Finite-temperature magnetization transport of the one-dimensional anisotropic Heisenberg model

TL;DR

This paper investigates finite-temperature magnetization transport in a one-dimensional anisotropic Heisenberg model, revealing diffusive behavior at finite temperatures and a temperature-dependent diffusion constant, with localized states persisting at low temperatures.

Contribution

It provides numerical evidence that magnetization transport is diffusive at finite temperatures in the gapped phase of the model, with detailed analysis of temperature effects on diffusion.

Findings

Transport is diffusive at finite temperatures.

Diffusion constant increases as temperature decreases.

Localized domain wall states persist at low temperatures.

Abstract

We study finite-temperature magnetization transport in a one-dimensional anisotropic Heisenberg model, focusing in particular on the gapped phase. Using numerical simulations by two different methods, a propagation of localized wavepackets and a study of nonequilibrium steady states of a master equation in a linear-response regime, we conclude that the transport at finite temperatures is diffusive. With decreasing temperature the diffusion constant increases, possibly exponentially fast. This means that at low temperatures the transition from ballistic to asymptotic diffusive behavior happens at very long times. We also study dynamics of initial domain wall like states, showing that on the attainable time scales they remain localized.