Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

3.3

Strongly Correlated
Quantum Systems

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Numerical Studies on
Superconductivity of Bilaye Cuprates andMott Insulating States of Kitaev Materials
Youhei YAMAJI
Research Center for Materials Nanoarchitectonics, National Institute for Materials Science
Namiki, Tsukuba-shi, Ibaraki 305-0044

We have studied properties of two families of typical correlated electron systems, cuprate high-temperature superconductors and quantum-spin-liquid candidates, byusing many-variable variational Monte Carlo
methods [1]. As detailed below, we foundthat adjacent CuO2 layer does not improvestability of the d-wave superconductivity in
Hubbard-type hamiltonians [2], which are effective hamiltonians for the bilayer cuprates.
We also studied propertie of an ab initio hamiltonian of a Kitaev material, Na2 IrO3 [3, 4].
We studied the superconducting correlation
function at long distance, Pd , for the bilayer
t-t0 Hubbard model around U/t = 10 andt0 /t ⇠ 0.3. When we change a hole concentration, we found that the maximum Pd isquantitatively similar for the single-layer andbilayer t-t0 Hubbard models [2]. From the momentum distribution functions, nk , we estimated the size of the superconducting gap .
Then, the e↵ective attractive interaction, Vd ,pcan be inferred by Vd = / Pd . For both of
the single-layer and bilayer systems, we obtain
Vd ⇠ 1.7t. The variety of the optimal criticaltemperatures of cuprates may originate fromthe screening from apical oxygen and, thus,
mainly from the Hubbard U [5, 6].
We also studied the properties of Na2 IrO3
beyond low-energy spin degrees of freedom.
First, we clarified the ground state of the abinitio t2g hamiltonian [3]. We confirmed thatthe ground state shows the zigzag magnetic or-der, and found that the the amplitude of theMott gap is 750 meV, which is larger than 340
meV reported by combining the optical conductivity and photoemission spectroscopy [7].
The discrepancy originates from the MottAndern nature of the experimentally observed
samples of Na2 IrO3 due to disorders, where theMott gap is filled by in-gap localized states.
When the principle energy scales, the on-site(o↵-site) Coulomb repulsion U (Vij ) and spinorbit coupling ⇣so , are deviated from the abinitio values, the first order phase transitions
from the zigzag state to ferromagnetic andcharge ordered states are found.

References[1] T. Misawa, et al.: Comput. Phys. Commun. 235, 447 (2019).
[2] A. Iwano and Y. Yamaji: J. Phys. Soc.
Jpn. 91, 094702 (2022).
[3] Y. Yamaji, et al.: Phys. Rev. Lett. 113,107201 (2014).
[4] C. Xu and Y. Yamaji: in preparation.
[5] J.-B. Morée, et al.: Phys. Rev. B 106,
235150 (2022).
[6] M. T. Schmid, et al.: arXiv:2303.06672.
[7] R. Comin, et al.: Phys. Rev. Lett. 109,
266406 (2012).

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of strongly-correlated topologicalphenomena by exploiting first-principles calculations andmachine learning
Yukitoshi MOTOME
Department of Applied Physics,
The University of Tokyo, Bunkyo, Tokyo 113-8656
We have theoretically studied a variety of

the number of Co kagome layers and the

intriguing topological phenomena in strongly-

surface termination, which will be useful forcorrelated electron systems by using numericalfuture experimental fabrication [4].

methods including first-principles calculations(iii) Topological spin crystals as spin moire:and machine learning (project numbers: 2022-

Extending the research in last year, we clarified

Ca-0013 and 2022-Cb-0013). During the last

the effect of phase shift on skyrmion andfiscal year, we have achieved substantial

hedgehog

progress

topological phase diagrams [5]. We also

on

the

following

topics.

We

crystalsandelucidated

thesummarize the main results below.

showed that hedgehog crystals can be stabilized(i) Development of new theoretical methods:

in centrosymmetric cubic lattices by itinerant

We developed a new framework to solve

frustration mechanism [6]. In addition, we“inverse problem”, namely to construct adeveloped a new exact method to solve

proper Hamiltonian which exhibits desired

thermodynamics of effective infinite-range

physicalinteraction models [7], and by applying it weproperties,

by

using

automatic

differentiation [1]. We also proposed a new

unveiled

scheme for physical reservoir computing by

associated with pair creation and annihilation of

exploiting frustrated magnets, which is usefulemergent magnetic monopoles [8].

to realize efficient parallel computing in both(iv) Kitaev quantum spin liquids: By using thespace and time [2,3].

pseudo-fermion(ii) Topological properties of thin films of Weylgroup (PFFRG) method, we clarified thesemimetals: Studying the structural, electronic,

feasibility of Kitaev quantum spin liquids inand magnetic properties of atomically thinultracold polar molecules [9], a complete phasefilms of Co-based shandite by first-principles

diagram for the Kitaev-Heisenberg model withcalculations, we clarified the changes ofarbitrary spin length S [10], and the phasemagnetism and band topology with respect todiagram for the S=1/2 Kitaev-Heisenberg

190

hiddentopological

functionaltransitions

renormalization

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

model on a three-dimensional hyperhoneycomb

preprint (arXiv:2212.09026).

lattice [11]. We also unveiled several exotic[5] K. Shimizu, S. Okumura, Y. Kato, and Y.

phases, including multiple-q chiral phases andMotome, Phys. Rev. B 105, 224405 (2022).

chiral spin liquid, in competing region between[6] S. Okumura, S. Hayami, Y. Kato, and Y.

spin nematics and spin liuqids in the S=1

Motome, J. Phys. Soc. Jpn. 91, 093702 (2022).

Kitaev[7] Y. Kato and Y. Motome, Phys. Rev. B 105,

model

with

bilinear-biquadraticinteractions by using the SU(3) formalism [12].

174413 (2022).

We elucidated linear and nonlinear thermal[8] Y. Kato and Y. Motome, Phys. Rev. B 107,transport in the presence of both uniform and094437 (2023).

staggered magnetic fields [13]. In addition, we[9] K. Fukui, Y. Kato, J. Nasu, and Y. Motome,

clarified that the dynamical spin transport

Phys. Rev. B 106, 014419 (2022).

induced by an AC magnetic field applied to an[10] K. Fukui, Y. Kato, J. Nasu, and Y. Motome,edge of the system is useful for the

Phys. Rev. B 106, 174416 (2022).

identification of fractional excitations in the[11] K. Fukui, Y. Kato, and Y. Motome,

Kitaev quantum spin liquids [14]. Furthermore,

preprint (arXiv:2303.09156).

we found a phase transition in the quantum spin[12] R. Pohle, N. Shannon, and Y. Motome,

liquid phase under a magnetic field in α-RuCl3

Phys. Rev. B 107, L140403 (2023).

in collaboration with experimentalists [15]. We[13] K. Nakazawa, Y. Kato, and Y. Motome,

also wrote a review article (in Japanese) [16] inPhys. Rev. B 105, 165152 (2022).

a special issue for “New Developments on the[14] T. Misawa, J. Nasu, and Y. Motome,

Physics of Kitaev Spin Liquids” edited by the

preprint (arXiv:2304.00528).

author and coworkers [17].

