Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study

TL;DR

This study employs advanced quantum Monte Carlo methods to analyze electron correlation effects in magic-angle twisted bilayer graphene, revealing competing metallic and insulating states and emphasizing the importance of precise many-body Hamiltonian modeling.

Contribution

It introduces the use of AFQMC to accurately study the IBM model of MATBG, addressing previous computational limitations and exploring many-body effects beyond mean-field approximations.

Findings

Identification of correlated metal states at various fillings.

Observation of competition between metallic and insulating phases.

Quantification of many-body correction effects on ground-state properties.

Abstract

Magic angle twisted bilayer graphene (MATBG) presents a fascinating platform for investigating the effects of electron interactions in topological flat bands. The Bistritzer-MacDonald (BM) model provides a simplified quantitative description of the flat bands. Introducing long-range Coulomb interactions leads to an interacting BM (IBM) Hamiltonian, a momentum-space continuum description which offers a very natural starting point for many-body studies of MATBG. Accurate and reliable many-body computations in the IBM model are challenging, however, and have been limited mostly to special fillings, or smaller lattice sizes. We employ state-of-the-art auxiliary-field quantum Monte Carlo (AFQMC) method to study the IBM model, which constrains the sign problem to enable accurate treatment of large system sizes. We determine ground-state properties and quantify errors compared to mean-field theory calculations. Our calculations identify correlated metal states and their competition with the insulating Kramers inter-valley coherent state at both half-filling and charge neutrality. Additionally, we investigate one- and three-quarter fillings, and examine the effect of many-body corrections beyond single Slater determinant solutions. We discuss the effect that details of the IBM Hamiltonian have on the results, including different forms of double-counting corrections, and the need to establish and precisely specify many-body Hamiltonians to allow more direct and quantitative comparisons with experiments in MATBG.