Coexistence of energy diffusion and local thermalization in nonequilibrium XXZ spin chains with integrability breaking

TL;DR

This paper investigates how energy diffusion and local thermalization coexist in a nonequilibrium XXZ spin chain when integrability is broken, revealing ballistic to diffusive transport transition and local thermal states in the nonintegrable regime.

Contribution

It demonstrates the simultaneous emergence of energy diffusion and local thermalization in a nonequilibrium quantum spin chain with broken integrability, using large-scale matrix product simulations.

Findings

Energy transport is ballistic in the integrable limit.

Energy transport becomes diffusive with finite staggered field.

Local thermal states emerge in the nonintegrable regime.

Abstract

In this work we analyze the simultaneous emergence of diffusive energy transport and local thermalization in a nonequilibrium one-dimensional quantum system, as a result of integrability breaking. Specifically, we discuss the local properties of the steady state induced by thermal boundary driving in a XXZ spin chain with staggered magnetic field. By means of efficient large-scale matrix product simulations of the equation of motion of the system, we calculate its steady state in the long-time limit.We start by discussing the energy transport supported by the system, finding it to be ballistic in the integrable limit and diffusive when the staggered field is finite. Subsequently, we examine the reduced density operators of neighboring sites and find that for large systems they are well approximated by local thermal states of the underlying Hamiltonian in the nonintegrable regime, even for weak staggered fields. In the integrable limit, on the other hand, this behavior is lost, and the identification of local temperatures is no longer possible. Our results agree with the intuitive connection between energy diffusion and thermalization.