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

Journal Article · 26 January 2025 · Physical Review Research

DOI: https://doi.org/10.1103/PhysRevResearch.7.013103 · OSTI ID:2507132

Xiao, Zhi-Yu ; Zhang, Shiwei

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 a 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 intervalley-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. Published by the American Physical Society 2025

• Sponsoring Organization: USDOE
• Grant/Contract Number: SC0001303
• OSTI ID: 2507132
• Journal Information: Physical Review Research, Journal Name: Physical Review Research Journal Issue: 1 Vol. 7; ISSN PPRHAI; ISSN 2643-1564
• Publisher: American Physical SocietyCopyright Statement
• Country of Publication: United States
• Language: English