強相関電子系を取り扱うソフトウェア開発とその適用
Software development and application for analyzing strongly
correlated electron systems
三澤 貴宏
東京大学物性研究所
150

Δe [meV]
0.8

As

0.6
0.4

Ab initio
Exp

0.2

Me4P

Fe

100

Me4As

La

Me4Sb

0
−0.2

T
30
40

N

[K]

20

−0.4 −0.4
010

predictexp.

O

EtMe3Sb−0.3

Et2Me2As
−0.2

−0.1

50
0

(t c-t b)/t a

0
0.975

1

1.025

1.05

1.075

1.1
1

Outline
1. Introduction: Ab initio method for correlated electron systems
2. Application to quantum spin liquid in β’-X[Pd(dmit)2]2
T. Misawa, K. Yoshimi, and T. Tsumuraya, Phys. Rev. Research 2, 032072(R) (2020)
K. Yoshimi, T. Tsumuraya, and T. Misawa, Phys. Rev. Research 3, 033224 (2021)
K . Ido, K. Yoshimi, T. Misawa, and M. Imada, npj Quantum Mater. 7, 48 (2022)

3. Application to iron-based high-Tc superconductors
K. Ido, Y. Motoyama, K. Yoshimi, and T. Misawa, J. Phys. Soc. Jpn 92, 064702 (2023)

4. Summary2

強相関電子系における新現象・新物質発見
電子がひしめき合う
強相関電子系ゆえの機能性

新しい物質の状態の出現(例)量子スピン液体70

銅酸化物高温超伝導体
鉄系高温超伝導体

Et2Me2Sb

60
Et2Me2Sb:
EtMe3Sb=88:12

T [K]

50
40

Me4P

Me4As

30
EtMe3As

20

AF order10
0
0.6
Y. Kamihara et al., JACS 130, 3296 (2008)

Et2Me2P
Me4Sb
Et2Me2AsCO
QSL

EtMe3Sb

0.7

0.8

t’/t

0.9

1.0

Read data from Fig. 17 in “K. Kanoda and R. Kato, Annu. Rev.
Condens. Matter Phys. 2, 167-188 (2011)” and replotted-強相関電子系は機能性材料の宝庫-電子相関の効果を取り扱える計算手法を開発することで、現象の起源解明を行い、予測・制御につなげることで、新奇現象・新物質の産業利用の可能性

3

Ab initio method for correlated electron systems✓ band calc.

✓ lattice structure

Energy [eV]5.5

✓Wannier func.

High-energy[virtual]

5

ta tb

b
X

EF

Target bands

tc
a

Y

4.5

High-energy[occupied]

4
3.5
Y

✓Clarifying electronic structures
Δe [meV]ΓX

M

ex-Hubbard type
Hamiltonians

HΦ

0.8
0.6
0.4

Ab initio
Exp

0.2<latexit sha1_base64="0Z1emXmp08cl1HV4PgMlhMxAMaI=">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</latexit>

H=

Me4P
Me4As

−0.2

T
30
40

]
K
[
N

20

−0.4 −0.4
010

EtMe3Sb−0.3

mVMC

Et2Me2As−0.2†
tij (ci cj

ij,

Me4Sb

0

X

−0.1

0

(t c-t b)/t a

+U

X
i

ni" ni# ++ H.c.)
X

Max-loc.
Wannier+cRPA

Vij Ni Nj

ij

Not only transfers, but also interaction parameters(t, U, V) are determined in an ab initio way

Open-source software packages
HΦ: exact diagonalization-Exact calc. for small system sizes(~40 sites)-Cutting-edge theoretical andmathematical method-Applications to QSL
https://github.com/issp-center-dev/HPhi

mVMC: many-variable variational MC-Applicable for large system sizes(~1000 sites)-Highly accurate and flexible method-# of variational parameters > 104-Applications to high-Tc SCs & QSL
https://github.com/issp-center-dev/mVMCRESPACK-Derivation of low-energy
effective Hamiltonians-Using wan2respack, user canuse wannier functions obtained by
Wannier90 as input for RESPACKRESPACK: https://sites.google.com/view/kazuma7k6r
wan2respack: https://github.com/respack-dev/wan2respack

Seamless combination with the ab initio
derivation of the low-energy effective models→ Systematic & comprehensive calculationsfor SCES are now possible(eg. Applications to molecular solids)

A part of development is supported
by PASUMS@ ISSP.

