The effect of interaction and electron fillings in twisted bilayer graphene: an auxiliary-field quantum Monte Carlo study

Twisted bilayer graphene (TBG) near the magic angle provides a rich and fascinating platform for studying electron correlation effects. We investigate a many-body model Hamiltonian which consists of the single-particle model of Bistritzer and MacDonald (BM) [1] and realistic electron-electron Coulomb interactions, employing a state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method [2]. The BM model gives a momentum-space continuum description of the most relevant topological flat bands. Our AFQMC approach allows accurate treatment of the many-body Hamiltonian while controlling the sign problem. We determine the ground-state properties of this model across different integer fillings and quantify the errors from mean-field theory calculations.

[1] R. Bistritzer and A. H. MacDonald, Moire bands in twisted double-layer graphene, Proceedings of the National Academy of Sciences 108, 12233 (2011).

[2]S. Zhang and H. Krakauer, Quantum monte carlo method using phase-free random walks with slater determinants, Phys. Rev. Lett. 90, 136401 (2003).