[15] S. Suetsugu, Y. Ukai, M. Shimomura, M.
Kamimura, T. Asaba, Y. Kasahara, N. Kurita, H.

References

Tanaka, T. Shibauchi, J. Nasu, Y. Motome, and[1] K. Inui and Y. Motome, Commun. Phys. 6,

Y. Matsuda, J. Phys. Soc. Jpn. 91, 124703

37 (2023).

(2022).

[2] K. Kobayashi and Y. Motome, preprint[16] 張 成燻、求 幸年：固体物理 57, 757(arXiv:2302.14496).

(2022).

[3] 特願 2023-025883「情報処理システム、[17] 固体物理特集号 57, 613-784 (2022), "キ

情報処理方法およびプログラム」求 幸年、

タエフスピン液体の新展開" (編集委員：芝小林海翔（2023 年 2 月 22 日出願）

内孝禎・遠山貴巳・求 幸年)[4] K. Nakazawa, Y. Kato, and Y. Motome,

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study on elementaly excitations andoptical control of topological phases in the
spin-charge coupled magnets
Rintaro ETO and Masahito MOCHIZUKI
Department of Applied Physics, Waseda University
Okubo, Shinjuku-ku, Tokyo 169-8555

We have theoretically studied elementaly
excitations and photoinduced topologicalphases in the Kondo-lattice magnets withcouplings between spin and charge degrees
of freedom (project ID: 2022-Ca-0012, 2022Cb-0014). Results of these projects are listed
below.

(a)

(b)

(c)

Figure 1: (a) Schematic of the quadruple-Q
hedgehog lattice. Magenta and cyan balls represent hedgehogs and antihedgehogs, respectively. Red and blue dashed lines represent
the Dirac strings A (vortex type) and B (antivortex type), respectively. (b),(c) Enlargements of the (b) hedgehog and (c) antihedgehog. Gray arrows denote local emergent magnetic fields.
(i) Spin-wave excitations in the quadrupleQ magnetic hedgehog lattices in 3D chiralmagnets: We have theoretically studied thespin-wave modes of the quadruple-Q magnetic hedgehog lattices in 3D chiral magnets[Fig. 1(a)] [1]. First, we constructed a microscopic Kondo-lattice model on the 3D cubic
lattice, which hosts the quadruple-Q hedgehog
lattice spin textures as the ground state.
In this model, interplay of the second- andfourth-order spin-spin interactions mediatedby nested Fermi surfaces is a key to stabilizing
the hedgehog lattice spin textures.
The
hedgehog lattice spin textures in this model
have two types of Dirac strings connecting
a hedgehog [Fig. 1(b)] and an antihedgehog[Fig. 1(c)], the vortex-type strings A andthe antivortex-type strings B. Using thismodel, we studied the spin-wave excitationsof the hedgehog lattice spin textures underan external magnetic field (∥ [001]) by usinglarge-scale adiabatic spin-dynamics simulations based on the kernel polynomial method.
By calculating the microwave absorption
spectra for microwave polarization parallel to
the Dirac strings (i.e. ∥ [001]), we found three
spin-wave nmodes, which are named L1, L2,and L3, in order from the lowest to highest
frequency. These modes are spatially localized
at the Dirac strings and are associated withtranslational motion of the Dirac strings. In
particular, the disappearance of L2 mode,
which is localized at the strings B, is observed simultaneously with the field-induced
hedgehog-antihedgehog pair annihilation at
the strings B.

192

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo(b)

freedom of the honeycomb lattice. This work
will extend the scope of Floquet engineering tomagnetic materials with sublattice degrees of
freedom of magnetic origin.

(a)References[1] R. Eto and M. Mochizuki, in preparation.
[2] R. Eto and M. Mochizuki, in preparation.

Figure 2: (a) Schematic of the three-sublatticeferrimagnetic order. Majority spins form ahoneycomb network. (b) Single-particle spectrum of a Floquet Chern insulator state. Greenlines represent the Floquet states. Numbers
are the Chern numbers of the corresponding
bands.
(ii) Floquet topological phases in the Dirac
half-metallic ferrimagnet: We have theoretically investigated photoinduced topologicalphases in the Dirac half-metallic state in the
spin-charge coupled Kondo-lattice magnets [2].
We here considered the three-sublattice ferrimagnetic order on the 2D triangular latticewhich appears spontaneously when the conduction electron filling is 1/3 [Fig. 2(a)]. We
analyzed this model using the Floquet theory
and found two types of Floquet Chern insulator (FCI) states with gapped spin-polarized
Dirac bands. One is associated with the gap
opening at K point [Fig. 2(b)], whereas theother originates from the gap closing and reopening at M point. The appearance of the former FCI state was also confirmed in our analysis of the periodic Anderson model, from which
the Kondo-lattice model is derived via the perturbational calculation. Both of these FCIstates are induced not by the first-order but by
the higher-order terms in the high-frequency
expansion, and are distinct from conventional
ones induced by the first-order terms associated with the original sublattice degrees of193

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Studies on superconductivity in trestle-type lattices
KAZUHIKO KUROKI
Department of Physics, Osaka University
1-1 Machikaneyama, Toyonaka, Osaka, 560-0043, JapanINTRODUCTION

Most cuprate superconductors possess CuO2
planes, which are considered to play the main rolein the occurrence of superconductivity. One exception is (Sr,Ca)14 Cu24 O41 [1], which consists of
two-leg ladder and chain structures. Yet anotherpossible example is Pr2 Ba4 Cu7 O15−δ [2]. This material is constructed from alternating stacking of
PrBa2 Cu3 O7 and PrBa2 Cu4 O8 , and does have
CuO2 planes, but they are considered to be insulating. There have been suggestions that the doublechain structure in PrBa2 Cu4 O8 is responsible forthe superconductivity, and some theoretical studies support this possibility[3–5]. Quite recently,
there has been stronger evidences that the doublechain structure is responsible for the occurrence ofsuperconductivity[6].

FLEX STUDIES ON THE HUBBARD
MODEL ON A TRESTLE-TYPE LATTICE

The double-chain structure can be modeled by a
Hubbard model on a trestle-type lattice, with intrachain hopping t2 and interchain hopping t1 . Thismodel can further be considered as a single band
one-dimensional system with nearest (t1 ) and next
nearest (t2 ) neighbor hoppings. We theoreticallystudied this model using the ﬂuctuation exchange(FLEX) approximation. We have varied t2 /t1 aswell as the band ﬁlling, and obtained the eigenvalueof the Eliashberg equation at a ﬁxed temperature,
which measures tendency towards superconductivity. Depending on the parameter values, there canbe either two or four Fermi points because the band
structure has a double-well shape. The case where
there are four Fermi points resembles the situation
for the two-leg ladder systems. We ﬁnd that the

eigenvalue of the Eliashberg equation becomes thelargest when the band intersects the Fermi level at
two Fermi points and also barely touches the Fermi
level at two other points. This is in fact reminiscentof the situation where one of the bands is incipientin the two-leg ladder system[7]. Studies applying
other many-body methods to this model are underway in order to verify these FLEX results.

