Chin. Phys. Lett.  2021, Vol. 38 Issue (7): 077305    DOI: 10.1088/0256-307X/38/7/077305
CONDENSED MATTER: ELECTRONIC STRUCTURE, ELECTRICAL, MAGNETIC, AND OPTICAL PROPERTIES |
Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene
Xu Zhang1†, Gaopei Pan2,3†, Yi Zhang4, Jian Kang5, and Zi Yang Meng1,2*
1Department of Physics and HKU-UCAS Joint Institute of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong SAR, China
2Beijing National Laboratory for Condensed Matter Physics and Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China
3School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
4Kavli Institute for Theoretical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China
5School of Physical Science and Technology and Institute for Advanced Study, Soochow University, Suzhou 215006, China
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Xu Zhang, Gaopei Pan, Yi Zhang et al  2021 Chin. Phys. Lett. 38 077305
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Abstract We report an implementation of the momentum space quantum Monte Carlo (QMC) method on the interaction model for the twisted bilayer graphene (TBG). The long-range Coulomb repulsion is treated exactly with the flat bands, spin and valley degrees of freedom of electrons taking into account. We prove the absence of the minus sign problem for QMC simulation when either the two valleys or the two spin degrees of freedom are considered. By taking the realistic parameters of the twist angle and interlayer tunnelings into the simulation, we benchmark the QMC data with the exact band gap obtained at the chiral limit, to reveal the insulating ground states at the charge neutrality point (CNP). Then, with the exact Green's functions from QMC, we perform stochastic analytic continuation to obtain the first set of single-particle spectral function for the TBG model at CNP. Our momentum space QMC scheme therefore offers the controlled computation pathway for systematic investigation of the electronic states in realistic TBG model at various electron fillings.
Received: 28 May 2021      Published: 04 June 2021
PACS:  73.21.Cd (Superlattices)  
  02.70.Ss (Quantum Monte Carlo methods)  
Fund: Supported by the RGC of Hong Kong SAR of China (Grant Nos. 17303019, 17301420, and AoE/P-701/20), the National Key Research and Development Program of China (Grant No. 2016YFA0300502), the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000 and XDB28000000), the National Natural Science Foundation of China (Grant Nos. 11674278, 12004383, 12074276, and 12074276), the Fundamental Research Funds for the Central Universities, and the Priority Academic Program Development (PAPD) of Jiangsu Higher Education Institutions.
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https://cpl.iphy.ac.cn/10.1088/0256-307X/38/7/077305       OR      https://cpl.iphy.ac.cn/Y2021/V38/I7/077305
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Xu Zhang
Gaopei Pan
Yi Zhang
Jian Kang
and Zi Yang Meng
[1] Trambly de Laissardière G T, Mayou D, and Magaud L 2010 Nano Lett. 10 804
[2] Trambly de Laissardière G T, Mayou D, and Magaud L 2012 Phys. Rev. B 86 125413
