Correlation effects in magic-angle twisted bilayer graphene: An auxiliary-field quantum Monte Carlo study
arXiv:2405.17808 · doi:10.1103/PhysRevResearch.7.013103
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.
References in corpus (53)
- Magic-angle graphene superlattices: a new platform for unconventional superconductivity
- Correlated Insulator Behaviour at Half-Filling in Magic Angle Graphene Superlattices
- Moire bands in twisted double-layer graphene
- Superconductors, Orbital Magnets, and Correlated States in Magic Angle Bilayer Graphene
- Origin of Magic Angles in Twisted Bilayer Graphene
- Maximally-localized Wannier orbitals and the extended Hubbard model for the twisted bilayer graphene
- Untying the insulating and superconducting orders in magic-angle graphene
- Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms
- Decoupling superconductivity and correlated insulators in twisted bilayer graphene
- Topological Superconductivity in Twisted Multilayer Graphene
- Faithful Tight-binding Models and Fragile Topology of Magic-angle Bilayer Graphene
- Phonon scattering dominated electron transport in twisted bilayer graphene
- Failure of Nielsen-Ninomiya theorem and fragile topology in two-dimensional systems with space-time inversion symmetry: application to twisted bilayer graphene at magic angle
- Quantum Monte Carlo method using phase-free random walks with Slater determinants
- Strong coupling phases of partially filled twisted bilayer graphene narrow bands
- Band Structure of Twisted Bilayer Graphene: Emergent Symmetries, Commensurate Approximants and Wannier Obstructions
- Symmetry, maximally localized Wannier states, and low energy model for the twisted bilayer graphene narrow bands
- Absence of superconductivity in the pure two-dimensional Hubbard model
- Ground State and Hidden Symmetry of Magic Angle Graphene at Even Integer Filling
- MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
- Phases of a phenomenological model of twisted bilayer graphene
- Designing Flat Band by Strain
- Twisted Bilayer Graphene IV. Exact Insulator Ground States and Phase Diagram
- Hofstadter subband ferromagnetism and symmetry broken Chern insulators in twisted bilayer graphene
- Ferromagnetic Mott State in Twisted Graphene Bilayers at the Magic Angle
- Visualization of the flat electronic band in twisted bilayer graphene near the magic angle twist
- Charged Skyrmions and Topological Origin of Superconductivity in Magic Angle Graphene
- Correlated insulating phases of twisted bilayer graphene at commensurate filling fractions: a Hartree-Fock study
- Twisted bilayer graphene. II. Stable symmetry anomaly
- Nematic topological semimetal and insulator in magic angle bilayer graphene at charge neutrality
- Strain-induced quantum phase transitions in magic angle graphene
- Quantum textures of the many-body wavefunctions in magic-angle graphene
- Efficient simulation of moire materials using the density matrix renormalization group
- Correlation-induced insulating topological phases at charge neutrality in twisted bilayer graphene
- Ground-state properties of the hydrogen chain: insulator-to-metal transition, dimerization, and magnetic phases
- Direct comparison of many-body methods for realistic electronic Hamiltonians
- Stripes and spin-density waves in the doped two-dimensional Hubbard model: ground state phase diagram
- Phaseless auxiliary-field quantum Monte Carlo calculations with planewaves and pseudopotentials--applications to atoms and molecules
- Some Recent Developments in Auxiliary-Field Quantum Monte Carlo for Real Materials
- Exact Diagonalization for Magic-Angle Twisted Bilayer Graphene
- Momentum space quantum Monte Carlo on twisted bilayer Graphene
- Valley Jahn-Teller effect in twisted bilayer graphene
- Issues and Observations on Applications of the Constrained-Path Monte Carlo Method to Many-Fermion Systems
- Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets
- Computation of ground-state properties in molecular systems: back-propagation with auxiliary-field quantum Monte Carlo
- Skyrmion Superconductivity: DMRG evidence for a topological route to superconductivity
- Dynamical correlations and order in magic-angle twisted bilayer graphene
- Correlated insulators, density wave states, and their nonlinear optical response in magic-angle twisted bilayer graphene
- Local Kekulé distortion turns twisted bilayer graphene into topological Mott insulators and superconductors
- Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study
- Interacting models for twisted bilayer graphene: a quantum chemistry approach
- Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene
- Interfacing branching random walks with Metropolis sampling: constraint release in auxiliary-field quantum Monte Carlo