Nonequilibrium current-carrying steady states in the anisotropic $XY$ spin chain

TL;DR

This paper investigates the out-of-equilibrium dynamics of the anisotropic XY spin chain, analyzing relaxation to steady states, correlation functions, and the effects of anisotropy and magnetic field on spin transport.

Contribution

It provides an analytical study of relaxation to nonequilibrium steady states in the anisotropic XY model, including the use of a generalized Gibbs ensemble and analysis of spatial correlations.

Findings

Correlation functions exhibit spatial oscillations with wavelength set by the initial domain wall.

The steady-state current strongly depends on anisotropy and magnetic field.

An effective generalized Gibbs ensemble accurately describes long-time observables.

Abstract

Out-of-equilibrium behavior is explored in the one-dimensional anisotropic $XY$ model. Initially preparing the system in the isotropic $XX$ model with a linearly varying magnetic field to create a domain-wall magnetization profile, dynamics is generated by rapidly changing the exchange interaction anisotropy and external magnetic field. Relaxation to a nonequilibrium steady state is studied analytically at the critical transverse Ising point, where correlation functions may be computed in closed form. For arbitrary values of anisotropy and external field, an effective generalized Gibbs' ensemble is shown to accurately describe observables in the long-time limit. Additionally, we find spatial oscillations in the exponentially decaying, transverse spin-spin correlation functions with wavelength set by the magnetization jump across the initial domain wall. This wavelength depends only weakly on anisotropy and magnetic field in contrast to the current, which is highly dependent on these parameters.