Quantum spin liquid in β’-X[Pd(dmit)2]2

T. Misawa, K. Yoshimi, and T. Tsumuraya, Phys. Rev. Research 2, 032072(R) (2020)
K. Yoshimi, T. Tsumuraya, and T. Misawa, Phys. Rev. Research 3, 033224 (2021)
K. Ido, K. Yoshimi, T. Misawa, and M. Imada, npj Quantum Mater. 7, 48 (2022)6Derivation of low-energy effective Hamiltonians
Mapping to the equivalent anisotropic triangular lattice

Ex. Hubbard Hamiltonians on anisotropic triangular lattice<latexit sha1_base64="0Z1emXmp08cl1HV4PgMlhMxAMaI=">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</latexit>

H=

X

†
tij (ci cj

ij,

+U

X
i

ni" ni# +9 compounds at room temperatures
5 compounds at low temperatures+ H.c.)

Not only transfers, but also interaction parameters(t, U, V) are determined in an ab initio way

X

Effects of dimensional downfolding [3D → 2D]
U=U-Δ,V=V-Δ, Δ=0.18 eV[cf. K.Nakamura et al., PRB 86,205117 (2012)]

ij

Vij Ni Nj

Derivation of low-energy effective Hamiltonians
Ex. Hubbard Hamiltonians on anisotropic triangular latticeta(tB)<latexit sha1_base64="0Z1emXmp08cl1HV4PgMlhMxAMaI=">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</latexit>

tc(tr)H=
tb(tS)

X†
tij (ci cj

ij,

+U

X

ni" ni# +i

Expected phase diagram
stripe[(π,0)]
tc

tb
ta

(tc-tb)/ta<0?
0+ H.c.)X

Vij Ni Nj

ij

Neel [(π,π)]For low-temperature structures,
all compounds show (tc-tb)/ta<0(tc-tb)/ta(tc-tb)/ta>0

Around (tc-tb)/ta~0, it is expected that magnetic order is melted and QSL appears

mVMC analysis
S<latexit sha1_base64="NLjtT86B6Jqw/S7EFVFWDRdlI0g=">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</latexit>| i = PJ PG L | pair i
Pair-product part<latexit sha1_base64="mmMHupgtqcbmX/WTOlT9w9j2jEY=">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</latexit>| pair i =hX† †FIJ cI cJ

I,J

iNe /2https://github.com/issp-center-dev/mVMC

Quantum number projection|0i

Total spin: LS
Point-group, momentum projections
are also possible<latexit sha1_base64="G3MTk0MbFeRdNamkPj0vE9Eg8OI=">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</latexit>

Projected BCS wave functions, which
can describe- Correlated metals- AF, CO order- Superconducting state & QSL

Optimization (SR method)
Mimimizing energy Eα<latexit sha1_base64="pJDGKxXtKB6z5p8y6cCuJOdQ72Y=">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</latexit>↵new

Correlation factors↵old = X

Gutzwiller-Jastrow factors<latexit sha1_base64="sAO7YPJIV7bAIHERNJcyxSAV2Vo=">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</latexit>"

PG = exp

X
i

#

2

gi ni" ni# , PJ = exp4

X
i,j

3

vij Ni Nj 5

1

g

⌦

X = ¯↵ ¯<latexit sha1_base64="J/tPsLm1zbAaUnpiB0PZ/Ik1/f4=">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</latexit>

g = @E↵ /@↵S. Sorella PRB (2001)↵

Equivalent to natural gradient method
S.-I. Amari Neural Comp. (1998)

By optimizing many variational parameters (#>=104), highly accurate calculations are possible!

Phase diagramΔe [meV]-Solving Hamiltonians for available low-temperature
structures

Δe=(EQSL-EAF)/Ns

0.8
0.6
0.4

Ab initio
Exp

0.2-Spin Jastrow factors, Composite-fermion pairing,
RBM factors are included

Me4P
Me4As
Me4Sb

0
−0.2

T
30
40

]
K
[
N

20

−0.4 −0.4010-Initial state of the QSL is projected BCS wave
functions→ 1D anisotropic QSL after optimization

EtMe3Sb−0.3

Et2Me2As
−0.2

−0.1

-Eigen-energies (zero-variance limit) are estimated(t c-t b)/t a by variance extrapolation
0

K. Ido et al., npj Quantum Mater. 7, 48 (2022)-Reproducing the trend of stability of the AF order:By changing cation X
from Me4P to EtMe3Sb, the AF order becomes unstable-Consistent w/ experimental Neel temperature TN-QSL becomes stable in EtMe3Sb !

