Energy transport in Heisenberg chains beyond the Luttinger liquid paradigm

TL;DR

This paper develops an analytical approach to study energy transport in Heisenberg spin chains beyond the low-energy Luttinger liquid approximation, accurately predicting steady-state energy currents at high temperatures.

Contribution

It introduces a novel analytical Ansatz for the non-equilibrium steady state in the XXZ model that remains valid beyond the low-energy regime.

Findings

Excellent agreement with numerical simulations at high temperatures.

Luttinger liquid predictions fail at higher temperatures.

Method accurately predicts steady energy currents across temperature regimes.

Abstract

We study the energy transport between two interacting spin chains which are initially separated, held at different temperatures and subsequently put in contact. We consider the spin-1/2 XXZ model in the gapless regime and exploit its integrability properties to formulate an analytical Ansatz for the non-equilibrium steady state even at temperatures where the low-energy Luttinger liquid description is not accurate. We apply our method to compute the steady energy current and benchmark it both with the known low-energy limit and at higher temperatures with numerical simulations. We find an excellent agreement even at high temperatures, where the Luttinger liquid prediction is shown to fail.