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

Zakharov, Vladimir A., J. Sánchez Fernán, C. W. J. Beenakker

Published Jan 9, 2026• 0 citations
Publisher

Abstract

This repository contains Python code based on TeNPy for constructing a finite-size MPO of a lattice-regularized helical Luttinger liquid using tangent fermion method. It includes DMRG simulations and routines to compute and compare fermionic propagators and transverse spin correlators with bosonization predictions.
DOI
10.5281/zenodo.18200001

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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.
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