Quantum Monte Carlo sign bounds, topological Mott insulator and thermodynamic transitions in twisted bilayer graphene model

Abstract

We show that for magic-angle twisted bilayer graphene (TBG) away from charge neutrality, although quantum Monte Carlo (QMC) simulations suffer from the sign problem, the computational complexity is at most polynomial at certain integer fillings. For even integer fillings, this polynomial complexity survives even if an extra inter-valley attractive interaction is introduced, on top of Coulomb repulsions. This observation allows us to simulate magic-angle twisted bilayer graphene and to obtain accurate phase diagram and dynamical properties. At the chiral limit and filling $\nu =1$, the simulations reveal a thermodynamic transition separating metallic state and a $C=1$ correlated Chern insulator -- topological Mott insulator (TMI) -- and the pseudogap spectrum slightly above the transition temperature. The ground state excitation spectra of the TMI exhibit a spin-valley U(4) Goldstone mode and a time reversal restoring excitonic gap smaller than the single particle gap. These results are qualitatively consistent with the recent experimental findings at zero-field and $\nu =1$ filling in $h$-BN nonaligned TBG.

References in corpus (24)

• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Topological Mott Insulators
• Continuum Model of the Twisted Bilayer
• Numerical studies of confined states in rotated bilayers of graphene
• MATBG as Topological Heavy Fermion: I. Exact Mapping and Correlated Insulators
• Possible Topological Superconducting Phases of MoS${}_2$
• Spin-orbit driven ferromagnetism at half moiré filling in magic-angle twisted bilayer graphene
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Using the average spectrum method to extract dynamics from quantum Monte Carlo simulations
• Cascades between light and heavy fermions in the normal state of magic angle twisted bilayer graphene
• Momentum space quantum Monte Carlo on twisted bilayer Graphene
• Reentrant Correlated Insulators in Twisted Bilayer Graphene at 25T ($2\pi$ Flux)
• Correlated insulators, density wave states, and their nonlinear optical response in magic-angle twisted bilayer graphene
• Emergence of broken-symmetry states at half-integer band fillings in twisted bilayer graphene
• Exciton Proliferation and Fate of the Topological Mott Insulator in a Twisted Bilayer Graphene Lattice Model
• Dynamical properties of collective excitations in twisted bilayer Graphene
• Phase diagram of twisted bilayer graphene at filling factor $\nu =\pm 3$
• Superconductivity and bosonic fluid emerging from Moiré flat bands
• Thermodynamic characteristic for correlated flat-band system with quantum anomalous Hall ground state
• Monte Carlo study of the pseudogap and superconductivity emerging from quantum magnetic fluctuations
• Fermion sign bounds theory in quantum Monte Carlo simulation
• Trions in Twisted Bilayer Graphene
• Evolution of Dynamical Signature in the X-cube Fracton Topological Order
• Projection of Infinite-$U$ Hubbard Model and Algebraic Sign Structure

Cited by in corpus (16)

• Symmetric Kondo Lattice States in Doped Strained Twisted Bilayer Graphene
• Dynamical correlations and order in magic-angle twisted bilayer graphene
• Phases of (2+1)D SO(5) non-linear sigma model with a topological term on a sphere: multicritical point and disorder phase
• Stable computation of entanglement entropy for 2D interacting fermion systems
• Kekulé spiral order in magic-angle graphene: a density matrix renormalization group study
• Anomalous Coherence Length in Superconductors with Quantum Metric
• Thermodynamic Response and Neutral Excitations in Integer and Fractional Quantum Anomalous Hall States Emerging from Correlated Flat Bands
• Evolution from quantum anomalous Hall insulator to heavy-fermion semimetal in magic-angle twisted bilayer graphene
• "Quantum Geometric Nesting" and Solvable Model Flat-Band Systems
• Dynamical properties of quantum many-body systems with long range interactions
• An integral algorithm of exponential observables for interacting fermions in quantum Monte Carlo simulation
• Moiré optical phonons dancing with heavy electrons in magic-angle twisted bilayer graphene
• Angle-Tuned Gross-Neveu Quantum Criticality in Twisted Bilayer Graphene: A Quantum Monte Carlo Study
• Perturbative solution of fermionic sign problem in lattice Quantum Monte Carlo
• Ubiquitous nematic Dirac semimetal emerging from interacting quadratic band touching system
• Mean-field Modelling of Moiré Materials: A User's Guide with Selected Applications to Twisted Bilayer Graphene