Spin transport in a one-dimensional anisotropic Heisenberg model

TL;DR

This paper investigates how spin transport behavior in a one-dimensional anisotropic Heisenberg model varies from ballistic to diffusive as the anisotropy parameter changes, providing analytical and numerical insights.

Contribution

It offers a comprehensive analysis of spin transport regimes in the anisotropic Heisenberg model, including a perturbative prediction of diffusion constants at large anisotropy.

Findings

Spin transport is ballistic for Delta<1.

Transport becomes anomalous at Delta=1.

Transport is diffusive for Delta>1.

Abstract

We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Delta is varied spin transport changes from ballistic for Delta<1 to anomalous at the isotropic point Delta=1, to diffusive for finite Delta>1, ending up as a perfect isolator in the Ising limit of infinite Delta. Using perturbation theory for large Delta a quantitative prediction is made for the dependence of diffusion constant on Delta.