Luttinger liquid tensor network: sine versus tangent dispersion of massless Dirac fermions

TL;DR

This paper compares sine and tangent dispersion discretizations of massless Dirac fermions in tensor network models, finding tangent dispersion better reproduces continuum physics with power-law decay, overcoming fermion-doubling issues.

Contribution

It introduces a tensor network approach for massless Dirac fermions using tangent dispersion, enabling local eigenproblems and accurate continuum limit representation.

Findings

Tangent dispersion yields a power-law propagator decay.

Sine dispersion results in an exponential decay due to interactions.

The method circumvents fermion-doubling by exploiting nonlocal Hamiltonians.

Abstract

To apply the powerful many-body techniques of tensor networks to massless Dirac fermions one wants to discretize the $p\cdot\sigma$ Hamiltonian and construct a matrix-product-operator (MPO) representation. We compare two alternative discretization schemes, one with a sine dispersion, the other with a tangent dispersion, applied to a one-dimensional Luttinger liquid with Hubbard interaction. Both types of lattice fermions allow for an exact MPO representation of low bond dimension, so they are efficiently computable, but only the tangent dispersion gives a power law decay of the propagator in agreement with the continuum limit: The sine dispersion is gapped by the interactions, evidenced by an exponentially decaying propagator. Our construction of a tensor network with an unpaired Dirac cone works around the fermion-doubling obstruction by exploiting the fact that the \textit{nonlocal} Hamiltonian of tangent fermions permits a \textit{local} generalized eigenproblem.