FIRST-PRINCIPLES MODELCONSTRUCTION OF PR2 BA4 CU7 O15−δ

In order to obtain a realistic model of
Pr2 Ba4 Cu7 O15−δ , we have performed ﬁrst principles band calculation of this material using VASP,
and obtained a tightbinding model for the doublechain structure through wannierization. A relatively large t1 /t2 ratio is obtained, consistent withprevious studies[3–5]. Many-body study of this realistic model is now underway. An important point
we are focusing on is (i) the band ﬁlling of the
double-chain structure as a function of oxygen deﬁciency δ and (ii) the origin of the relatively large
t1 /t2 , which is essential in obtaining the tendency
toward superconductivity.

[1] M. Uehara et al., J. Phys. Soc. Jpn. 65, 2764 (1996).
[2] M. Matsukawa et al., Physica C 411, 1011 (2004).
[3] K. Sano, Y.Ono, and Y. Yamada, J. Phys. Soc. Jpn.
74, 2885 (2005).
[4] T. Nakano and K. Kuroki, Phys. Rev. B 76, 014515(2007).
[5] T. Habaguchi et al., J. Phys. Soc. Jpn. 80, 024708(2011).
[6] S. Nishioka et al., Appl. Phys. Exp. 15, 023001(2022).
[7] K. Matsumoto, D. Ogura, and K. Kuroki, Phys.
Rev. B 97, 014516 (2018).

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

First-principles calculations of dynamical susceptibilities for strongly
correlated materials
Hiroshi SHINAOKA
Department of Physics, Saitama University, Saitama 338-8570
research has been conducted as a collaboration
This report details our recent computational

between Prof. Atsushi Hariki at Osaka City

investigation of SrRu2O6, a material around the

University and the group of Jan Kuneš at TU

boundary between covalent and Mott insulators.

Wien.

Our study aimed to compare the results withthose of inelastic scattering experiments, andfor this purpose, we employed the density
functional theory plus the dynamical meanfield theory (DFT+DMFT) approach. We used
DCore

[1]

and

ALPS/CT-HYB

[2]

for

DFT+DMFT calculations. The codes areparallelized by MPI. We constructed the tightbinding model using Wien2k.

Fig. 1: Temperature dependence of magnetic

We successfully created a phase diagram as a

momentfunction of temperature. Notably, we observed
an antiferromagnetic phase at low temperatures

References

consistent with experimental findings. Figure 1[1] H. Shinaoka, J. Otsuki, M. Kawamura, N.

plots the temperature dependence of the

Takemori, K. Yoshimi, SciPost Phys. 10, 117

magnetic moment.

(2021).

Currently, we are calculating the dynamic[2] H. Shinaoka, E. Gull, P. Werner, Comput.

susceptibility in the low-temperature phase by

Phys. Commun. 215, 128 (2017).

solving the Bethe-Salpeter equation. We expect[3] Diana Csontosová, H. Shinaoka, A. Hariki,

to release our results as a preprint [3].

and J. Kuneš, in preparation.

It is important to acknowledge that this195

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Nonlocal correlation effects in a Hund Ferromagnet
Yusuke NOMURA
Department of Applied Physics and Physico-Informatics, Keio University,
3-14-1 Hiyoshi, Kohoku-ku, Yokohama, 223-8522, Japan
Understanding

electroncorrelation

to the efficient continuous-time quantum Monteeffects

beyond Fermi liquid theory is a fundamental

Carlo methods developed in Refs. [1-4].

problem in condensed matter physics, since

We find that the Fermi surface expands evenvariousasabove the Curie temperature as if the spin

superconductivity and magnetism emerge frompolarization occurred, contrary to a naïve view

pseudogap and strange-metal states.

that the Fermi surface should recover non-spin-

intriguing

phenomena

suchpolarized behavior. Behind this phenomenon,

A well-known example is the pseudogap
behavior observed in doped cuprates, where

effective“Hund’sstrong nonlocal antiferromagnetic fluctuations

momentumare believed to play an important role. This

correlations induce effective Hund’s coupling

phenomenon has been intensively studied byin momentum space, leading to a large

the cluster extension of the dynamical mean-

modulation of the momentum space occupancy.

field theory.

The reconstruction of the Fermi surface differs

However, nonlocal correlation effects infrom the antiferromagnetic case, where it

multi-orbital systems remain largely elusive. In

creates hot and cold spots in the Fermi surface.

particular, the influence of ferromagnetic

Our finding will give a deeper insight into thefluctuations in the strong-coupling regime isphysics of Hund’s ferromagnets above thestill poorly understood compared to theCurie temperature.

space;

physics”

works

ferromagnetic

in
spin

antiferromagnetic case.

References

Such a strong-coupling ferromagnetic regime
is expected in the multiorbital Hubbard model.

[1] Y. Nomura, S. Sakai, and R. Arita, Phys.

Therefore, we study the two-orbital Hubbard

Rev. B 89, 195146 (2014)

model on the two-dimensional square lattice[2] H. Shinaoka, Y. Nomura et al., Phys. Rev. B

using cellular dynamical mean-field theory.

92, 195126 (2015)

Although the cluster extension in multiorbital[3] Y. Nomura, S. Sakai, and R. Arita, Phys.

systems is computationally expensive, we have

Rev. B 91, 235107 (2015)

managed to accomplish the calculations thanks[4] H. Shinaoka, Y. Nomura and E. Gull,

196

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Comput. Phys. Commun. 252, 106826 (2020)Rev. Lett. 128, 206401 (2022)[5] Y. Nomura, S. Sakai, and R. Arita, Phys.

197

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Transient absorption spectrum in photo-excited
one-dimensional Mott insulators
Takami TOHYAMA
Department of Applied Physics, Tokyo University of Science, Tokyo 125-8585

The elucidation of nonequilibrium states instrongly correlated systems is of great interest since it promises to open a door to theemergence of novel quantum phases. One of
the most signiﬁcant challenges is how to preserve nonequilibrium states, such as the Floquet states, from thermalization, for which therealization of many-body localization may holdthe key. Also, the nonequilibrium-induced
insulator-to-metal transition studied extensively in the one-dimensional (1D) Mott insulator is a fundamental issue associated withcompetition between itinerancy and localization of charge degrees of freedom. Similarly,
non-absorbable terahertz photons with strong
intensity may induce a metallic state via quantum tunneling. Until now it has been commonly accepted that the breakdown of theMott insulators via electric pulses leads tometallic states. However, we raise question
about the validity of this understanding.
To answer this question, in this project
we focus on the possibility of the emergence of novel quantum phases such as glass
phases with intermediate properties between
itinerancy and many-body localization. We
investigate pulse-excited states of the halfﬁlled 1D extended Hubbard model using thetime-dependent density-matrix renormalization group (tDMRG). Our tDMRG makes useof the Legendre polynomial for the calculationof time-evolution operator. We use two target states at a given time t and t + ∆t toconstruct a basis set that can express wavefunctions in the time-dependent Hilbert space.

