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
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.
. [J]. 中国物理快报, 2021, 38(7): 77305-077305.
Xu Zhang, Gaopei Pan, Yi Zhang, Jian Kang, and Zi Yang Meng. Momentum Space Quantum Monte Carlo on Twisted Bilayer Graphene. Chin. Phys. Lett., 2021, 38(7): 77305-077305.
Cao Y, Fatemi V, Fang S, Watanabe K, Taniguchi T, Kaxiras E, and Jarillo-Herrero P 2018 Nature556 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 Nature556 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 Nature579 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 Nature572 95
Lu X, Stepanov P, Yang W, Xie M, Aamir M A, Das I, Urgell C, Watanabe K, Taniguchi T, Zhang G et al.2019 Nature574 653
[13]
Xie Y, Lian B, Jäck B, Liu X, Chiu C L, Watanabe K, Taniguchi T, Bernevig B A, and Yazdani A 2019 Nature572 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 Nature588 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
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
2021, Vol. 38 
