Energy transport between two integrable spin chains

TL;DR

This paper investigates energy transport between two integrable XXZ spin chains initially at different temperatures, revealing the roles of bosonic modes and fermionic quasi-particles, and observing a slow decay of energy current due to local integrability breaking.

Contribution

It combines bosonisation and matrix-product-state simulations to analyze how low-lying modes contribute to energy transport in nearly integrable spin chains, highlighting pre-equilibration effects.

Findings

Energy current reaches a finite value and decays slowly.

Matching sound velocities leads to almost stationary energy current.

Thermalization occurs on longer, numerically inaccessible time scales.

Abstract

We study the energy transport in a system of two half-infinite XXZ chains initially kept separated at different temperatures, and later connected and let free to evolve unitarily. By changing independently the parameters of the two halves, we highlight, through bosonisation and time-dependent matrix-product-state simulations, the different contributions of low-lying bosonic modes and of fermionic quasi-particles to the energy transport. In the simulations we also observe that the energy current reaches a finite value which only slowly decays to zero. The general pictures that emerges is the following. Since integrability is only locally broken in this model, a pre-equilibration behaviour may appear. In particular, when the sound velocities of the bosonic modes of the two halves match, the low-temperature energy current is almost stationary and described by a formula with a non-universal prefactor interpreted as a transmission coefficient. Thermalisation, characterized by the absence of any energy flow, occurs only on longer time-scales which are not accessible with our numerics.