With the two-target tDMRG procedure, we
can calculate time-dependent physical quantities with high accuracy even when the Hamiltonian varies rapidly with time.
From our tDMRG simulations, we propose
a Mott transition to glassy states induced bymono- and half-cycle terahertz pulses ??. If
we excite the Mott insulating state via photon absorption, we obtain metallic states withlarge Drude weight. In contrast, we ﬁnd thatstrong electric ﬁelds inducing the Zener breakdown strongly suppress the Drude weight evenin the presence of a large number of carriers.
We consider that the Hilbert-space fragmentation due to high ﬁelds leads to glassy dynamics as seen in fracton systems. The glassy
state is accompanied by electric polarizationthat breaks inversion symmetry ??. We also
demonstrate a steady electric current induced
by an ultrashort subcycle pulse. This is due
to an Aharonov-Bohm ﬂux introduced throughthe phase of an electric ﬁeld. Consequently,
time-reversal symmetry is broken. Both symmetry breakings can be monitored by second
harmonic generation. These ﬁndings propose a
new methodology for designing the symmetriesof electronic states and open up a new ﬁeld ofsubcycle-pulse engineering.

References[1] K. Shinjo, S. Sota, and T. Tohyama:
Phys. Rev. Res 4 (2022) L032019.
[2] K. Shinjo, S. Sota, S. Yunoki, and T. Tohyama: arVix:2211.08694.

198

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Research of Three-Channel Kondo Eﬀect
Emerging from Holmium Ions
Takashi HOTTA
Department of Physics, Tokyo Metropolitan University
1-1 Minami-Osawa, Hachioji, Tokyo 192-0397

In 2021, we have discovered the threechannel Kondo eﬀect emerging from Ho ions[1]. Here we brieﬂy report the subsequent development of the research, in particular, themagnitude of the eﬀective impurity spin of thethree-channel Kondo eﬀect.
First we explain the model Hamiltonian. For
the construction of the model, we deﬁne one
f -electron state by the eigenstate of spin-orbit
and crystalline electric ﬁeld (CEF) potential
terms. 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 under the cubic CEF potential. Then,
we include the Γ7 and Γ8 conduction electron
bands. Here we consider only the hybridization
between the conduction and j = 7/2 electrons.
The model Hamiltonian is given byH =∑εk c†kµτckµτ +k,µ,τ

+ nEf +∑∑

V (c†kµτ fbµτ +h.c.)

k,µ,τ
†
fjµτ
(λj + Bj,µ )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 is the dispersion of conduction electron with wave vector k, ckµτ is the annihilation operator of a conduction electron, fjµτis the annihilation operator of a localized felectron in the bases of (j, µ, τ ), j is the total angular momentum, j = 5/2 and 7/2 aredenoted by “a” and “b”, respectively, µ distinguishes the cubic irreducible representation, Γ8states are distinguished by µ = α and β, whilethe Γ7 and Γ6 states are labeled by µ = γ
and δ, respectively, τ denotes the pseudo-spin,
which distinguishes the degeneracy concerning
the time-reversal symmetry, V denotes the hybridization between f electron in the µ orbitaland conduction electron of the µ band, n is the
local f -electron number at an impurity site,and Ef is the f -electron level to control n.
As for the spin-orbit term, we obtain λa =−2λ and λb = (3/2)λ, where λ is the spin-orbit
coupling of f electron and we set λ = 0.265 eV
for the Ho 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 forthe angular momentum ℓ = 3. For j = 7/2,
we obtain Bb,α = Bb,β = 360B40 /7 + 2880B60 ,Bb,γ = −3240B40 /7 − 2160B60 , and Bb,δ =360B40 − 3600B60 /7. In the following calculations, we use the parametrization as B40 =W x/15 and B60 = W (1 − |x|)/180 for ℓ = 3,
where x speciﬁes the CEF scheme for the Oh
point group, while W determines the energy
scale of the CEF potentials. In this work, we
set W = 10−3 eV and treat x as the parameterto control the CEF ground state.
For the Coulomb interaction terms, we donot show the explicit forms of I here, but they
are expressed by the four Slater-Condon parameters, F 0 , F 2 , F 4 , and F 6 . These values should be determined from experimental
results, but here we simply set the ratio as
F 0 /10 = F 2 /5 = F 4 /3 = F 6 = U , where U indicates the Hund’s rule interaction among the199

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Simp = log

sin[(2S + 1)π/(nc + 2)],
sin[π/(nc + 2)](2)

where S denotes the local impurity spin andnc indicates the number of channels. In thepresent case with nc = 3, we obtain Simp =log ϕ for both the cases of S = 1/2 and 1.
Thus, in any case, the residual entropy log ϕis considered to be characteristic of the threechannel Kondo eﬀect, but the value of S is notdetermined only from the residual entropy.
To conﬁrm the value of S, we hit upon an
idea to explore a quantum critical point (QCP)
between the three-channel Kondo and Fermiliquid phases. The QCP between the threechannel Kondo and Fermi-liquid phases is expected to be characterized by the residual entropy of the four-channel Kondo eﬀect. Fromeq. (2), we obtain Simp = 0.5 log 3 and log 2 for
S = 1/2 and 1, respectively, for nc = 4.
In Fig. 3(a), we show the f -electron entropies for W = 10−3 and V = 0.7 between
x = 0.65 and 0.7. For x = 0.65, we observe the three-channel Kondo phase, while for
x = 0.7, the local singlet phase appears. At
x = 0.6849, the entropy plateaus with a value
between 0.5 log 3 and log 2, and it eventuallyexits the plateau at around T ∼ 10−10 . We de-

1.5(a) n=10

Simp

1.0

U=1
l=0.265
W=10-3
V=0.7

0.5

x=0.65x=0.6849
x=0.7

L=8.0
M=5000log 2
0.5 log 3
log f

0.0
-7
-10
-9
-8
-6
-5
-4
-3
-2
-1
10 10 10 10 10 10 10 10 10 10
temperature T [eV]1(b) n=10log 2
0.5 log 3
0.5
log f
U=1
W=10-3l=0.265 V=0.7
0-1 -0.8 -0.6 -0.4 -0.2 0 0.2 0.4 0.6 0.8 1xSimp @T=1.7x10-7

f orbitals. In this work, we set U = 1 eV.
The model is analyzed with the use of a numerical renormalization group (NRG) method.
We introduce a cut-oﬀ Λ for the logarithmic
discretization of the conduction band. Due tothe limitation of computer resources, we keep
M low-energy states. Here we use Λ = 8 and
M = 5, 000. In the NRG calculation, the temperature T is deﬁned as T = DΛ−(N −1)/2 ,where D is half the conduction band width,
which was set as 1 eV, and N is the number ofrenormalization steps.
From the NRG calculations, we have found a
residual entropy Simp of log ϕ with the golden√
ratio ϕ = (1 + 5)/2 for the local Γ5 triplet
ground state. For the multi-channel Kondo effect, the analytic value of the residual entropy
Simp has been found to be given by [2]Figure 1: (a) Entropies vs. temperature for
x = 0.65, 0.6849, and 0.7 with W = 10−3 andV = 0.7. (b) Residual entropies at T = 1.7 ×
10−7 vs. x for −1 ≤ x ≤ 1.
duce this as the signal of the QCP between thethree-channel Kondo and Fermi-liquid phases.
Note that this behavior has also been observed
around at x = −0.64.
In Fig. 3(b), we plot the value of the entropy at T = 1.7 × 10−7 as a function of xfor −1 ≤ x ≤ 1. We ﬁnd sharp two peaks
at around x ≈ −0.646 and x ≈ 0.685, andthe peaks assume values between 0.5 log 3 andlog 2. Since these values are apparently larger
than 0.5 log 3, we deduce that the peaks indicates the QCP characterized by the residual
entropy of the four-channel Kondo eﬀect with
S = 1. This result is consistent with the local
Γ5 triplet ground state.