Spin correlations in EtMe3Sby direction

x direction

−1

r

10

-1.88(1)−2|C(ry)||C(rx)|

10
−1

10

10

tc

1

tb
ta

6

8

−3

10

ta(tB)−4

10tc(tr)

tb(tS)

−5

L=12
L=16
L=20
L=24

−2

e

-0.75(2)r

10

−6

rx

10

10

2

4

ry

10

x direction → power low decay [r-p, p~1.88 (1)] (gapless)y direction → exponential decay (gapped)

12

鉄系超伝導体の有効模型導出+データ科学的解析

K. Ido, Y. Motoyama, K. Yoshimi, and T. Misawa,
J. Phys. Soc. Jpn. 92, 064702 (2023)
12

鉄系超伝導体の網羅的な有効模型導出
鉄系高温超伝導体への網羅計算[36物質]
K. Ido, Y. Motoyama, K. Yoshimi, and T. Misawa,
J. Phys. Soc. Jpn. 92, 064702 (2023)
一部はトヨタ自動車株式会社の支援を受けて実施

11

11

1111

111 42622

10

U: 軌道平均したクーロン相互作用9tmax : 最近接ホッピングの最大値

122

Others87
6
5
BaNi2As2
LaNiAsO
BaMn2As2BaMnAsF
BaFe2P2
SrFe2P2
CaFe2As2
BaFe2As2
KFe2As2
CaFe2P2
SrFe2As2
KFe2P2
Ca4Al2O6Fe2P2
Ca4Al2O6Fe2As2
Sr4Sc2O6Fe2P2
LiFeP
LiFeAsNaFeAsGdFePO
SmFePO
NdFePO
LaFePOPrFePO
GdFeAsO
TbFeAsO
SmFeAsO
CeFeAsO
LaFeAsO
PrFeAsO
NdFeAsO
CaFeAsH
CaFeAsF
SrFeAsF
FeTe
FeS
FeSe

cf. T. Miyake et al., JPSJ (2010).
6物質への適用

- 相互作用が物質によって2倍程度変化- 超伝導転移温度の実験値と有効模型のパラメータの間に関係は？

13

Low-energy effective Hamiltonians for iron-based SCs
5-orbital extended Hubbard models

Microscopic parameters: Hopping tij,
Coulomb interaction Vij, Exchange terms Jij

Main questions:-How are there any relation between microscopic parameters and Tc?
→ Principle component analysis (PCA)-If so, is it possible to predict Tc only from the microscopic parameters?
→ Construction of regression modelPrinciple Component Analysis (PCA)

descriptors: x1, x2, … = U,V,t, J..

In this case, v1 is a good descriptor
for characterizing materials

By performing the orthogonal trans., we can obtain
independent (uncorrelated) variables that describe therelevant features of parameter sets
→ Hint for searching the descriptors

PCA for iron-based SCs
1st component → U and V
2nd component → t and J

81111:P

6
4

FeS

2nd

2
0

FeSe

11 Fe-Te
11 Fe-S
11 Fe-Se
111 Fe-As
111 Fe-P
122 Fe-As
1111 Fe-As
1111 Fe-P
42622 Fe-As
42622 Fe-P

1111:As

-2
-4
-6
-8
-15

-10

-5

1st

0

5

10

Difference in intra- and inter families are characterized by 1st & 2nd components.
1111, 111 family has similar 1st comp. = U and V [Difference is characterized by t and J ]122, 4262 family has similar 2nd comp. = t and J [Difference is characterized by U and V ]11 family is exceptional (origin of exotic phenomena in FeSe ?)16

