Momentum space quantum Monte Carlo on twisted bilayer Graphene

TL;DR

This paper presents a momentum space quantum Monte Carlo method for twisted bilayer graphene, enabling accurate simulations of electronic states and spectral functions at various fillings without the sign problem.

Contribution

The authors develop and benchmark a sign-problem-free momentum space QMC approach for realistic TBG models, including long-range Coulomb interactions and exact Green's functions.

Findings

Confirmed insulating ground states at charge neutrality point.

Obtained the first single-particle spectral functions for TBG at CNP.

Validated QMC results against exact band gap at the chiral limit.

Abstract

We report an implementation of the momentum space quantum Monte Carlo (QMC) method on the interaction model for the twisted bilayer graphene (TBG) at integer fillings. 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 at integer fillings when either the two valley 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.