「富岳」成果創出加速プログラム 物質・材料系課題 合同研究会プログラム

強相関電⼦系における励起スペクトルのための⼿法開発とPd(dmit)2塩における基底状態の網羅的解析
K. Ido (ISSP)
Collaborators:
K. Yoshimi (ISSP), T. Misawa (BAQIS), M. Imada (Waseda/Toyota RIKEN)
Outline・Multi-scale Ab initio scheme for Correlated Electrons (MACE)
・Application to Pd(dmit)2 salts
・Dynamical structure factors in strongly correlated systems

量⼦物質の創発と機能のための基礎科学―「富岳」と最先端実験の密連携による⾰新的強相関電⼦科学
創発粒⼦や“量⼦スープ”が⽣む
室温超伝導や次々世代デバイスへの期待に基づく「新たな概念の基礎科学解明」と「機能性開拓」
From http://www.aoni.waseda.jp/imada/fugaku/fugaku_top.html• Target: strongly correlated materials• High-Tc superconductors• Cuprate, Iron-based superconductors• Topological materials/spin liquids• Iridate, Ruthenate• Pd(dmit)2 salts

Can we reproduce/predict physical properties ofstrongly correlated materials based on ab initial calculations?
1Multi-scale Ab initio scheme for CorrelatedElectrons (MACE) For a review, M. Imada and T. Miyake, JPSJ 79,112001(2010)l Band calculationl Derive low-energy effective Hamiltonian<latexit sha1_base64="VbiNx4kKFP8cQuzSvl89ptr5YCk=">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</latexit>

H=

XXX

†
tnRmR0 cnR
cmR0→ Hopping term

R,R0 n,m

1 X X Xn† ⇢†+UnRmR0 cnR
cmR0 c⇢mR0 cnR
2 ,⇢
0 n,m

→ Coulomb term

R,R

† ⇢†
† ⇢† ⇢+JnRmR0 (cnR
cmR0 c⇢nR cmR0 + cnRcnR cmR0 cmR0 )o→ Exchange terml Solve Hamiltonian by a many-body solver• Exact diagonalization✔ Exact wavefunction, excited states❌ only small system size (< 20 electrons)• Variational Monte Carlo (VMC)✔ Ground state in large system size (100~1000 electrons)✔ ab initio Hamiltonian with long-range interactions❌ Biased wavefunction, excited states

2Recent research activity
Study 1: ab initio study onPd(dmit)2 salts to reveal
QSL nature

Study 2: How to obtain charge
dynamical structure factor
based on VMC method

K. Ido, M. Imada, T. Misawa,Phys. Rev. B 101, 075124 (2020).

3

Study 2
How to obtain charge
dynamical structure factors
in electron systems
K. Ido, M. Imada, T. Misawa, Phys. Rev. B 101, 075124 (2020).

4

Measurable quantities in VMC✔ “Static” physical quantities††
hc†i cj 0 i hci i cj j ck k cl l i<latexit sha1_base64="AMjCTjmFdGnkhjK8TPyxD8eIJ4c=">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</latexit><latexit sha1_base64="r0n7aoOOaDcB4mPpOpKayBDPuJg=">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</latexit>

Order parameters,
Momentum distribution…

❌ “Dynamical” physical quantities

Experiments

How to measuredynamical quantities
by VMC?

• ARPES• Neutron• RIXSA(k, !)<latexit sha1_base64="Rp438byVvR+1zeWu/6DR+ToJowc=">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</latexit>
sha1_base64="59nY6sevVWVvq/OqClhMfJaCAPI=">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</latexit>
sha1_base64="ivn5Wqx5DX5BtbmEOME8Gwxjs0g=">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</latexit>
sha1_base64="So6PnY9ywzCJILabKnrLwBwuesw=">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</latexit>

