
Hitosugi: ACS Appl. Mater. interfaces 11 (2019) 45150.
4. Mechanically Tunable Spontaneous Vertical Charge Redistribution in Few-Layer WTe2
Z. Ni, E. Minamitani, K. Kawahara, R. Arafune, C.-L. Lin, N. Takagi, and S. Watanabe: J. Phys.
Chem. C 124 (2019) 2008.
5. Moisture eﬀect on the diﬀusion of Cu ions in Cu/Ta2 O5 /Pt and Cu/SiO2 /Pt resistance switches:
a ﬁrst-principles study
B. Xiao and S. Watanabe: Sci. Technol. Adv. Mater. 20 (2019) 580.
6. First-principles study of Li-ion distribution at γ-Li3 PO4 /metal interfaces
K. Shimizu, W. Liu, W. Li, S. Kasamatsu, Y. Ando, E. Minamitani, and S. Watanabe: Phys.
Rev. Mater. 4 (2020) 015402.
7. The eﬀect of phonon anharmonicity on the lattice thermal conductivity of rare-earth pyrochlores:
A ﬁrst-principles study
Z. Li, Y. Xing, S. Watanabe,and W. Pan: Ceram. Int’l 46 (2020) 9947.
8. Atomistic Simulations for Understanding Microscopic Mechanism of Resistive Switches
S. Watanabe and B. Xiao: in M. Aono (Ed.) ”Atomic Switch: From Invention to Practical Useand Future Prospects” (Springer, 2020), p. 95.
YAMADA, Atsuo [ C class; 5000 (B), 750 (C) ] (94)
— First-principles analyses on the cathode materials for rechargeable batteries
1. Sodium‐ and Potassium‐ Hydrate Melts Containing Asymmetric Imide Anions for High‐ Voltage
Aqueous Batteries
Q. Zheng, S. Miura, K. Miyazaki, S. Ko, E. Watanabe, M. Okoshi, C.‐ P. Chou, Y. Nishimura,
H. Nakai, T. Kamiya, T. Honda, J. Akikusa, Y. Yamada, A. Yamada: Angew. Chem. Int. Ed.
58 (2019) 2358.
YAMADA, Atsushi [ C class; 500 (B), 300 (C) ] (231)— Superconductivity and magnetic properties of the Hubbard model
YAMAJI, Youhei [ E class; 15000 (B), 2300 (C) ] (200)— Numerical studies on energy current correlations in frustrated quantum spin systems
1. Possible Kitaev Quantum Spin Liquid State in 2D Materials with S=3/2
C. Xu, J. Feng, M. Kawamura, Y. Yamaji, Yousra Nahas, S. Prokhorenko, Y. Qi, H. Xiang, L.
Bellaiche: Phys. Rev. Lett. 124(2020) 087205.
YAMAMOTO, Kaoru [ B class; 500 (B), 80 (C) ] ()— First-principles calculation of thermoelectric properties for magnetic tunneling junctions and giant
magneto-resistance devices
YAMAMOTO, Norifumi [ B class; 700 (B), 90 (C) ] (175)— Theoretical Study on the Aggregation-Induced Emission

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YAMASHITA, Koichi [ C class; 3000 (B), 0 (C) ] (129)— Large scale ab initio calculations on the fundamental processes of solar energy convergence devices
and on designing principles for new materials
1. Simulation of Conductive Atomic Force Microscopy of Organic Photovoltaics by Dynamic Monte
Carlo Method
E. Kawashima, M. Fujii, and K. Yamashita: Chem. Lett. 48 (2019) 513.
2. Laser-induced ﬂuorescence of the CHFCHO radical and reaction of OH radicals with halogenatedethylenes
I. Masumoto, N. Washida, S. Inomata, A. Muraoka, and K. Yamashita: J. Chem. Phys. 150(2019) 174302.
3. A route for minimizing emissions: sun-mediated processes & clean batteries
G. Giorgi, K. Yamashita, M. Palummo, and S. Fabris: Curr. Opin. Green. Sustain. Chem. 17(2019) A1.
4. Entropy Promotes Charge Separation in Bulk Heterojunction Organic Photovoltaics
E. Kawashima, M. Fujii, and K. Yamashita: J. Photochem. Photobiol. A: Chem. 382 (2019)111875.
5. Importance of Side-Chains on Molecular Characteristics of Interacting Organic Molecules
K. Mishima, K. Yamashita: ACS Omega 4 (2019) 10396.
6. Application of accelerated long-range corrected exchange functional [LC-DFT(2Gau)] to periodic
boundary condition systems: CO adsorption on Cu(111) surface
K. Mishima, M. Kaneko, J.-W. Song, H. Kawai, K. Yamashita, and K. Hirao: J. Chem. Phys.
152 (2020) 104105.
YAMASHITA, Tomoki [ C class; 2500 (B), 600 (C) ] (127)— Development of algorithms in crystal structure prediction
YAMAUCHI, Kunihiko [ C class; 5000 (B), 0 (C) ] (102)— First-principles density functional calculations of transition-metal magnetic oxides
1. Bulk Rashba eﬀect in multiferroics: A theoretical prediction for BiCoO3
Kunihiko Yamauchi, Paolo Barone, Silvia Picozzi: Phys. Rev. B 100 (2019) 245115.
2. Conversion of a conventional superconductor into a topological superconductor by topologicalproximity eﬀect
C.X. Trang, N. Shimamura, K. Nakayama, S. Souma, K. Sugawara, I. Watanabe, K. Yamauchi,
T. Oguchi, K. Segawa, T. Takahashi, Yoichi Ando, and T. Sato: Nat. Commun. 11 (2020) 159.
3. Dimensionality reduction and band quantization induced by potassium intercalation in 1T-HfTe2
Y. Nakata, K. Sugawara, A. Chainani, K. Yamauchi, K. Nakayama, S. Souma, P.-Y. Chuang,
C.-M. Cheng, T. Oguchi, K. Ueno, T. Takahashi, and T. Sato: Phys. Rev. Materials 3 (2019)071001(R).
4. Evidence for bulk nodal loops and universality of Dirac-node arc surface states in ZrGeXc (Xc =S, Se, Te)
Takechika Nakamura, Seigo Souma, Zhiwei Wang, Kunihiko Yamauchi, Daichi Takane, Hikaru
Oinuma, Kosuke Nakayama, Koji Horiba, Hiroshi Kumigashira, Tamio Oguchi, Takashi Takahashi,
Yoichi Ando, and Takafumi Sato: Phys. Rev. B 99 (2019) 245105.
5. Topology analysis for anomalous Hall eﬀect in the noncollinear antiferromagnetic states of Mn3AN(A = Ni, Cu, Zn, Ga, Ge, Pd, In, Sn, Ir, Pt)
Vu Thi Ngoc Huyen, Michi-To Suzuki, Kunihiko Yamauchi, and Tamio Oguchi: Phys. Rev. B
100 (2019) 094426.
6. Possible emergence of a skyrmion phase in ferroelectric GaMo4S8
Hui-Min Zhang, Jun Chen, Paolo Barone, Kunihiko Yamauchi, Shuai Dong, and Silvia Picozzi:
Phys. Rev. B 99 (2019) 214427.
YANAGISAWA, Susumu [ C class; 5000 (B), 0 (C) ] (100)— Implementation of the phonon analysis for organic semiconductor crystals— Structural distortion or defect in organic molecular thin ﬁlm: theoretical study
1. Determination of the ionization energy and the electron aﬃnity of organic molecular crystals from430

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo2.