References[1] T. Hotta, J. Phys. Soc. Jpn. 90, 113701(2021).
[2] I. Aﬄeck and A. W. W. Ludwig, Nucl.
Phys. B 360, 641 (1991).

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Magnetic ﬁeld eﬀect on excitonic phase inmulti-orbital Hubbard model
Joji NASU
Department of Physics, Tohoku University
Sendai 980-8578

Excitonic insulators are insulating states
where pairs of an electron in a conduction band
and a hole in a valence band are condensed
coherently. Although this state was proposed
as a superconductivity analog about 50 years
ago, recent discoveries of materials that could
potentially exhibit excitonic insulators have renewed interest in studying this system. Amongthe candidates, cobalt oxides have received signiﬁcant attention due to their multiple spinstates, including low-spin, intermediate-spin,and high-spin states, which are aﬀected by
crystalline ﬁelds and Hund couplings. Recent
research has suggested that excitonic condensation could occur through spontaneous hybridization between distinct spin states. The
theoretical and experimental examinations ofcobalt oxides in this perspective has revealed
the emergence of a magnetic-ﬁeld-induced excitonic phase and spin-splitting. The simpliﬁed two-orbital Hubbard model has been usedin these studies to consider low-spin and highspin states [1, 2, 3].

netic ﬁeld results in the appearance of two excitonic phases [4]. The low-ﬁeld phase is not accompanied by spin-state alignments, while theexcitonic phase appearing higher ﬁeld is associated with a spin-state order and interpreted asa supersolid in terms of excitonic condensation.
The magnetization curve should display signatures of these phases, which is consistent witha recent experiment measuring volume change
up to 600T [4].

In this project, we have investigated magnetic ﬁeld eﬀects on the multi-orbital Hubbard model with the expressive ability of thethree spin states, including the intermediatespin state. We have derived a low-energy eﬀective model and performed mean-ﬁeld calculations, but due to the complexity of the model,
ﬁnding solutions is computationally expensive.
To reduce computation time, we have utilized
the technique of parallel computation. Ourﬁndings show that increasing the applied mag-

[4] A. Ikeda, Y. H. Matsuda, K. Sato,
Y. Ishii, H. Sawabe, D. Nakamura, S.
Takeyama, and J. Nasu: Nat. Commun.
14 (2023) 1744.

References[1] T. Tatsuno, E. Mizoguchi, J. Nasu, M.
Naka, S. Ishihara: J. Phys. Soc. Jpn. 85(2016) 083706.
[2] J. Nasu, M. Naka, S. Ishihara: Phys. Rev.
B 102 (2020) 045143.
[3] J. Nasu and M. Naka: Phys. Rev. B 103(2021) L121104.

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Correlation-induced phenomena in Kondo lattice systems
Robert PETERS
Department of Physics,
Kyoto University, Kyoto, 606-8502
correlated

correlations. While energetically low-lying spin

insulators where the resistivity becomes large at

excitations emerge approximately at the Kondo

low temperatures due to a gap in the single-

temperature, which exponentially depends onparticle spectrum [1]. Recently, quantum

the interaction strength, charge correlations

oscillations in strong magnetic fields have been

vanish already at high temperatures.

observed in these materials while insulating.

Furthermore, we analyzed the charge andFurthermore, specific heat and thermal transport

thermal conductivities at finite temperatures bymeasurements on YbB12 and YbIr3Si7 havecalculating the time-dependent current-current

revealed low-lying excitations in these Kondo

correlation functions. While both charge andinsulators that can transport heat but no electric

thermal conductivities can be fitted for all

current [2,3]. Thus, it has been argued that thereinteraction strengths by gapped systems with aare itinerant charge-neutral excitations that are

renormalized band gap, the gap in the system

responsible for thermal transport and lead todescribing the thermal conductivity is generally

observable quantum oscillations in strong

smaller than the system describing the chargemagnetic fields. However, a conclusion to these

conductivity. Furthermore, the maximum of therecent experiments is not yet found.

charge conductivity over the temperature

Using variational matrix product states, wedecreases

analyzed the finite temperature behavior of ainteraction strength. On the other hand, thehalf-filled periodic Anderson model in one

maximum of the thermal conductivity generally

dimension, a prototypical model of a Kondo

lies at smaller temperatures than the maximum

insulator. In our calculations [4], we confirmedof the charge conductivity and follows athe existence of energetically low-lying spin

nonmonotonic behavior , see Fig. 1. We thus

excitations [1] in this model and studied theirfound that charge and thermal conductivities areenergy-momentum dispersion and temperature

affected very differently by correlations anddependence. We demonstrated that charge-

show a different temperature behavior.

Kondo

insulators

arestrongly

charge correlations at the Fermi energy exhibit adifferent temperature dependence than spin-spin

202

monotonicallywithincreasing

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

GQM in the Qi-Wu-Zhang model with andwithout interaction.

References[1] H. Tsunetsugu, M. Sigrist, and K. Ueda
Rev. Mod. Phys. 69, 809 (1997)[2]
Figure 1: Charge conductivity and thermal
conductivity for different interaction strengths. The
insets show the effective gap in both conductivities.

Y. Sato, Z. Xiang, Y. Kasahara, T.

Taniguchi, S. Kasahara, L. Chen, T. Asaba, C.
Tinsman, H. Murayama, O. Tanaka, Y. Mizukami,

In another work [5], we introduced a generalized

T. Shibauchi, F. Iga, J. Singleton, Lu Li, and Y.

quantum metric(GQM) on the Brillouin zone for

Matsudacorrelated electron systems. This quantum

Nature Physics 15, 954 (2019)

metric is based on the optical conductivity that[3] Y Sato, S Suetsugu, T Tominaga, Y Kasahara,is written by single-particle Green’s functions.