[3] Bistritzer R and MacDonald A H 2011 Proc. Natl. Acad. Sci. USA 108 12233
[4] Rozhkov A V, Sboychakov A O, Rakhmanov A L, and Nori F 2016 Phys. Rep. 648 1
[5] Lopes dos Santos J M B, Peres N M R, and Neto A H C 2007 Phys. Rev. Lett. 99 256802
[6] Lopes dos Santos J M B, Peres N M R, and Neto A H C 2012 Phys. Rev. B 86 155449
[7] Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, and Jarillo-Herrero P 2018 Nature 556 43
[8] Cao Y, Fatemi V, Demir A, Fang S, Tomarken S L, Luo J Y, Sanchez-Yamagishi J D, Watanabe K, Taniguchi T, Ashoori Ray C, and Jarillo-Herrero P 2018 Nature 556 80
[9] Chen G, Sharpe A L, Fox E J, Zhang Y H, Wang S, Jiang L, Lyu B, Li H, Watanabe K, Taniguchi T, Shi Z, Senthil T, Goldhaber-Gordon D, Zhang Y, and Wang F 2020 Nature 579 56
[10] Kerelsky A, McGilly L J, Kennes D M, Xian L, Yankowitz M, Chen S, Watanabe K, Taniguchi T, Hone J, Dean C, Rubio A, and Pasupathy A N 2019 Nature 572 95
[11] Tomarken S L, Cao Y, Demir A, Watanabe K, Taniguchi T, Jarillo-Herrero P, and Ashoori R C 2019 Phys. Rev. Lett. 123 046601
[12] Lu X, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G et al. 2019 Nature 574 653
[13] Xie Y, Lian B, Jäck B, Liu X, Chiu C L, Watanabe K, Taniguchi T, Bernevig B A, and Yazdani A 2019 Nature 572 101
[14] Shen C, Chu Y, Wu Q, Li N, Wang S, Zhao Y, Tang J, Liu J, Tian J, Watanabe K, Taniguchi T, Yang R, Meng Z Y, Shi D, Yazyev O V, and Zhang G 2020 Nat. Phys. 16 520
[15] Nuckolls K P, Myungchul O, Wong D, Lian B, Watanabe K, Taniguchi T, Bernevig B A, and Yazdani A 2020 Nature 588 610
[16] Pierce A T, Xie Y, Park J M, Khalaf E, Lee S H, Cao Y, Parker D E, Forrester P R, Chen S, Watanabe K, Taniguchi T, Vishwanath A, Jarillo-Herrero P, and Yacoby A 2021 arXiv:2101.04123 [cond-mat.mes-hall]
[17] Moriyama S, Morita Y, Komatsu K, Endo K, Iwasaki T, Nakaharai S, Noguchi Y, Wakayama Y, Watanabe E, Tsuya D, Watanabe K, and Taniguchi T 2019 arXiv:1901.09356 [cond-mat.supr-con]
[18] Rozen A, Park J M, Zondiner U, Cao Y, Rodan-Legrain D, Taniguchi T, Watanabe K, Oreg Y, Stern A, Berg E, Jarillo-Herrero P, and Ilani S 2020 arXiv:2009.01836 [cond-mat.mes-hall]
[19] Liu X, Chiu C L, Lee J Y, Farahi G, Watanabe K, Taniguchi T, Vishwanath A, and Yazdani A 2020 arXiv:2008.07552 [cond-mat.mes-hall]
[20] Shen C, Ying J, Liu L, Liu J, Li N, Wang S, Tang J, Zhao Y, Chu Y, Watanabe K, Taniguchi T, Yang R, Shi D, Qu F, Lu L, Yang W, and Zhang G 2021 Chin. Phys. Lett. 38 047301
[21] Po H C, Watanabe H, and Vishwanath A 2018 Phys. Rev. Lett. 121 126402
[22] Po H C, Zou L, Senthil T, and Vishwanath A 2019 Phys. Rev. B 99 195455
[23] Bultinck N, Chatterjee S, and Zaletel M P 2020 Phys. Rev. Lett. 124 166601
[24] Po H C, Zou L, Vishwanath A, and Senthil T 2018 Phys. Rev. X 8 031089
[25] Tarnopolsky G, Kruchkov A J, and Vishwanath A 2019 Phys. Rev. Lett. 122 106405
[26] Yuan N F Q and Fu L 2018 Phys. Rev. B 98 045103
[27] Kang J and Vafek O 2018 Phys. Rev. X 8 031088
[28] Koshino M, Yuan N F Q, Koretsune T, Ochi M, Kuroki K, and Fu L 2018 Phys. Rev. X 8 031087
[29] Roy B and Juričić V 2019 Phys. Rev. B 99 121407