3.

ﬁrst-principles: dependence on the molecular orientation at the surface
S. Yanagisawa: Jpn. J. Appl. Phys. 59 (2020) 031002.
Nanoscale First-Principles Electronic Structure Simulations of Materials Relevant to Organic Electronics
S. Yanagisawa and I. Hamada: In: T. Onishi (eds) Theoretical Chemistry for Advanced Nanomaterials. Springer, Singapore (2020) 89.
Enhancement of the GW space-time program code for accurate prediction of the electronic properties of organic electronics materials
S. Yanagisawa, T. Yamashita, and R. Egawa: Sustained Simulation Performance 2018 and 2019.
Springer (2020) 225.

YANAGISAWA, Takashi [ B class; 1100 (B), 150 (C) ] (229)— Study of strongly correlated electron systems based on optimization Monte Carlo method and ﬁrstprinciples calculations
1. Antiferromagnetism, Superconductivity and phase diagram in the two-dimensional Hubbard model
T. Yanagisawa: J. Phys. Soc. Jpn. 88 (2019) 054702.a
2. Mechanism of high-temperature superconductivity in correlated electron systems
T. Yanagisawa: Condensed Matter 2019 (2019) 57.a
3. Fractional Skyrmion and Absence of Low-lying Andreev Bound States in a Micro Fractional-ﬂux
Quantum Vortex
T. Yanagisawa: J. Phys. Soc. Jpn. 88 (2019) 104704.
4. Flat-band in Pyrochlore Oxides: A First-Principles Study
I. Hase, T. Yanagisawa, K. Kawashima: Nanomaterials 2019 (2019) 876.
5. Renormalization group analysis of the hyperbolic sine-Gordon model
T. Yanagisawa: Prog. Theor. Exp. Phys. 2019 (2019) 023A01.
6. Antiferromagnetism, Superconductivity and phase diagram in the three-band model of hightemperature superconductors
T. Yanagisawa: J. Phys. Conf. Ser. 1293 (2019) 012027.a
7. Electronic Structure of Novel Non-centrosymmetric Superconductor Mg2 Rh3 P
I. Hase, T. Yanagisawa, A. Iyo, H. Fujihisa, Y. Goto, H, Eisaki, K. Kawashima: J. Phys. Conf.
Ser. 1293 (2019) 012028.
8. Flattened remnant-ﬁeld distribution in superconducting bilayer
Y. Tanaka, H. Yamamori, T. Yanagisawa, S. ooi, M. Tachiki, S. Arisawa: Physica C 567 (2019)1253489.
9. Phase diagram of cuprate high-temperature superconductors based on the optimization Monte
Carlo method
T. Yanagisawa, M. Miyazaki, K. Yamaji: Modern Phys. Lett. (2019) in press.a
10. Phase diagram and mechanism of superconductivity in strongly correlated electrons
T. Yanagisawa, M. Miyazaki, K. Yamaji: J. Super. Novel Magne. (2019) in press.a
11. Electronic structure of novel superconductor doped ZrPSe
I. Hase, T. Yanagisawa, H. Kito et al.: J. Phys. Conf. Ser. (2019) in press.
YASUDA, Chitoshi [ B class; 700 (B), 90 (C) ] (334)— Magnetism in the system with the multiple-spin exchange interactions
YOKO, Akira [ B class; 1400 (B), 180 (C) ] (150)— Theoretical calculation of solvation and reaction in supercritical ﬂuids— Theoretical study for structure and property of organic modiﬁed metal oxide nanoparticles
YOKOI, Tatsuya [ C class; 3000 (B), 500 (C) ] (117)— Machine-learning-driven molecular simulations for grain-boundary atomic dynamics
YOSHIDA, Tsuneya [ C class; 7500 (B), 0 (C) ] (213)— Non-Hermitian topological phenomena in strongly correlated systems— Novel topological phenomena induced by strongly correlated dynamics

431

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

1.
2.
3.
4.
5.
6.
7.
8.

9.

Exceptional band touching for strongly correlated systems in equilibrium
Tsuneya Yoshida, Robert Peters, Norio Kawakami, Yasuhiro Hatsugai: arXiv:2002.11265
Antiferromagnetic Topological Insulator in Three-Dimensional Heavy-Fermion Systems
Kazuhiro Kimura, Tsuneya Yoshida, and Norio Kawakami: JPS Conf. Proc. 30, 011012 (2020).
Relationship between exceptional points and the Kondo eﬀect in f-electron materials
Yoshihiro Michishita, Tsuneya Yoshida, and Robert Peters: Phys. Rev. B 101, 085122 (2020).
Mirror skin eﬀect and its electric circuit simulation
Tsuneya Yoshida, Tomonari Mizoguchi, and Yasuhiro Hatsugai: arXiv:1912.12022
Non-Hermitian fractional quantum Hall states
Tsuneya Yoshida, Koji Kudo, and Yasuhiro Hatsugai: Scientiﬁc Reports 9, 16895 (2019).
Higher-Order Topological Mott Insulators
Koji Kudo, Tsuneya Yoshida, and Yasuhiro Hatsugai: Phys. Rev. Lett. 123, 196402(2019).
Chiral-symmetry protected exceptional torus in correlated nodal-line semimetals
Kazuhiro Kimura, Tsuneya Yoshida, and Norio Kawakami: Phys. Rev. B 100, 115124 (2019)
Eﬃcient method to compute Z4 -indices with glide symmetry and applications to Möbius materials,
CeNiSn and UCoGe
Tsuneya Yoshida, Akito Daido, Norio Kawakami, and Youichi Yanase: Phys. Rev. B 99, 235105(2019).
Exceptional rings protected by emergent symmetry for mechanical systems
Tsuneya Yoshida and Yasuhiro Hatsugai: Phys. Rev. B 100, 054109 (2019).