Tc vs 2nd principal components
70

1st component → U and V
60 2nd component → t and J

11 Fe-Te
11 Fe-S
11 Fe-Se
111 Fe-As
111 Fe-P
122 Fe-As
1111 Fe-As
1111 Fe-P
42622 Fe-As
42622 Fe-P

50

Tc

40
30
20
10
0-8

-6

-4

-2

0
2nd

2

4

6

2nd comp. well describes mat. dep. of experimental Tc! [similar to Lee’s plot]✓ Hamiltonians have information for describing Tc✓ PCA automatically detects a key parameter w/o a priori knowledge

817超伝導転移温度を予測する回帰モデル
出力: 超伝導転移温度 Tc

入力:微視的なパラメータ
Uij, Vij, tij, Vij/Uii, …

回帰モデル

f (z; w) = w0 +<latexit sha1_base64="arHEprJoEbxp/w59Iqz1ey6+Fs0=">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</latexit>X

zi w ii-LASSOによる重みの最適化-leave-one-out cross validation(LOO-CV)を模型の評価として使用

Outer CV

有効模型の微視的なパラメータの情報のみから超伝導転移温度を再現・予測する回帰モデルの作成

Inner CV18

超伝導転移温度を予測する回帰モデル
出力: 超伝導転移温度 Tc

入力:微視的なパラメータ
Uij, Vij, tij, Vij/Uii, …

回帰モデル

f (z; w) = w0 +<latexit sha1_base64="arHEprJoEbxp/w59Iqz1ey6+Fs0=">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</latexit>X

zi w iizi: 記述子 (Uij,tij, Vij2,(Vij/t)2…)
wi: 重み-LASSOによる重みの最適化

Outer CV

Inner CV
(ii)

(i)

(iii)

-leave-one-out cross validation(LOO-CV)を学習器の評価として使用(iv)

average(v)

有効模型の微視的なパラメータの情報のみから超伝導転移温度を再現・予測する回帰モデルの作成

(vi)

19

超伝導転移温度を予測する回帰モデル
Tc予測の回帰モデル

f (z; w) = w0 +[Tc = f(U, V, t, J, U/V…)]

60

11 Fe-Se
11 Fe-S
11 Fe-Te
111 Fe-As
111 Fe-P
122 Fe-As
1111 Fe-As
1111 Fe-P
42622 Fe-As
42622 Fe-P

40
30
20

zi w ii<latexit sha1_base64="arHEprJoEbxp/w59Iqz1ey6+Fs0=">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</latexit>

50

X

10
0

0

10

20

30

40

50

60

実験の超伝導転移温度をよく再現する回帰モデルの作成に成功

20

超伝導転移温度上昇の指針提示
Tc予測の回帰モデル

仮想物質の有効模型導出[Tc = f(U, V, t, J, U/V…)]→回帰モデルを用いたTc予測

150

60

11 Fe-Se
11 Fe-S
11 Fe-Te
111 Fe-As
111 Fe-P
122 Fe-As
1111 Fe-As
1111 Fe-P
42622 Fe-As
42622 Fe-P

50
40
30
20

As

predict
exp.
LaFeAsO

Fe

100
La
O

50

10
0

0

10

20

30

40

50

60

0
0.975

1

1.025

Tcを予測する学習器を用いて、転移温度をあげる指針を模索→Asの高さを制御することで転移温度上昇の可能性[レーザー照射での実現可能性]

1.05

1.075

1.1

K. Kuroki et al., PRB (2009)
FeSeへのレーザー照射
T. Suzuki et al., Commun. Phys.
(2019)
21

Summary
強相関第一原理計算の適用例として、以下の例について述べた- β’-X[Pd(admit)2]2 における量子スピン液体の解析
T. Misawa, K. Yoshimi, and T. Tsumuraya, Phys. Rev. Research 2, 032072(R) (2020)
K. Yoshimi, T. Tsumuraya, and T. Misawa, Phys. Rev. Research 3, 033224 (2021)
K. Ido, K. Yoshimi, T. Misawa, and M. Imada, npj Quantum Mater. 7, 48 (2022)-鉄系超伝導体の有効模型のパラメータと超伝導転移温度の関係の解析
K. Ido, Y. Motoyama, K. Yoshimi, and T. Misawa, J. Phys. Soc. Jpn. 92, 064702 (2023)

ソフトウェアの整備によって、物質の結晶構造(cifファイル)をもとに、強相関第一原理計算を網羅的に行うことが可能になりつつある→新奇現象の記述子を同定することで新材料提案へ!