S Kasahara, T Kobayashi, Shunsaku Kitagawa, K

We analytically proved that this definition is

Ishida, R Peters, T Shibauchi, AH Nevidomskyy,

equivalent to the existing definition of the

L Qian, E Morosan, Y Matsuda, Nature comm.

quantum metric in noninteracting systems and13, 394 (2022)

that it is positive semi-definite as necessary for[4] R Peters and R Rausch, submitted to SciPosta metric. Furthermore, we pointed out the

Physics

relationship between the GQM and the Chern[5] T. Kashihara, Y. Michishita, and R. Peters

number in interacting systems. We thenPhys. Rev. B 107, 125116 (2023)

numerically confirmed these properties of the203

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Electronic Structures of Nickel Dithiolene Complex-based
Ambipolar Semiconductors
Tomoko FUJINO
Institute for Solid State Physics,
The University of Tokyo, Kashiwa-no-ha, Kashiwa, Chiba 277-8581
Air-stablesingle-component

ambipolar

organic semiconductors that conduct both holes
and electrons are highly desired, but have beenrarely realized. We synthesized neutral nickelbis(dithiolene) complexes (Fig. 1) that fulfill thestringent electronic requirements (i.e., shallow
HOMO levels and deep LUMO levels) for airstable ambipolar semiconductors [1]. The planar

Fig. 1: Nickel dithiolene-based ambipolarstructures

semiconductors.

facilitatedeffectivedenseintermolecular

packingwithinteractions.

Remarkably, changing the methoxy substituentsachieved for a single-component ambipolar

to ethoxy or propoxy groups led to a dramatic

semiconductor material driven in air.

change in the packing mode from onedimensional
maintaining

toherringbone-like,effective

while

intermolecularinteractions, supported by the first-principles

References

band calculation (OpenMX software). They are[1] M. Ito, T. Fujino*, L. Zhang, S. Yokomori, T.

readily solution-processible to form active

Higashino, R. Makiura, K. J. Takeno, T. Ozaki,

layers with well-defined and well-ordered

H. Mori*, J. Am. Chem. Soc. 145, 2127 (2023),

structures in field-effect transistors. Devices

Supplementary Cover.

based on these compounds exhibited efficient[2]. R. Kameyama, T. Fujino*, S. Dekura, S.

ambipolar characteristics, even after several

Imajo, T. Miyamoto, H. Okamoto, H. Mori*, J.

months of exposure to air, whose carrier

Mater. Chem. C 10, 7531 (2022).

mobilityarethe

top-classperformances

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Inhomogeneous ground state due to kinetic energy
eﬀect in correlated electron systems
Takashi YANAGISAWA
National Institute of Advanced Industrial Science and Technology (AIST)
1-1-1 Umezono, Tsukuba 305-8568

1

Introduction

Our research is based on the optimized variational Monte Carlo method[1].
We usethe optimized wave function improved by oﬀdiagonal exponential operators such as e−λK
and e−αD (K and D are the kinetic operator and the double occupancy operator, respectively), and the Gutzwiller-Jastrow wave
function where the doublon-holon correlation
is taken into account. We have investigated
the ground-state phase diagram of the twodimensional Hubbard model and the twodimensional d-p model.
We performed parallel computation inMonte Carlo calculations. In order to reduce
statistical errors, we carried out ∼ 500 parallel
calculations. Parallel computing is very important to reduce Monte Carlo statistical errors.
The many-body wave function is written in
the form ψ (1) = exp(−λK)PG ψ0 , where K denotes the kinetic energy part (non-interactingpart) of the Hamiltonian and PG = PG (g) is
the Gutzwiller operator to control the double occupancy with the variational parameterg. ψ0 indicates a trial wave function which
is usually taken as the Fermi sea, the BCS
wave function or the state with some magnetic(or charge) orders. We can improve the wave
function systematically by multiplying by operators PG and e−λK repeatedly. We can consider ψ (2) = exp(−λ′ K)PG (g ′ )ψ (1) for diﬀerent
variational parameters λ′ and g ′ . This wave
function is a very good many-body wave function because the ground-state energy is lowered greatly and the ground-state energy islower than those that are evaluated by anyother wave functions. We also employ the
Jastrow-type wave function which is written

205

as ψJ = PG PQ PJ ψ0 where PJ indicates anearest-neighbor number correlation operator
and PQ controls the nearest-neighbor doublonholon correlation.

2

Ferromagnetic
diagonal
striped states in the Hubbard model

We have performed a variational Monte Carlosimulation to study the ground state of thetwo-dimensional Hubbard model on a squarelattice. The energy gain of possible inhomogeneous electron states are computed as a function of U in the case where the hole density
is δ = 1/8 and next nearest-neighbor transfer
t′ /t = −0.30. The wave function is written asψstripe = PNe PG PJ PDH ψM F ,(1)where ψM F is the eigenstate of the following
Hamiltonian
HM F = −Xijσtij c†iσ cjσ +UX(ρi −sgn(σ)mi )niσ ,
2 iσ

(2)
with ρi = ρ cos(q·(ri −r0 )) and mi = m sin(Q·(ri − r0 )). ρ and m are variational operators. Two incommensurate wave vectors q
and Q characterize the charge and spin conﬁgurations, respectively. We set q = 2Q.
r0 denotes the position of the domain boundary. PNe is the projection operator that extracts only the components with a ﬁxed total number of electrons Ne . PDH = PQ isthe doublon-holon operator given by PDH =Q
Q
i (1 − (1 − η) τ di (1 − ei+τ )) where 0 ≤ η1,
di = ni↑ ni↓ , ei = (1 − ni↑ )(1 − ni↓ ), and τ runs
over all nearest-neighbor sites.

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

In Fig. 1, the energy diﬀerence per site between the normal and stripe states, ∆E =(Enormal − Estripe )/Ns , of various stripe states
at 1/8 doping, is shown as a function of U .
The calculations were carried out on a 16 × 16
lattice. The results show that FM stripe states(open symbols) are more stable than AF stripe
states (ﬁlled symbols) for U/t ≥ 16.
The bond-centered ferromagnetic diagonal
stripe state is stabilized in the strong couplingregion with U/t ≥ 16; this is due to the gainof both kinetic energy and on-site Coulombinteraction energy. The kinetic energy gain
originates from the holon moving over the ferromagnetic domain and the gain of kineticexchange-interaction energy at the antiferromagnetic domain wall. For large U , the gain in
the kinetic energy due to the transfer of holeson the ferromagnetic domain and that of theon-site Coulomb interaction energy exceed theloss of the kinetic exchange interaction energy,
which leads to form an incommensurate electron state with the ferromagnetic domain.

3

Summary

We examined the ground state of the twodimensional Hubbard model by using an advanced variational Monte Carlo method. In
the strong coupling region where U is large, thekinetic energy gain is important in determining
the ground state. In fact, the kinetic energy
gain stabilizes superconducting state for the
optimized BCS wave functions[3]. The kinetic
term also plays an important role in striped
states and the diagonal stripe becomes stablein this region due to the kinetic energy eﬀect.

Figure 1: Optimized energy diﬀerence per site
between the normal and striped states ∆E =(Enormal − Estripe )/Ns as a function of U . The
data are from 16 × 16 lattices where electron number Ne = 224 (1/8 hole doping) andt′ = −0.30. Filled squares indicate the period8 bond-centered AF diagonal stripe state (8period BC-FN-DS). Open squares (circles) denote the bond-centered FM diagonal stripe
state (BC-FM-DS) with period-8 (period-16).
Inset ﬁgure shows the system size dependenceof the optimized energy diﬀerence per site forthe period-8 BC-F-DS state with U = 100 at
1/8 hole doping. The error bars are smaller
than the size of symbols.
T. Yanagisawa, Condensed Matter 4, 57(2019).
[3] T. Yanagisawa, Phys. Lett. A403, 127382(2021).
T. Yanagisawa et al., EPL 134, 27004(2021).
[4] M. Miyazaki, T. Yanagisawa, Phys. Lett.
A448, 128276 (2022).