YOSHIDOME, Takashi [ C class; 500 (B), 550 (C) ] (325)— Investigation of dynamics of a supercooled liquid and proteins using the free-energy landscape
1. Eﬀects of a Low-Pass Filter on the Classiﬁcation of Protein Electron-Density Maps in termsof Structural Polymorphism using Manifold Learning: A Simulation Study for Cryo-Electron
Microscopy Experiments
N. Takano and T. Yoshidome: J. Phys. Soc. Jpn. 88 (2019) 094801.
YOSHINO, Hajime [ C class; 9000 (B), 0 (C) ] (35)
— Phase transitions of an antiferromagnetic Heisenberg spin model with a dynamical Jahn-Teller eﬀect
on a pyrochlore lattice— Simultaneous spin and Jahn-Teller glass transitions in a model frustrated system on pyrochlore lattice
1. Spin-Orbital Glass Transition in a Model of a Frustrated Pyrochlore Magnet without Quenched
DisorderKota Mitsumoto, Chisa Hotta and Hajime Yoshino: Phys. Rev. Lett. 124, 087201 (2020).
YUKAWA, Satoshi [ B class; 800 (B), 100 (C) ] (332)— Statistical Properties in a Branching Network

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2 SCCMS Projects
FUJITA, Takatoshi [ 7000 (B), 0 (C) ] (371)— Development of Fragment-Based GW/BSE Method and Application to Organic Optoelectronic Materials— Large-scale GW+BSE excited-state calculations for organic optoelectronic materials
1. Charge-transfer excited states in the donor/acceptor interface from large-scale GW calculations
T. Fujita, Y. Noguchi, T. Hoshi, J. Chem. Phys. 151 (2019) 114109.
2. Numerical aspect of large-scale electronic state calculation for ﬂexible device material
T. Hoshi, H. Imachi, A. Kuwata, K. Kakuda, T. Fujita, H Matsui, Japan J. Indust. Appl. Math.
36 (2019) 685.
FUKUSHIMA, Tetsuya [ 5000 (B), 500 (C) ] (372)— Data-driven materials design for new functional high entropy alloys
1. Theoretical prediction of maximum Curie temperatures of Fe-based dilute magnetic semiconductors by ﬁrst-principles calculations
T. Fukushima, H. Shinya, A. Masago, K. Sato and H. Katayama-Yoshida: Appl. Phys. Exp. 12(2019) 063006
2. Experimental veriﬁcation of the origin of positive linear magnetoresistance in CoFe(V1 − xMnx)Si
Heusler alloys
S. Yamada, S. Kobayashi, A. Masago, L. S. R. Kumara, H. Tajiri, T. Fukushima, S. Abo, Y.
Sakuraba, K. Hono, T. Oguchi, and K. Hamaya: Phys. Rev. B 100 (2019) 195137
3. High Curie temperature in Eu-doped GaN caused by volume-compensated Ga-vacancy
A. Masago, H. Shinya, T. Fukushima, K. Sato, and H. Katayama-Yoshida: AIP Advances 10(2020) 025216
4. Valence states and the magnetism of Eu ions in Eu-doped GaN
T. Nunokawa, Y. Fujiwara, Y. Miyata, N. Fujimura, T. Sakurai, H. Ohta, A. Masago, H. Shinya,
T. Fukushima, K. Sato, and H. Katayama-Yoshida: J. Appl. Phys. 127 (2020) 083901
GOHDA, Yoshihiro [ 5000 (B), 500 (C) ] (99)
— First-principles study of magnetic-material interfaces
1. First-principles study on surface stability and interface magnetic properties of SmFe12
Y. Ainai, T. Shiozawa, Y. Tatetsu, and Y. Gohda: Appl. Phys. Express 13, 045502 (2020).
2. First-principles study of crystalline Nd-Fe alloys
Y. Ainai, Y. Tatetsu, A. Terasawa, and Y. Gohda: Appl. Phys. Express 13, 017006 (2020).
3. Enhancement of magnetoelectric coupling by insertion of Co atomic layer into Fe3 Si/BaTiO3 (001)interfaces identiﬁed by ﬁrst-principles calculations
Y. Hamazaki and Y. Gohda: J. Appl. Phys. 126, 233902 (2019).
4. Great Diﬀerences between Low-Temperature Grown Co2 FeSi and Co2 MnSi Films on SingleCrystalline Oxides
K. Kudo, Y. Hamazaki, S. Yamada, S. Abo, Y. Gohda, and K. Hamaya: ACS Appl. Electron.
Mater. 1, 2371 (2019).
5. Eﬃcient Algorithm Based on Liechtenstein Method for Computing Exchange Coupling Constants
Using Localized Basis Set
A. Terasawa, M. Matsumoto, T. Ozaki, and Y. Gohda: J. Phys. Soc. Jpn. 88, 114706 (2019).
HOSHI, Takeo [ 10000 (B), 1000 (C) ] (76)
— Massively parallel electronic structure calculation and data-driven science for next-generation supercomputers
1. Kω –Open-source library for the shifted Krylov subspace method
Takeo Hoshi, Mitsuaki Kawamura, Kazuyoshi Yoshimi, Yuichi Motoyama, Takahiro Misawa,
Youhei Yamaji, Synge Todo, Naoki Kawashima, Tomohiro Sogabe: arXiv:2001.08707
2. Two-stage data-analysis method for total-reﬂection high-energy positron diﬀraction (TRHEPD)

433

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.

4.

5.

6.

7.

8.

9.

