Quantum Monte Carlo at the Graphene Quantum Hall Edge

TL;DR

This paper employs sign-problem-free quantum Monte Carlo to explore the topological phase transition at the graphene quantum Hall edge, revealing detailed edge behaviors and bulk properties relevant for experiments.

Contribution

It introduces a large-scale quantum Monte Carlo study of the graphene quantum Hall edge, elucidating the interplay of topology and strong interactions during a phase transition.

Findings

Identification of kinks in edge dispersion branches

Observation of large charge susceptibility in the bulk

Detailed characterization of the topological phase transition

Abstract

We study a continuum model of the interface of graphene and vacuum in the quantum hall regime via sign-problem-free quantum Monte Carlo, allowing us to investigate the interplay of topology and strong interactions in a graphene quantum Hall edge for large system sizes. We focus on the topological phase transition from the spin polarized state with symmetry protected gapless helical edges to the fully charge gapped canted-antiferromagnet state with spontaneous symmetry breaking, driven by the Zeeman energy. Our large system size simulations allow us to detail the behaviour of various quantities across this transition that are amenable to be probed experimentally, such as the spatially and energy-resolved local density of states and the local compressibility. We find peculiar kinks in the branches of the edge dispersion, and also an unexpected large charge susceptibility in the bulk of the canted-antiferromagnet associated with its Goldstone mode.