References[1] T. Yanagisawa et al., J. Phys. Soc. Jpn.
67, 3867 (1998).
T. Yanagisawa, Phys. Rev. B75, 224503(2007) (arXiv: 0707.1929).
[2] T. Yanagisawa, J. Phys. Soc. Jpn. 85,
114707 (2016).
T. Yanagisawa, J. Phys. Soc. Jpn. 88,
054702 (2019).

206

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Unified description of cuprate high-temperature
superconductors using multiband models
Hiroshi WATANABE
Research Organization of Science and Technology, Ritsumeikan University
1-1-1 Noji-Higashi, Kusatsu-shi, Shiga 525-8577

Understanding the various competing
phases in cuprate high-temperature superconductors is a long-standing challenging
problem. Although we have not yet reacheda unified understanding of their properties,
recent studies have shown that orbital degrees
of freedom, both Cu eg and O p orbitals,
are key ingredient. Here we investigate thefour-band d-p model that explicitly includes
the dx2 −y2 , dz 2 , px , and py orbitals [1, 2]. We
construct the tight-binding energy bands for
La2 CuO4 and HgBa2 CuO4 systems based on
the first-principles calculation and examine
the effect of Coulomb interactions with thevariational Monte Carlo (VMC) method. The
Gutzwiller-Jastrow type wave function is used
for the VMC trial wave function. The systemsize for the calculation is N =24×24=576 unit
cells (and thus 576×4=2304 orbitals in total)
and the computation has been done mainlywith the system B of the ISSP Supercomputer
Center. We have compared the variationalenergies of various competing phases including
superconductivity, ferro- and antiferromagnetic phases, and stripe phases with different
periodicities to determine the ground statephase diagram for the hole doping rate x.
We have also calculated physical quantities
such as superconducting correlation functions,charge- and spin correlation functions, andlocal magnetic moments.

with the superconducting correlation function
P dd . In La2 CuO4 , ndz2 increases with x andis strongly enhanced by the Hund’s coupling.
This is because the system tends to increasendz2 to obtain the energy gain from the Hund’s
coupling. Since ndz2 works destructively forsuperconductivity due to its localized character [1, 2], P dd is suppressed by the Hund’s coupling. On the other hand, in HgBa2 CuO4 , suchan increase of ndz2 and a suppression of Pdd
are not so pronounced even for relatively large
Hund’s coupling. It results from the lower siteenergy εdz2 in the HgBa2 CuO4 system thatmakes the dz 2 orbital almost inactive. The difference between two systems are well describedin our four-band d-p model.

References[1] H. Watanabe et al., Phys. Rev. Research
3, 033157 (2021).
[2] H. Watanabe et al., J. Phys.: Condens.
Matter 35, 195601 (2023).

In Fig. 1, we show the hole density of the dz 2
orbital ndz2 as a function of x for several values of Hund’s coupling J/Ud at Ud /t1 =8, along207

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Figure 1: The hole doping rate x dependence of the hole density of the dz 2 orbitalndz2 (solid lines with symbols) and superconducting correlation function P dd (dotted lines)for (a) La2 CuO4 and (b) HgBa2 CuO4 , respectively [2]. Solid (open) symbols correspond to
the superconducting (paramagnetic) phase.

208

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Gap opening mechanism for organic Dirac electron
systems α-(BEDT-TTF)2I3 and α-(BEDT-TSeF)2I3
Akito Kobayashia , Daigo Ohkia , Kazuyoshi Yoshimib and Takahiro MisawabaDepartment of Physics, Nagoya University, Nagoya 464-8602
bInstitute for Solid State Physics, University of Tokyo, Chiba 277-8581, Japan

In the Dirac electron system of organic conductors, phase transitions due to spontaneous
symmetry breaking due to electron-electron interactions have been observed, and this has
attracted interest as a research target for correlated Dirac electron systems. In α-(BEDTTTF)2 I3 , it has been reported that the horizontal stripe charge order with inversion symmetry breaking induces a gap for massless
Dirac electrons [1]. A related compound α(BEDT-TSeF)2 I3 , on the other hand, has adistinctly diﬀerent insulating state from α(BEDT-TTF)2 I3 2 [2]. The gap opening mechanism has not yet been fully clarified.

TSeF)2 I3 , as in the one-dimensional Hubbard
model [4]. Thus we found that α-(BEDTTSeF)2 I3 hosts massive Dirac electrons without symmetry breaking via dimensional reduction [5].

To determine the origin of the diﬀerencesin the gap opening mechanisms in α-(BEDTTTF)2 I3 and α-(BEDT-TSeF)2 I3 , we derive
ab initio low-energy eﬀective Hamiltonians
and solve this using the many-variable variational Monte Carlo method (mVMC) [3]. It
is found that an insulating state with thehorizontal stripe charge order appears in α(BEDT-TTF)2 I3 , which is consistent with experiments and previous studies as shown in
Fig. 1(a). However, in α-(BEDT-TSeF)2 I3 ,we find that an insulating state without any
explicit symmetry breaking is realized. Because of the frustration in the inter-chain magnetic interactions, a dimensional reduction of
the spin correlations occurs. As a result,one-dimensional spin correlations develop in
α-(BEDT-TSeF)2 I3 as shown in Fig. 1(b).
This result suggests that the one-dimensional
spin correlation induces the gap in α-(BEDT-[4] E. H. Lieb and F. Y. Wu, Phys. Rev. Lett.
20, 1445 (1968).

References[1] H. Seo, J. Phys. Soc. Jpn. 69, 805 (2000).
[2] S. Kitou et al., Phys. Rev. B 103, 035135(2021).
[3] T. Misawa et al., Phys. Commun. 235,
447 (2019).

[5] D. Ohki et al., Phys. Rev. B 107, L041108(2023)

Figure 1: Schematic diagrams of α-type organic conductors for (a) α-(BEDT-TTF)2 I3and (b) α-(BEDT-TSeF)2 I3 .