Kazuyuki Tanaka, Izumi. Mochizuki, Takashi Hanada, Ayahiko Ichimiya, Toshio Hyodo, andTakeo Hoshi: Submitted; Preprint:https://arxiv.org/abs/2002.12165
Development of data-analysis software for total-reﬂection high-energy positron diﬀraction (TRHEPD)
Kazuyuki Tanaka, Takeo Hoshi, Izumi Mochizuki, Takashi Hanada, Ayahiko Ichimiya, Toshio Hyodo: Acta. Phys. Pol. A 137, 188-192 (2020).
An a posteriori veriﬁcation method for generalized Hermitian eigenvalue problems in large-scale
electronic state calculations
Takeo Hoshi, Takeshi Ogita, Katsuhisa Ozaki, Takeshi Terao: J. Comp. Appl. Math. 376,
112830/1-13 (2020).
Charge-Transfer Excited States in the Donor/Acceptor Interface from Large-Scale GW Calculations
Takatoshi Fujita, Yoshifumi Noguchi, Takeo Hoshi: J. Chem. Phys. 151, 114109/1-8 (2019).
EigenKernel - A middleware for parallel generalized eigenvalue solvers to attain high scalability
and usability
Kazuyuki Tanaka, Hiroto Imachi, Tomoya Fukumoto, Akiyoshi Kuwata, Yuki Harada, Takeshi
Fukaya, Yusaku Yamamoto, Takeo Hoshi: Japan J. Indust. Appl. Math 36, 719-742 (2019).
Numerical aspect of large-scale electronic state calculation for ﬂexible device material
Takeo Hoshi, Hiroto Imachi, Akiyoshi Kuwata, Kohsuke Kakuda, Takatoshi Fujita, Hiroyuki Matsui: Japan J. Indust. Appl. Math 36, 685-698 (2019).
Recent progress in large-scale electronic state calculations and data-driven sciences
Takeo Hoshi and Satoshi Ito: Chap. 14 of Handbook of Silicon Based MEMS Materials andTechnologies 3rd Ed., Elsevier (2020).
Numerical methods for large scale electronic state calculation on supercomputer
Takeo Hoshi, Yusaku Yamamoto, Tomohiro Sogabe, Kohei Shimamura, Fuyuki Shimojo, Aiichiro
Nakano, Rajiv Kalia, Priya Vashishta: Chap. 15 of 21st Century Nanoscience - A Handbook:
Nanophysics Sourcebook (Volume One), CRC Press (2019).

IITAKA, Toshiaki [ 10000 (B), 1000 (C) ] (379)— Order-disorder transition in the superhigh-pressure phase of Mg2SiO4IMADA, Masatoshi [ 20000 (B), 2000 (C) ] (197)— Studies on Quantum Spin Liquids in Materials with Strong Spin-Orbit Interaction— Studies on quantum spin liquids in molecular conductors based on ﬁrst-principles Hamiltonian
1. Charge dynamics of correlated electrons: Variational description with inclusion of composite
fermions
Kota Ido, Masatoshi Imada, Takahiro Misawa: Phys. Rev. B 101 (2020) 075124.
2. Ab initio study of superconductivity and inhomogeneity in a Hg-based cuprate superconductor
Takahiro Ohgoe, Motoaki Hirayama, Takahiro Misawa, Kota Ido, Youhei Yamaji, Masatoshi
Imada: Phys. Rev. B 101 (2020) 045124.
3. Eﬀective Hamiltonian for cuprate superconductors derived from multiscale ab initio scheme withlevel renormalization
Motoaki Hirayama, Takahiro Misawa, Takahiro Ohgoe, Youhei Yamaji, Masatoshi Imada: Phys.
Rev. B 99 (2019) 245155.
4. Ab initio derivation of an eﬀective Hamiltonian for the La2 CuO4 /La1 .55Sr0 .45CuO4 heterostructure
Terumasa Tadano, Yusuke Nomura, Masatoshi Imada: Phys. Rev. B 99 (2019) 155148.
KAWAKATSU, Toshihiro [ 20000 (B), 2000 (C) ] (378)— Multiscale simulations on complex multiphase ﬂows
1. Coupling Finite Element Method with Large Scale Atomic/Molecular Massively Parallel Simulator(LAMMPS) for Hierarchical Multiscale Simulations
T. Murashima, S. Urata, S. Li: Euro. Phys. J. B 92 (2019) 211.
2. ミクロスケールとマクロスケールのシミュレーション連成による高分子材料系のマルチスケールシ
ミュレーション
村島隆浩: 日本化学会情報化学部会誌 37 (2019) 87.

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3.
4.

Multiscale Modeling of Plasticity in Amorphous & Polymeric Materials
S. Li, S. Urata, T. Murashima: IACM Expressions 46 (2020) 10.
Lagrangian Multiscale SImulation of Complex Fluids. I.
Y. Morii, T. Kawakatsu: to be submitted.

KAWASHIMA, Naoki [ 20000 (B), 2000 (C) ] (239)— Application of Tensor Network Method to Condensed Matter Physics
1. Tensor network wavefunction of S = 1 Kitaev spin liquids
Hyun-Yong Lee, Naoki Kawashima, and Yong Baek Kim:arXiv:1911.07714
2. Boundary conformal spectrum and surface critical behavior of classical spin systems:A tensor
network renormalization study
Shumpei Iino, Satoshi Morita, and Naoki Kawashima: Phys. Rev. B 101, 155418 (2020)
3. Magnetic ﬁeld induced quantum phases in a tensor network study of Kitaev magnets
Hyun-Yong Lee, Ryui Kaneko, Li Ern Chern, Tsuyoshi Okubo, Youhei Yamaji, Naoki Kawashima
and Yong Baek Kim: Nature Communications 11, 1639 (2020)
4. Abelian and non-Abelian chiral spin liquids in a compact tensor network
Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, Naoki Kawashima: Phys. Rev. B 101, 035140(2020)
5. Thermal-transport studies of kagom antiferromagnets
Minoru Yamashita, Masatoshi Akazawa, Masaaki Shimozawa, Takasada Shibauchi, Yuji Matsuda,
Hajime Ishikawa, Takeshi Yajima, Zenji Hiroi, Migaku Oda, Hiroyuki Yoshida, Hyun-Yong Lee,
Jung Hoon Han and Naoki Kawashima: J. Phys: Condens. Matter 32, 074001(11pp) (2019)
6. Entropy Governed by the Absorbing State of Directed Percolation
Kenji Harada and Naoki Kawashima: Phys. Rev. Lett. 123, 090601 (2019)
7. Boundary Tensor Renormalization Group
Shumpei Iino, Satoshi Morita, and Naoki Kawashima: Phys. Rev. B 100, 035449 (2019)
8. Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks
Hyun-Yong Lee, Ryui Kaneko, Tsuyoshi Okubo, and Naoki Kawashima: Phys. Rev. Lett. 123,
087203 (2019)9. Tensor-Ring Decomposition with Index-Splitting
Hyun-Yong Lee and Naoki Kawashima: J. Phys. Soc. Jpn. 89, 054003 (2020)
KOHYAMA, Masanori [ 20000 (B), 2000 (C) ] (360)— First-Principles Phase Field Mapping
1. A ﬁrst-principles phase ﬁeld method for quantitatively predicting multi-composition phase separation without thermodynamic empirical parameter
Swastibrata Bhattacharyya, Ryoji Sahara, and Kaoru Ohno: Nature Communications 10 (2019)3451.
2. Clear evidence of element partitioning eﬀects in a Ti-6Al-4V alloy by the ﬁrst-principles phaseﬁeld method
Thi Nu Pham, Kaoru Ohno, Riichi Kuwahara, and Swastibrata Bhattacharyya: J. Phys.: Cond.
Mat. ￥bf 32 (2020) 264001.
MATUBAYASI, Nobuyuki [ 5000 (B), 500 (C) ] (381)— Development of calculation method of chemical potential for long-chain polymer melt using all-atom
molecular dynamics simulation
1. Chain-Increment Method for Approaching the Chemical Potential of a Polymer with All-AtomModel
K. Yamada and N. Matubayasi: Macromolecules 53 (2020) 775.
MISAWA, Takahiro [ 10000 (B), 1000 (C) ] (366)— Numerical Study of Quantum Spin Liquid in Organic Conductors using Ab initio Calculation— Development of numerical method for calculating dynamical structure factors based on many-variablevariational Monte Carlo method
1. Eﬀective Hamiltonian for cuprate superconductors derived from multi-scale ab initio scheme with435

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2.
3.
4.
5.