[30] Zhang Y, Jiang K, Wang Z, and Zhang F 2020 Phys. Rev. B 102 035136
[31] Bultinck N, Khalaf E, Liu S, Chatterjee S, Vishwanath A, and Zaletel M P 2020 Phys. Rev. X 10 031034
[32] Hejazi K, Chen X, and Balents L 2021 Phys. Rev. Res. 3 013242
[33] Xie M and MacDonald A H 2020 Phys. Rev. Lett. 124 097601
[34] Liu J, Liu J, and Dai X 2019 Phys. Rev. B 99 155415
[35] Liu J and Dai X 2020 npj Comput. Mater. 6 1
[36] Liu J and Dai X 2021 Phys. Rev. B 103 035427
[37] Cea T and Guinea F 2020 Phys. Rev. B 102 045107
[38] Liu S, Khalaf E, Lee J Y, and Vishwanath A 2021 Phys. Rev. Res. 3 013033
[39] Carr S, Fang S, Zhu Z, and Kaxiras E 2019 Phys. Rev. Res. 1 013001
[40] Kwan Y H, Wagner G, Soejima T, Zaletel M P, Simon S H, Parameswaran S A, and Bultinck N 2021 arXiv:2105.05857 [cond-mat.str-el]
[41] Chatterjee S, Ippoliti M, and Zaletel M P 2020 arXiv:2010.01144 [cond-mat.str-el]
[42] Khalaf E, Chatterjee S, Bultinck N, Zaletel M P, and Vishwanath A 2021 Sci. Adv. 7 eabf5299
[43] Kang J and Vafek O 2020 Phys. Rev. B 102 035161
[44] Soejima T, Parker D E, Bultinck N, Hauschild J, and Zaletel M P 2020 Phys. Rev. B 102 205111
[45] Huang Y, Hosur P, and Pal H K 2020 Phys. Rev. B 102 155429
[46] Xie F, Cowsik A, Song Z D, Lian B, Bernevig B A, and Regnault N 2021 Phys. Rev. B 103 205416
[47] Ochi M, Koshino M, and Kuroki K 2018 Phys. Rev. B 98 081102
[48] Dodaro J F, Kivelson S A, Schattner Y, Sun X Q, and Wang C 2018 Phys. Rev. B 98 075154
[49] Potasz P, Xie M, and MacDonald A H 2021 arXiv:2102.02256 [cond-mat.str-el]
[50] Vafek O and Kang J 2020 Phys. Rev. Lett. 125 257602
[51] Kang J and Vafek O 2019 Phys. Rev. Lett. 122 246401
[52] Song Z D, Lian B, Regnault N, and Bernevig B A 2021 Phys. Rev. B 103 205412
[53] Bernevig B A, Song Z D, Regnault N, and Lian B 2021 Phys. Rev. B 103 205413
[54] Lian B, Song Z D, Regnault N, Efetov D K, Yazdani A, and Bernevig B A 2021 Phys. Rev. B 103 205414
[55] Bernevig B A, Lian B, Cowsik A, Xie F, Regnault N, and Song Z D 2021 Phys. Rev. B 103 205415
[56] Alavirad Y and Sau J 2020 Phys. Rev. B 102 235123
[57] Hirsch J E 1985 Phys. Rev. B 31 4403
[58] Xu X Y, Sun K, Schattner Y, Berg E, and Meng Z Y 2017 Phys. Rev. X 7 031058
[59] Liu Z H, Pan G, Xu X Y, Sun K, and Meng Z Y 2019 Proc. Natl. Acad. Sci. USA 116 16760
[60] Liao Y D, Meng Z Y, and Xu X Y 2019 Phys. Rev. Lett. 123 157601
[61] Liao Y D, Kang J, Breiø C N, Xu X Y, Wu H Q, Andersen B M, Fernandes R M, and Meng Z Y 2021 Phys. Rev. X 11 011014
[62] Liao Y D, Xu X Y, Meng Z Y, and Kang J 2021 Chin. Phys. B 30 017305
[63] Xu X Y, Law K T, and Lee P A 2018 Phys. Rev. B 98 121406
[64] Huang T, Zhang L, and Ma T 2019 Sci. Bull. 64 310
[65] Liu Z H, Xu X Y, Qi Y, Sun K, and Meng Z Y 2019 Phys. Rev. B 99 085114
[66] Wang Z, Zaletel M P, Mong R S K, and Assaad F F 2021 Phys. Rev. Lett. 126 045701
[67] Ippoliti M, Mong R S K, Assaad F F, and Zaletel M P 2018 Phys. Rev. B 98 235108
[68]The symmetry properties of the form factor and the proofs of the sign structure of the fermion determinant, the QMC measurements and brief description of the stochastic analytic continuation, are presented in the Supplemental Material.
