Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study
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 interact...
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American Physical Society
2025-01-01
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| Series: | Physical Review Research |
| Online Access: | http://doi.org/10.1103/PhysRevResearch.7.013103 |
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| author | Zhi-Yu Xiao Shiwei Zhang |
| author_facet | Zhi-Yu Xiao Shiwei Zhang |
| author_sort | Zhi-Yu Xiao |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-c5fc74340a7949e198af193e4cf4d6b5 |
| institution | Kabale University |
| issn | 2643-1564 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review Research |
| spelling | doaj-art-c5fc74340a7949e198af193e4cf4d6b52025-01-27T15:07:12ZengAmerican Physical SocietyPhysical Review Research2643-15642025-01-017101310310.1103/PhysRevResearch.7.013103Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo studyZhi-Yu XiaoShiwei ZhangMagic-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.http://doi.org/10.1103/PhysRevResearch.7.013103 |
| spellingShingle | Zhi-Yu Xiao Shiwei Zhang Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study Physical Review Research |
| title | Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study |
| title_full | Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study |
| title_fullStr | Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study |
| title_full_unstemmed | Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study |
| title_short | Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study |
| title_sort | correlation effects in magic angle twisted bilayer graphene an auxiliary field quantum monte carlo study |
| url | http://doi.org/10.1103/PhysRevResearch.7.013103 |
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