6.

7.

level renormalization
Motoaki Hirayama, Takahiro Misawa, Takahiro Ohgoe, Youhei Yamaji, and Masatoshi Imada:
Phys. Rev. B 99, 245155 (2019).
Real-time evolution and quantized charge pumping in magnetic Weyl semimetals
Takahiro Misawa, Ryota Nakai, and Kentaro Nomura : Phys. Rev. B 100, 155123 (2019).
Spin nematics in frustrated spin-dimer systems with bilayer structure
Toshiya Hikihara, Takahiro Misawa, and Tsutomu Momoi : Phys. Rev. B 100, 214414 (2019).
Semi-quantized Spin pumping and Spin-orbit torques in topological Dirac Semimetals
Takahiro Misawa and Kentaro Nomura : Scientiﬁc Reports 9, 19659 (2019).
Ab initio study of superconductivity and inhomogeneity in a Hg-based cuprate superconductor
Takahiro Ohgoe, Motoaki Hirayama, Takahiro Misawa, Kota Ido, Youhei Yamaji and Masatoshi
Imada : Phys. Rev. B 101, 045124 (2020).
Charge dynamics of correlated electrons: Variational description with inclusion of composite
fermions
Kota Ido, Masatoshi Imada, and Takahiro Misawa : Phys. Rev. B 101, 075124 (2020).
Correlation eﬀects on the magnetization process of the Kitaev model
Kota Ido and Takahiro Misawa : Phys. Rev. B 101, 045121 (2020).

MIYAKE, Takashi [ 6000 (B), 0 (C) ] (376)— High performance permanent magnets and magnetic materials
1. Cerium as a possible stabilizer of ThMn12-type iron-based compounds: A ﬁrst-principles studya
Yosuke Harashima, Taro Fukazawa, and Takashi Miyake: Scripta Materialia 179 (2020) 12.
2. Adjusting the descriptor for a crystal structure search using Bayesian optimizationa Nobuya Sato,
Tomoki Yamashita, Tamio Oguchi, Koji Hukushima and Takashi Miyake: Phys. Rev. Mater. 4(2020) 033801.
3. Thermal decomposition of ThMn12 -type phase and its optimum stabilizing elements in SmFe12based alloys I. Dirba, Y. Harashima, H. Sepehri-Amin, T. Ohkubo, T. Miyake, S. Hirosawa, K.
Hono: J. Alloy Compounds 813 (2020) 152224.
4. Bayesian optimization of chemical composition: a comprehensive framework and its application
to RFe12 -type magnet compounds
Taro Fukazawa, Yosuke Harashima, Zhufeng Hou and Takashi Miyake: Phys. Rev. Mater. 3(2019) 053807.
5. Ensemble learning reveals dissimilarity between rare-earth transition-metal binary alloys withrespect to the Curie temperature
Duong-Nguyen Nguyen, Tien-Lam Pham, Viet-Cuong Nguyen, Hiori Kino, Takashi Miyake, HieuChi Dam: J. Phys. Materials 2 (2019) 034009.
NOGUCHI, Hiroshi [ 10000 (B), 1000 (C) ] (241)— Molecular Dynamics Simulation of Complex Fluids
1. Eﬀects of Cavitation on Karman Vortex Behind Circular-Cylinder Arrays: A Molecular Dynamics
Study
Y. Asano, H. Watanabe, and H. Noguchi: J. Chem. Phys. 152, 034501 (2020).
2. 分子動力学計算による複雑流体中のカルマン渦の解析
浅野 優太, 渡辺 宙志, 野口 博司: 分子シミュレーション研究会会誌 アンサンブル 22, 157 (2020).
OGUCHI, Tamio [ 5000 (B), 0 (C) ] (374)— Electron Theory on Secondary-Battery Materials
1. First-Principles Study of Na-Ion Battery Performance and Reaction Mechanism of Tin Sulﬁde as
Negative ElectrodeHiroki Kotaka, Hiroyoshi Momida, Ayuko Kitajou, Shigeto Okada, and Tamio Oguchi, Chem.
Rec. 19, 811 (2019).
2. First-Principles Study of X-Ray Absorption Spectra in NaFeSO4 F for Exploring Na-Ion Battery
Reactions
Hiroyoshi Momida, Ayuko Kitajou, Shigeto Okada, and Tamio Oguchi, J. Phys. Soc. Jpn. 88,
124709 (2019).

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3.

4.

Amorphous xNaF-FeSO4 Systems (1 ≤ x ≤ 2) with Excellent Cathode Properties for Sodium Ion
Batteries
A. Kitajou, H. Momida, T. Yamashita, T. Oguchi, and S. Okada, ACS Appl. Energy Mater. 2,5968 (2019).
Signiﬁcant Role of Oxygen Redox Reaction with O2 -Release in Li-Excess Cation-Disordered RockSalt Cathodes Li2+2x Mn1−x Ti1−x O4 : First-Principles Calculations
Motoyuki Hamaguchi, Hiroyoshi Momida, and Tamio Oguchi, Electrochimica Acta 330, 135286(2020).

