Lattice fermion simulation of spontaneous time-reversal symmetry breaking in a helical Luttinger liquid

TL;DR

This paper develops a lattice simulation method for a helical Luttinger liquid that captures spontaneous time-reversal symmetry breaking and confirms the emergence of a gapped phase through tensor network calculations.

Contribution

It introduces a tangent fermion discretization approach that preserves time-reversal symmetry and enables numerical study of symmetry-breaking in helical Luttinger liquids.

Findings

A gapped phase with broken time-reversal symmetry appears at the Dirac point.

The tensor network calculations confirm analytical predictions.

The tangent dispersion avoids fermion doubling issues.

Abstract

We extend a recently developed "tangent fermion" method to discretize the Hamiltonian of a helical Luttinger liquid on a one-dimensional lattice, including two-particle backscattering processes that may open a gap in the spectrum. The fermion-doubling obstruction of the sine dispersion is avoided by working with a tangent dispersion, preserving the time-reversal symmetry of the Hamiltonian. The numerical results from a tensor network calculation on a finite lattice confirm the expectation from infinite-system analytics, that a gapped phase with spontaneously broken time-reversal symmetry emerges when the Fermi level is tuned to the Dirac point and the Luttinger parameter crosses a critical value.