S(q, !)<latexit sha1_base64="2XxDN8teja9eaRmfXzikG8juH78=">AAACwXichVHLLgRRED3ae7waG4mNmBASmVSLhFgJG0uMQWJk0t2ucTP90t0zCR0/4Acs2JCQiM+wsbG08AliSWJjobqnE0GM6vS9VeeeU7duleFZMgiJnpqU5pbWtvaOzkxXd09vn9o/sBG4Vd8UBdO1XH/L0ANhSUcUQhlaYsvzhW4bltg0Kkvx+WZN+IF0nfXw0BM7tl525J409ZChkqrmJ4qGHR0cTxVdW5T1yZKapRwlNvLb0VIni9RWXPUBRezChYkqbAg4CNm3oCPgbxsaCB5jO4gY89mTybnAMTKsrTJLMENntMJrmaPtFHU4jnMGidrkWyz+fVaOYIwe6YZe6Z5u6Zk+/swVJTniWg55N+pa4ZX6Toby7/+qbN5D7H+pGigMrkznWLAi5jdi2g0Z8ftD7GEuebfkPngJEnfErNdSOzp9zc+vjUXjdEkv3IsLeqI77oZTezOvVsXaGTI8TO3n6H47G9M5jXLa6kx2YTEdaweGMYoJnt0sFrCMFRT43hrOcYVrZUmRiqf4darSlGoG8c2U6BOE758p</latexit>
sha1_base64="59nY6sevVWVvq/OqClhMfJaCAPI=">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</latexit>
sha1_base64="AK6R7m9oUFihTwRMd2w+61kS3uA=">AAACtnichVE9SwNBEH2e3zGa00qwESUSQcKcjWIl2FiqMSokIdydm7jkvry7BDT4B/wDFtooKIg/w8bG0sKfIJYKNhbOXQKiwTjH7c68nTc7O8/wLBmERM89Sm9f/8Dg0HBiJDk6llLHkzuBW/dNkTddy/X3DD0QlnREPpShJfY8X+i2YYldo7YWne82hB9I19kOjzxRsvWqIyvS1EOGyqqayxQNu3l4slB0bVHV58vqLGUptulOR2s7s2jbhqs+ooh9uDBRhw0BByH7FnQE/BWggeAxVkKTMZ89GZ8LnCDB3DpnCc7QGa3xWuWo0EYdjqOaQcw2+RaLf5+Z00jTE93SGz3QHb3Q55+1mnGNqJcj3o0WV3jl1Olk7uNfls17iINvVheGwZ3pHAtmRPndMu2uGdH7Q1SwHL9b8hy8GIkmYrZ6aRyfveVWttLNObqiV57FJT3TPU/Dabyb15ti6xwJFlP7LV2ns7OY1SirbRKGMIUZZFiyJaxiHRvI83UNXOAaN8qaIhWvJbvS09Z/Aj9M8b8Aozid/A==</latexit>
sha1_base64="T00uZx89KwsHRpwPENYUCoae9FU=">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</latexit>

N (q, !)
S(q, !)<latexit sha1_base64="y7SOOXGbUk5LboPF5tHoiV9IUqs=">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</latexit>
sha1_base64="59nY6sevVWVvq/OqClhMfJaCAPI=">AAACoXichVG7SgNRED1ZXzFGEzvBJhgiVmHWRrESbCw1mgfEEHY3N3HJvtjdBGLwB9JaWFgpWIifYWNjaeEniGUEGwtnNwuiwTjL3jtz7py5c+eojqF7PtFLTJqanpmdi88nFpKJxaVUOlny7I6riaJmG7ZbURVPGLolir7uG6LiuEIxVUOU1fZecF7uCtfTbevY7zmiZiotS2/qmuIzdFBPZylPoWXGHTlysojMTj/hBA3Y0NCBCQELPvsGFHj8VSGD4DBWQ58xlz09PBc4R4K5Hc4SnKEw2ua1xVE1Qi2Og5peyNb4FoN/l5kZ5OiZ7mhIj3RPr/T5Z61+WCPopce7OuIKp54arBx9/Msyefdx+s2awFC5M4VjwYwgf1KmOTEjeL+PJrbDd+s8BydEgoloo166Z5fDo51Crr9ON/TGs7imF3rgaVjdd+32UBSukGAt5d/KjTulzbxMefmQEMcq1rDBkm1hF/s4QJGva2CAC4mkklQbaS7FIvGX8cOk+hdlXZaE</latexit>
sha1_base64="vaKFgddINeWR359wjuibnHd3K78=">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</latexit>
sha1_base64="fNvnr1icWiZL9GLawzm2wdl6hiM=">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</latexit>• Pump-probe・・・<latexit sha1_base64="2XxDN8teja9eaRmfXzikG8juH78=">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</latexit>
sha1_base64="59nY6sevVWVvq/OqClhMfJaCAPI=">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</latexit>
sha1_base64="AK6R7m9oUFihTwRMd2w+61kS3uA=">AAACtnichVE9SwNBEH2e3zGa00qwESUSQcKcjWIl2FiqMSokIdydm7jkvry7BDT4B/wDFtooKIg/w8bG0sKfIJYKNhbOXQKiwTjH7c68nTc7O8/wLBmERM89Sm9f/8Dg0HBiJDk6llLHkzuBW/dNkTddy/X3DD0QlnREPpShJfY8X+i2YYldo7YWne82hB9I19kOjzxRsvWqIyvS1EOGyqqayxQNu3l4slB0bVHV58vqLGUptulOR2s7s2jbhqs+ooh9uDBRhw0BByH7FnQE/BWggeAxVkKTMZ89GZ8LnCDB3DpnCc7QGa3xWuWo0EYdjqOaQcw2+RaLf5+Z00jTE93SGz3QHb3Q55+1mnGNqJcj3o0WV3jl1Olk7uNfls17iINvVheGwZ3pHAtmRPndMu2uGdH7Q1SwHL9b8hy8GIkmYrZ6aRyfveVWttLNObqiV57FJT3TPU/Dabyb15ti6xwJFlP7LV2ns7OY1SirbRKGMIUZZFiyJaxiHRvI83UNXOAaN8qaIhWvJbvS09Z/Aj9M8b8Aozid/A==</latexit>
sha1_base64="T00uZx89KwsHRpwPENYUCoae9FU=">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</latexit>