OKAZAKI, Susumu [ 10000 (B), 1000 (C) ] (370)— Conversion and storage of energy - Fuel cells and secondary batteries: Research and development offundamental technologies of battery simulators
1. Hydrogen Permeation in Hydrated Perﬂuorosulfonic Acid Polymer Membranes: Eﬀect of Polymer
Crystallinity and Equivalent Weight
K. Takeuchi, A. Kuo, T. Hirai, T. Miyajima, S. Urata, S. Terazono, S. Okazaki, and W. Shinoda:
J. Phys. Chem. C, 123, 20628-20638 (2019)
2. Structure of Hydrated Crystal (Lc), Tilted Gel (Lβ ′ ), and Liquid Crystal (Lα) Phases of Linear
Alkylbenzene Sulfonate (LAS) Studied by X-ray Diﬀraction and Molecular Dynamics Simulation
K. Takeda, Y. Andoh, S. Shinoda, and S. Okazaki: Langmuir, 35, 9011-9019 (2019).
3. Molecular Behavior of Linear Alkylbenzene Sulfonate in Hydrated Crystal, Tilted Gel, and Liquid
Crystal Phases Studied by Molecular Dynamics Simulation
K. Takeda, Y. Andoh, S. Shinoda, and S. Okazaki: Langmuir, 35, 10877-10884 (2019).
4. Molecular dynamics study of solubilization of cyclohexane, benzene, and phenol into mixed micelles composed of sodium dodecyl sulfate and octaethylene glycol monododecyl ether
K. Takeda, K. Fujimoto, N. Yoshii, and S. Okazaki: J. Comput. Chem., 40, 2722-2729 (2019).
5. Fast multipole method for three dimensional systems with periodic boundary condition in two
directions
N. Yoshii, Y. Andoh, S. Okazaki: J. Comput. Chem., 41, 940-948 (2020).
6. Extension of the fast multipole method for the rectangular cells with an anisotropic partition tree
structure
Y. Andoh, N. Yoshii, S. Okazaki: J. Comput. Chem., 41, 1353-1367 (2020).
OSHIYAMA, Atsushi [ 20000 (B), 2000 (C) ] (44)— Exploration of new-functionality and high-performance semiconductor devices
1. Microscopic Identiﬁcation of Surface Steps on SiC by Density-Functional Calculations
K. Seino and A. Oshiyama: Proc. ICSRM2019
2. Energetics of the surface step and its morphology on the 3C-SiC(111) surface clariﬁed by thedensity-functional theory
K. Seino and A. Oshiyama: Appl. Phys. Exp. 13 (2020) 015506
3. Density-Functional Calculations for Structures and Energetics of Atomic Steps and their Implication for Surface Morphology on Si-face SiC Polar Surfaces
K. Seino and A. Oshiyama: Phys. Rev. B (2020) to be published4. A two-dimensional liquid-like phase on Ga-rich GaN (0001) surfaces evidenced by ﬁrst principles
molecular dynamics
K. M. Bui, M. Boero, K. Shiraishi and A. Oshiyama: Jpn. J. Appl. Phys. 59 (2020) SGGK04
5. Computational study of oxygen stability in vicinal m(10-10)-GaN growth by MOVPE
F. Shintaku, D. Yosho, Y. Kangawa, J.-I. Iwata, A. Oshiyama, K. Shiraishi, A. Tanaka aand H.
Amano: Appl. Phys. Exp. 13 (2020) 055507
6. Oxygen incorporation kinetics in vicinal m(10-10)-GaN growth by MOVPE
D. Yosho, F. Shintaku, Y. Inatomi, Y. Kangawa, J.-I. Iwata, A. Oshiyama, K. Shiraishi, A. Tanaka
and H. Amano: Phys. Sta. Solidi - Rapid Res. Lett. (2020) 2000142
OZAKI, Taisuke [ 10000 (B), 1000 (C) ] (383)— Study on thermodynamic properties and NOx redox reactions of ternary alloy nanoclusters by O(N)density functional calculations

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1.

Study on thermodynamic properties and NOx redox reactions of ternary alloy nanoclusters by
O(N) density functional calculations
S.-H. Hung, A. Hiroshi, Y. Osamu, and T. Ozaki, RSC Advances, in press.

SAITO, Susumu [ 5000 (B), 500 (C) ] ()— Materials design using B, C, and N for next-generation device
SHIBA, Hayato [ 10000 (B), 1000 (C) ] (363)— Molecular dynamics study of long-ranged ﬂuctuation and transport properties of electrolyte and glassy
liquids— Simulation of electrolyte liquids under constant potential bias
1. Local Density Fluctuation Governs the Divergence of Viscosity Underlying Elastic and Hydrodynamic Anomalies in a 2D Glass-Forming Liquid
H. Shiba, T. Kawasaki, and K. Kim: Phys. Rev. Lett. 123, 2655 (2019).
SUGINO, Osamu [ 10000 (B), 1000 (C) ] (361)— Priority project 5— energy conversion (chemical energy)
1. Nuclear quantum eﬀect for hydrogen adsorption on Pt(111)
L. Yan, Y. Yamamoto, M. Shiga, and O. Sugino: Phys. Rev. B 101, 165414 (2020)
2. Scaling Relation of Oxygen Reduction Reaction Intermediates at Defective TiO2 Surfaces
Y. Yamamoto, S. Kasamatsu, and O. Sugino: J. Phys. Chem. C 123, 19486 (2019)
TAKETSUGU, Tetsuya [ 5000 (B), 500 (C) ] (375)— Ab initio study toward abundant element nanocatalysts with less precious metals
1. Photo-Induced Pyramidal Inversion Behavior of Phosphines Involved with the Aggregation-Induced
Emission (AIE) Behavior
T. Machida, T. Iwasa, T. Taketsugu, K. Sada, and K. Kokado, Chemistry A European J., inpress.
2. Single-molecule resonance Raman eﬀect in a plasmonic nanocavity
R. B. Jaculbia, H. Imada, K. Miwa, T. Iwasa, M. Takenaka, B. Yang, E. Kazuma, N. Hayazawa,T. Taketsugu, and Y. Kim, Nature Nanotechnology, 15, (2020) 105.
3. Observations and theories of quantum eﬀects in proton transfer electrode processes
K. Sakaushi, A. Lyalin, and T. Taketsugu, Current Opinion in Electrochemistry, 19, (2020) 96.
4. Surface adsorption model calculation database and its application to activity prediction of heterogeneous catalysts
M. Kobayashi, H. Onoda, Y. Kuroda, and T. Taketsugu, J. Comput. Chem. Jap. 18, (2019) 251.
5. Single-Phase Borophene on Ir(111): Formation, Structure and Decoupling from the Support
N. A. Vinogradov, A. Lyalin, T. Taketsugu, A. S. Vinogradov, and A. Preobrajenski, ACS Nano,
13, (2019) 14511.
6. Roles of silver nanoclusters in surface-enhanced Raman spectroscopy
T. Tsuneda, T. Iwasa, and T. Taketsugu, J. Chem. Phys. 151, (2019) 094102.
7. Anharmonic Vibrational Computations with a Quartic Force Field for Curvilinear Coordinates
Y. Harabuchi, R. Tani, N. DeSilva, B. Njegic, M. S. Gordon, and T. Taketsugu, J. Chem. Phys.
151,(2019) 064104.
8. Additive-Dependent Iptycene Incorporation in Polyanilines: Insights into the Pentiptycene Clipping Eﬀect and the Polymerization Mechanism
W. S. Tan, T.-Y. Lee, S.-F. Tseng, Y.-F. Hsu, M. Ebina, T. Taketsugu, S.-J. Huang, and J.-S.
Yang, J. Chin. Chem. Soc. 66, (2019) 1141.
9. Synthesis of polyaminophosphonic acid-functionalized poly(glycidyl methacrylate) for the eﬃcientsorption of La(III) and Y(III)A. A. Galhoum, E. A. Elshehy, D. A. Tolan, A. M. El-Nahas, T. Taketsugu, K. Nishikiori, T.
Akashi, A. S. Morshedy, and E. Guibal, Chem. Eng. J. 375, (2019) 121932.
10. Suppression of Pyrite Oxidation by Ferric-catecholate Complexes: An Electrochemical Study
X. Li, M. Gao, N. Hiroyoshi, C. B. Tabelin, T. Taketsugu, and M. Ito, Minerals Eng. 138, (2019)
226.

