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

TL;DR

This paper demonstrates polynomial-time quantum Monte Carlo simulations of twisted bilayer graphene at certain fillings, revealing a topological Mott insulator and thermodynamic transitions consistent with experiments.

Contribution

It shows that QMC simulations can be efficiently performed for TBG at specific fillings, enabling detailed phase diagram and dynamical property analysis.

Findings

Identification of a thermodynamic transition to a topological Mott insulator at $ u=1$

Observation of a spin-valley Goldstone mode in the TMI spectrum

Qualitative agreement with recent experimental results in TBG

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.