Many-body perturbation theory for moir\'{e} systems

TL;DR

This paper develops a systematic many-body perturbation theory framework for moiré systems like twisted bilayer graphene, going beyond mean-field approaches to better understand strong correlations and symmetry-breaking phenomena.

Contribution

It introduces a Green's function-based perturbation theory for moiré systems, including analytical solutions at the Hartree-Fock level and GW corrections, advancing the study of electron correlations beyond mean-field.

Findings

Hartree-Fock solutions match known numerical results.

First-order GW diagrams overestimate electronic fluctuations.

Framework enables exploration of strong correlations beyond mean-field.

Abstract

Moir\'{e} systems such as magic-angle twisted bilayer graphene have attracted significant attention due to their ability to host correlated phenomena including superconductivity and strongly correlated insulating states. By defining the single-particle Green's function in the band basis, we systematically develop a many-body perturbation theory framework to address correlations beyond the usual mean-field Hartree-Fock approaches. As a specific example, we first analyze twisted bilayer graphene within the Hartree-Fock approximation. We derive analytical solutions for symmetry-breaking states at integer fillings and the finite-temperature metal-insulator transition that closely match previously known numerical results in the literature. Moving beyond Hartree-Fock, we incorporate self-consistent GW corrections demonstrating that first-order diagrams significantly overestimate the filling-dependent fluctuations in the electronic compressibility. This framework provides a comprehensive pathway for exploring strong electronic correlations in moir\'{e} systems beyond mean-field, giving new insights into the interplay of symmetry breaking and electron correlations.