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TOHYAMA, Takami [ 5000 (B), 500 (C) ] (369)— Cooperation Research with Big Experimental Facilities
1. Magnetic excitations in magnetization plateaus of a frustrated spin ladder
K. Sasaki, T. Sugimoto, T. Tohyama, and S. Sota: Phys. Rev. B 101, (2020) 144407.
2. Spin dynamics in the t-t′ -J model: Dynamical density-matrix renormalization group study
T. Tohyama, S. Sota, and S. Yunoki: submitted to Phys. Rev. B
YABANA, Kazuhiro [ 10000 (B), 1000 (C) ] (368)— Uniﬁed Photonic-Electronic Devices
YAMADA, Atsuo [ 5000 (B), 500 (C) ] (94)
— Dynamical analyses on electrolytes for Na-ion batteries
1. Sodium‐ and Potassium‐ Hydrate Melts Containing Asymmetric Imide Anions for High‐ Voltage
Aqueous Batteries
Q. Zheng, S. Miura, K. Miyazaki, S. Ko, E. Watanabe, M. Okoshi, C.‐ P. Chou, Y. Nishimura,
H. Nakai, T. Kamiya, T. Honda, J. Akikusa, Y. Yamada, A. Yamada: Angew. Chem. Int. Ed.
58 (2019) 2358.
YOSHIMI, Kazuyoshi [ 10000 (B), 1000 (C) ] (364, 388)
— Development of accuracy veriﬁcation method on analytic continuation results using cross validation
1. SpM: Sparse modeling tool for analytic continuation of imaginary-time Green s function
K. Yoshimi J. Otsuki, Y. Motoyama, M. Ohzeki, and H. Shinaoka: Comput. Phys. Commun.
244 (2019) 319.

439

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2 Doctor Theses
1.

ADACHI, Daiki
High-accuracy tensor renormalization group algorithms and their applications
The University of Tokyo, 2020-03

2.

ARAKI, Hiromu
Numerical study of higher order topological insulators by machine learning and Berry phases
Tsukuba University, 2020-03

3.

DOMON, Kaoru
Theory of novel excitonic order in the electron-hole systems with the multiple bands
Niigata University, 2020-03

4.

HAMAGUCHI, Motoyuki
First-Principles Investigations of Cation-Disordered Rock-Salt Type Oxides for Li-Ion Battery
CathodesOsaka University, 2020-03

5.

KANEKO, Kazuya
Quantum information-theoretic study of complexity in chaotic many-body dynamics
The University of Tokyo, 2020-03

6.

KATO, Daichi
Many-Variable Variational Monte Carlo Study of Unconventional Superconductivity in Multiband
Systems
Osaka University, 2020-03

7.

MANAF, Muhamad Nasruddin
Electronic Structure Calculation of Muonium in SiliconKanazawa University, 2019-09

8.

MINAMI, Susumu
First-Principles Study of Magneto-Thermoelectric Properties in Ferromagnetic Heusler Alloys
Kanazawa University, 2020-03

9.

MISHCHENKO, Petr
Quantum Monte Carlo study of the extended Kitaev models
The University of Tokyo, 2020-03

10. MIYAZAKI, Kasumi
Molecular simulation study on microscopic electrochemical stability of lithium-ion battery electrolyte
The University of Tokyo, 2020-03
11. MIYAZAKI, Yusuke
Molecular dynamics study of membrane pore formation induced by antimicrobial peptides
Nagoya University, 2020-03
12. OKAUE, Daijiro
Interfacial Polarization Eﬀects of Ionic-Liquid Dielectrics on Carrier Transports in Electric Double
Layer Organic Field Eﬀect Transistors
Osaka University, 2020-03

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

13. PARDEDE, IndraFirst-principles design of magnetic anisotropy in nanostructures by electric-ﬁeld, strain, and metalalloying
Kanazawa University, 2019-09
14. SAMPEI(UCHIDA), Kazuki
Electron Emission and Atom Evaporation under Femtosecond Laser Pulses Studied by TimeDependent Density Functional Theory
Tokyo University of Science, 2020-03
15. UEMATSU, Kazuki
Randomness-induced universal quantum spin liquids in frustrated magnets – Cooperation of frustration and randomness in quantum magnets –Osaka University, 2020-03
16. WELLA, Sasfan Arman
DFT Study of the Adsorption States of an Organic Molecule Overlayer and a Single Platinum
Atom on Graphene
Osaka University, 2019-09

441

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

2 Master Theses
1.

AINAI, Yuta
First-principles study on structures of Nd-Fe alloys
Tokyo Institute of Technology, 2020-03

2.

BABA, Keita
Electronic states of Si(111)-B surfaces with metallic adatoms
Tokyo Institute of Technology, 2020-03

3.

CHO, Sanghun
Theory of tunneling currents at Si-p/n junctions with potential modulations
Chiba University, 2020-03

4.

KONDO, Chihiro
Measurement of entanglement entropy by ground-state quantum Monte Carlo method
The University of Tokyo, 2020-03

5.

HAMAZAKI, YasunariFirst-principles calculations of magnetoelectric eﬀects at ferromagnetic-Heusler-alloy/BaTiO3 interfaces
Tokyo Institute of Technology, 2020-03

6.

HARA, Soichiro
Theoretical Calculations on Defect Properties of Two-Dimensional Topological Insulator W2 CO2The University of Tokyo, 2020-03

7.

