Scaling of electrical and thermal conductivities in an almost integrable chain

TL;DR

This paper investigates how small deviations from integrability affect electrical, spin, and thermal conductivities in one-dimensional quantum chains, using numerical methods and scaling theory to understand transport behavior.

Contribution

It provides quantitative conductivity values in nearly integrable chains and validates a scaling theory based on bosonization for low-temperature transport.

Findings

Conductivities show singular behavior near integrability.

Numerical results agree with bosonization scaling predictions.

Weak perturbations lead to finite conductivities in otherwise dissipationless models.

Abstract

Many low-dimensional materials are well described by integrable one-dimensional models such as the Hubbard model of electrons or the Heisenberg model of spins. However, the small perturbations to these models required to describe real materials are expected to have singular effects on transport quantities: integrable models often support dissipationless transport, while weak non-integrable terms lead to finite conductivities. We use matrix-product-state methods to obtain quantitative values of spin/electrical and thermal conductivities in an almost integrable gapless chain (an XXZ spin chain with staggered fields, or equivalently a spinless fermion chain with staggered on-site potentials). The results at low temperatures validate a scaling theory based on bosonization.