209

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Theoretical study of thermoelectric properties in
Heusler compounds: A weak-coupling approach
Kazutaka NISHIGUCHI
Graduate School of System Informatics, Kobe University
Rokkodai-Cho, Nada-Ku, Kobe 657-8501

Heusler compound Fe2 VAl is a promisingthermoelectric material, which exhibits large
power factor P = σS 2 with σ and S being theelectrical conductivity and Seebeck coeﬃcient,
respectively. On the other hand, the thermal the dimensionless figure of merit ZT =σS 2 T /κ is not so large yet reflecting its large
thermal conductivity κ. Recently, it is experimentally observed in doped Fe2 VAl (i.e.,
Fe2 V0.9 Cr0.1 Al0.9 Si0.1 and Fe2.2 V0.8 Al1−y Siy )as a weekly ferromagnetic material that ferromagnetic fluctuations enhance the thermoelectric properties such as S and P around theCurie temperature (Tc = 285 K). [1] It is not
only a desirable property for practical use inrealistic (room) temperatures, but also a fundamental and intriguing quantum phenomena
where quantum fluctuations and thermoelectric eﬀects are entangled by electron correlations.
Motivated above, we have studied electronic
properties of Fe2 VAl using first-principles calculations based on the density functional theory (DFT) within the generalized gradient approximation (GGA). We performed DFT calculations with the Perdew–Burke–Ernzerhof(PBE) exchange-correlation functional and the
projector augmented wave (PAW) method using The Vienna Ab Initio Simulation Package(VASP) [2] and Quantum ESPRESSO package. [3]Using the maximally localized Wannierfunctions, we could construct a low-energy effective model from the first- principles bands
around the Fermi level. The eﬀective model
is composed of the Fe-3d, V-3d, and Al-2sp3
Wannier orbitals, namely, 19 orbitals. The
DFT b and structure and Wannier orbitals areshown in Fig. 1.
4Band structure
Wannierization

3
2

E−EF (eV)

Heusler compound Fe2 VAl

1
0
−1
−2
−3
−4
W

L

Γ

X

W

K

Γ

k−PathFigure 1: DFT band structure and Wannierization of Fe2 VAl.
Planar Defect in Layered Perovskite
Photocatalyst Y2 Ti2 O5 S2
Layered perovskite Y2 Ti2 O5 S2 (YTOS) is astrong candidate for semiconductor photocatalysts suitable for overall water splitting undervisible light. On the other hand, structuraldefects during synthesis should be controlled
to improve photocatalytic performance similar to other photocatalysts [5]. Very recently,
transmission electron microscopy (TEM) haverevealed extremely large planar defects com-210

Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

posed of S–Mg–S layers in YTOS synthesizedusing the flux method.
We investigated the planar defect structureand electronic structure using first-principles
calculations based on the density functional
theory (DFT) [6]. The DFT calculations were
performed within the PBE+U functional using
PAW method, as implemented in VASP [2].
Here we set U = 7.5 eV for the 3d orbitals
at the Ti sites to reproduce the experimental
band gap, 1.9–2.0 eV [5].

we have finally evaluated the defect formationenergy (Ef ). The chemical potentials µi were
determined by the phase diagram of the relevant compounds in the synthesis of YTOS. The
evaluation of the formation energy suggeststhat Ef increases with decreasing µS and/orµMg . Therefore, the optimum conditions for
the S and Mg environments must be optimized
for the synthesis of YTOS, which suppresses
the formation of the planar defect.

References[1] N. Tsujii, A. Nishide, J. Hayakawa, andT. Mori: Sci. Adv. 5, eaat5935 (2019).
[2] G. Kresse et. al.: Phys. Rev. B 47, 558(1993); Phys. Rev. B 49, 14251 (1994);
Computational Materials Science 6 (1996)
15–50; Phys. Rev. B 54, 11169 (1996).
[3] P. Giannozzi et. al.: J. Phys.: Condens.
Matter 21, 395502 (2009) ; J. Phys.: Condens. Matter 29, 465901 (2017) ; J. Chem.
Phys. 152, 154105 (2020).
Figure 2: Planar defect in YTOS is investigated by electron microscopy and firstprinciples calculations.
We have microscopically determined the planar defect structure using the structural optimization, where a Mg atom is centered in
the ab-square intersecting the defect S layers. The obtained defect structure is consistent with the ADF–STEM image. To understand the electronic structures, we have investigated the projected density of states (PDOS)
and band structure, which shows that the defect bands appear within the original band gap.
It is expected that such defect bands considerably increase the electron–hole recombination rate, enhancing the interband transitionsof the defect valence and/or defect conduction bands via radiative or nonradiative transitions, which is an undesirable factor for the efficiency of the overall water splitting of YTOS.
To consider the stability of the planar defect,[4] I. Souza, N. Marzari, and D. Vanderbilt:
Phys. Rev. B 65, 035109 (2001) ; A. A.
Mostofi et. al.: Comput. Phys. Commun.
178 (2008) 685–699; A. A. Mostofi et.
al.: Comput. Phys. Commun. 185 (2014)
2309–2310; G. Pizzi et. al.: J. Phys.: Condens. Matter 32, 165902 (2020).
[5] Q. Wang et. al.: Nat. Mater. 18, 827(2019) ; Z. Pan et. al.: Res. Chem. Intermed. 47, 225 (2021).
[6] M. Nakabayashi, K. Nishiguchi, X. Liang,
T. Hisatomi, T. Takata, T. Tsuchimochi,
N. Shibata, K. Domen, and S. L. Tenno: J. Phys. Chem. C 2023, 127, 7887–
7893 (M.N. and K.N. contributed equallyto this work).

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Activity Report 2022 / Supercomputer Center, Institute for Solid State Physics, The University of Tokyo

Nonequilibrium dynamics induced by optical driving
Atsushi ONO
Department of Physics, Tohoku University,
Sendai 980-8578

The ultrafast dynamics of electrons in solids
have been actively studied in recent years.
For example, high-harmonic generation, whichyields harmonics several tens of times higher
than the incident light, has attracted interest
as a phenomenon for generating broadband ultrashort pulses, while its mechanism involves
nonperturbative and nonlinear processes, requiring accurate numerical calculations to understand such intriguing ultrafast phenomena.

energy-band echo, can be observed in various
insulators and reflects the dispersion relationof itinerant quasiparticles.
(a)
0.4

0.0
10−2

−0.4

This year, we focused mainly on thenonequilibrium dynamics of photocarriers excited by a resonant optical pulse and thendriven by an optical electric-field pulse. We
considered theoretical models of band insulators, Mott insulators, and charge-ordered insulators and calculated the real-time evolution using exact diagonalization and infinite
time-evolving block decimation methods on
the ISSP supercomputer system.
We found that in a band insulator, theoptical driving pulse changes the relative
velocity of photocarriers, resulting in carrier
recombination and the generation of echoesof the excitation pulse. A detailed analysis
revealed that the frequency of the echo pulses
reflects the energy dispersion relation of thephotocarriers. Furthermore, we performed
numerical calculations for Mott insulators
described by the Hubbard model and foundthat echo pulses can also be generated despite
the breakdown of the single-electron picture,and their frequencies coincide with the energyof the doublon–holon pairs obtained fromthe Bethe ansatz, as shown in Fig. 1. We
found that this echo phenomenon, termed an

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(b) 15

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Figure 1: Echoes in a one-dimensional Mott
insulator [1]. (a) Time profile of the electric
current. The inset shows the Fourier spectrum.
(b) Fourier spectral map of the electric current.
The red curves show the dispersion relations of
the doublon–holon pair. Af is proportional tothe amplitude of the optical driving pulse.

References[1] S. Imai, A. Ono, and S. Ishihara, Phys.
Rev. Research 4, 043155 (2022).

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