HORI, AkihiroFirst-principles Study of Thermal Conductivity in Half-Heusler Thermoelectric Materials
Kanazawa University, 2020-03

8.

ICHIHASHI, Kodai
Role of impurities in wide band-gap semiconductors: magnetism and optics
Yokohama National University, 2020-03

9.

INOUE, Kouki
Theoretical study for thermodynamic properties of the spherical Kagome system {W72 V30 }Tokyo University of Science, 2020-03

10. KIKUCHI, Asuka
Density Functional Theory Study on Water Clusters on Cu(110)
Osaka University, 2020-03
11. KINOSHITA, TakahiroFirst-principles Theoretical Study of Graphene Adsorption on Metal Surfaces Including Van Der
Waals Correction
Osaka University, 2020-03
12. KIYOZAWA, Fumihito
Theoretical prediction of crystal structure by energy regression utilizing sparse representation
The University of Tokyo, 2020-03
13. KOSHINO, Koichi
HCl gas sensing principle of porphyrin functionalized solid-state device442

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Yokohama National University, 2020-03
14. MASAKI, Rina
Calculation of photoelectron spectroscopy in Rashba systems
Ochanomizu University, 2020-03
15. MIYAZAKI, Ryota
Atomic Structures and Electronic States of Organic Semiconductors using Van Der Waals Density
Functional
Osaka University, 2020-03
16. MIZOO, Yoshiki
Microscopic theory for superconductivity in plutonium compounds: Analysis on the basis of a
two-orbital modelTokyo Metropolitan University, 2020-03
17. MORISHITA, Hirotaka
Structural Analysis of Ag-Adsorbed Si(001) Surface Using Neural Network Potentials
The University of Tokyo, 2020-03
18. MORIYAMA, Masaya
Stacking Eﬀect on Vacancy Stability of MoSe2
Shimane University, 2020-03
19. MURASE, Fumiya
Theoretical investigation of electrochemical promotion eﬀect in surface reaction of nitrogen
The University of Tokyo, 2020-03
20. NAKANO, Takashi
First-principles electronic structure calculations for the complexes of the screw dislocation and
Mg impurity in GaN
Nagoya University, 2020-03
21. NARUTA, Hiroki
Evaluation of entropy change associated with a formation of molecular networks in a ﬂuid
Ehime University, 2020-03
22. OCHIAI, Kesuke
appearing of ferromagnetism in Pt (100) ultra thin ﬁlms dependent on ﬁlm thickness
Keio University, 2020-03
23. OGINO, Takuhiro
Quantum phase transition in S = 1 two-leg XXZ spin-ladder systems with a four-spin interaction
The University of Tokyo, 2020-03
24. OHARA, Kazuhisa
Improving activity of dihydrofolate reductase by theoretical saturation mutagenesis
The University of Tokyo, 2020-03
25. SAITOH, Rikio
Ocygen storage property change of Ca2 AlMnO5+δ by element substitution
Hokkaido University, 2020-03
26. SANO, Mio
Studies toward the development of an interleukin-33 responsible for allergic asthma

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Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

The University of Tokyo, 2020-03
27. SASAKI, Shu
First-principles study of magnetic structures in manganese hydride
The University of Tokyo, 2020-03
28. SHIMIZU, Makoto
Spin ﬂuctuation theory for pressure and doping eﬀects in iron-based superconductors
Okayama University, 2020-03
29. SHIOZAWA, Tomoharu
Development of ﬁrst-principles method to evaluate magnetic refrigerants
Tokyo Institute of Technology, 2020-03
30. SHIRAISHI, Yuto
Charging-induced formation of ferroelectric orthorhombic HfO2: ﬁrst-principles study
Chiba University, 2020-03
31. SHIROTA, Riku
Study of magnetic compounds doped with impurities using ﬁrst principles calculations
Yokohama National University, 2020-03
32. SUDO, Kaori
Theoretical Study of Isotope Eﬀects on the Elastic Constants of Diamond
Osaka University, 2020-03
33. TACHI, Kyosuke
Global thermodynamics for inhomogeneous systems under extend force and heat conduction
Ibaraki University, 2020-03
34. TAKAMIZAWA, Taichi
Theoretical study of electronic and magnetic properties in thin ﬁlms of Weyl semimetals
The University of Tokyo, 2020-03
35. TAKAYA, Kei
Aridity dependence of the characteristic bifurcation angle in a model drainage network.
Osaka University, 2020-03
36. TAKEUCHI, Yuki
Magnetism in the double exchange model on the quasiperodic latticeTokyo Institute of Technology, 2020-03
37. TANAKA, Yoko
Theoretical study on electrical conduction properties of higher-order topological insulators
Ochanomizu University, 2020-03
38. TARUOKA, Yushi
First-Principles Calculations on Defects in Fe Based Sueprconductor LiFeAs
The University of Tokyo, 2020-03
39. TERASAKI, Tomoaki
Density functional theory study of formic acid dehydrogenation reaction activity of metal clusters
on light-element doped graphene
Hokkaido University, 2020-03

444

Activity Report 2019 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

40. USHIKI, Ryota
Theoretical analysis of diﬀusion mechanism of highly concentrated organic electrolytes for secondary batteries
The University of Tokyo, 2020-03
41. WATANABE, Kei
Growth of density ﬂuctuations during phase separation toward nucleation or spinodal decomposition
Ehime University, 2020-03
42. WATANABE, Takeru
The characteristic bifurcation angle in a nonlinear growth network model.
Osaka University, 2020-03
43. WICAKSONO, Yusuf
Theory on controlling the opening and closing of gapped Dirac cone in Ni/Graphene/Ni nanostructure
Osaka University, 2019-09
44. WU, Yan
Study of Defects in GaN with High-Dimensional Neural Network Potential
The University of Tokyo, 2019-09
45. YAMADE, Takufumi
Femtosecond Carrier Dynamics in Rare-earth Monooxide Thin Films
University of Fukui, 2020-03
46. YAMAGUCHI, Kotaro
Fist-principles study of Ni3Al surfaces
Kagoshima University, 2020-03
47. YAMAUCHI, Takuya
First-principles Theoretical Study on Oxygen Reduction Reaction over Pt(111)
Osaka University, 2020-03
48. YASUDA, Hironori
Theoretical study of spontaneous inversion symmetry breaking in a spin-orbital coupled metal
Cd2 Re2 O7
The University of Tokyo, 2020-03
49. YATA, Kohei
Study of VO diﬀusion barrier in SiO2 with lattice constant modulation
Shimane University, 2020-03
50. ZHOU, Ling
First-Principles Calculation of Electron and Phonon Properties of α-MoO3
The University of Tokyo, 2019-09445