5

Previous study: Spin dynamical structure factor
T. Li and F. Yang, Phys. Rev. B, 81, 214509 (2010) B. Dalla Piazza et al., Nat. Phys. 11, 62 (2015)
F. Ferrari et al., Phys. Rev. B, 97, 235103 (2018). F. Ferrari et al., PRB 98, 100405(R) (2018)• Make Excited states (Spin systems)†
example: | n i = |i, Ri = Pci+R, ci,<latexit sha1_base64="DsJsE+gUFRdIkz84npYJH3xo3Cc=">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</latexit>| i<latexit sha1_base64="(null)">(null)</latexit>• Construct restricted Hamiltonian & overlap matrix

Hnm = h n |H| m i Onm = h n | m i<latexit sha1_base64="0FQ8HuoKlmWIUPDCCCGPqtMBfPo=">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</latexit><latexit sha1_base64="RSfDCdeja3AdbIgv2MbQYR8Ef3M=">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</latexit>• Solve generalized eigenvalue problem

Hv = EOv<latexit sha1_base64="IQ0QU5NC6F8n/Gjfek/U91M+w4o=">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</latexit>• Calculate spin dynamical structure factor
X
S(q, !) =| hvnq |Sq | i |2 (! Enq + E0 )<latexit sha1_base64="bBD+ws35rhhvWmH2UfLC1IVLn2k=">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</latexit>n6Extension to correlated electron systems
K. Ido, M. Imada, T. Misawa, Phys. Rev. B 101, 075124 (2020).

Q: What is variational description forcharge dynamics of correlated electrons ?
A: Efficient basis set: Hubbard operators<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

F. Mancini and A. Avella, Adv. Phys. 53, 537 (2004).
<latexit sha1_base64="(null)">(null)</latexit>: doublon → spinon: spinon → holon<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

・Benchmark: Hubbard model7

N(q, ω) of 1D Hubbard model for L=14
K. Ido, M. Imada, T. Misawa, Phys. Rev. B 101, 075124 (2020).

ED, half filling, U/t=8

VMC-BF
BF

ED, hole dope, U/t=12

VMC-BF

16

0.3

12

0.2

8

0.5

0.1

0

0.5

1

0

VMC-CF

12
8

4
0

16

VMC-CF

0.25

4
0

0

0.5

1

0

VMC-CF can well reproduce ED

8

N(q, ω) of 2D Hubbard model<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

K. Ido, M. Imada, T. Misawa, Phys. Rev. B 101, 075124 (2020).

<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>• Ns=4x4, U/t=8
・U-dependence ofmean absolute error<latexit sha1_base64="ee2roWC4TmKmnbI7WsW0gDTUYuA=">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</latexit>

Nq

1 X✏MAE =✏(q)
Nq q

CF approach improves accuracy,
but there is still discrepancy…

9

Outlook for Two dimensional systems
K. Ido, M. Imada, T. Misawa, Phys. Rev. B 101, 075124 (2020).

• Other composite fermions?
Onsite configuration

Configuration on neighbor sites<latexit sha1_base64="(null)">(null)</latexit>

etc.

<latexit sha1_base64="(null)">(null)</latexit>• Multiple excitations?

<latexit sha1_base64="(null)">(null)</latexit><latexit sha1_base64="(null)">(null)</latexit>

10Summary and outlook
Study 1: ab initio study onPd(dmit)2 salts to reveal
QSL nature

Study 2: How to obtain charge
dynamical structure factor
based on VMC method• Composite-fermion excitation
play an important role
• Improve variational description
in 2D systems

K. Ido, M. Imada, T. Misawa,Phys. Rev. B 101, 075124 (2020).

11