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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http://cpl.iphy.ac.cn/10.1088/0256-307X/38/7/077305       OR      http://cpl.iphy.ac.cn/Y2021/V38/I7/077305
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Xu Zhang
Gaopei Pan
Yi Zhang
Jian Kang
and Zi Yang Meng
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