[69]Assaad F and Evertz H 2008 World-Line and Determinantal Quantum Monte Carlo Methods for Spins, Phonons and Electrons, in Computational Many-Particle Physics, ed Fehske H, Schneider R and A. Weiße (Berlin: Springer) pp 277–356
[70] Xu X Y, Liu Z H, Pan G, Qi Y, Sun K, and Meng Z Y 2019 J. Phys.: Condens. Matter 31 463001
[71]Lee J Y, Hofmann J, Khalaf E, Vishwanath A, and Berg E 2021 APS March Meeting S43 00013
[72] Hofmann J S, Khalaf E, Vishwanath A, Berg E, and Lee J Y 2021 arXiv:2105.12112 [cond-mat.str-el]
[73] Sandvik A W 1998 Phys. Rev. B 57 10287
[74] Beach K 2004 arXiv:cond-mat/0403055 [cond-mat.str-el]
[75] Sandvik A W 2016 Phys. Rev. E 94 063308
[76] Syljuåsen O F 2008 Phys. Rev. B 78 174429
[77] Shao H, Qin Y Q, Capponi S, Chesi S, Meng Z Y, and Sandvik A W 2017 Phys. Rev. X 7 041072
[78] Sun G Y, Wang Y C, Fang C, Qi Y, Cheng M, and Meng Z Y 2018 Phys. Rev. Lett. 121 077201
[79] Ma N, Sun G Y, You Y Z, Xu C, Vishwanath A, Sandvik A W, and Meng Z Y 2018 Phys. Rev. B 98 174421
[80] Huang C J, Deng Y, Wan Y, and Meng Z Y 2018 Phys. Rev. Lett. 120 167202
[81] Yan Z, Wang Y C, Ma N, Qi Y, and Meng Z Y 2021 npj Quantum Mater. 6 1
[82] Li H, Liao Y D, Chen B B, Zeng X T, Sheng X L, Qi Y, Meng Z Y, and Li W 2020 Nat. Commun. 11 1111
[83] Hu Z, Ma Z, Liao Y D, Li H, Ma C, Cui Y, Shangguan Y, Huang Z, Qi Y, Li W et al. 2020 Nat. Commun. 11 5631
[84] Zhou C, Yan Z, Wu H Q, Sun K, Starykh O A, and Meng Z Y 2020 arXiv:2007.12715 [cond-mat.str-el]
[85] Wang Y C, Yan Z, Wang C, Qi Y, and Meng Z Y 2021 Phys. Rev. B 103 014408
[86] Jiang W, Liu Y, Klein A, Wang Y, Sun K, Chubukov A V, and Meng Z Y 2021 arXiv:2105.03639 [cond-mat.str-el]
[87] Xu X Y, Klein A, Sun K, Chubukov A V, and Meng Z Y 2020 npj Quantum Mater. 5 65
[88] Wang W, Davis A, Pan G, Wang Y, and Meng Z Y 2021 Phys. Rev. B 103 195108
[89] Pan G, Wang W, Davis A, Wang Y, and Meng Z Y 2021 Phys. Rev. Res. 3 013250
[90] Chen C, Yuan T, Qi Y, and Meng Z Y 2021 Phys. Rev. B 103 165131
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