Quantum Quenches in an XXZ Spin Chain from a Spatially Inhomogeneous Initial State

TL;DR

This paper investigates the nonequilibrium dynamics of an XXZ spin chain with an initial domain wall profile, revealing long-time inhomogeneous correlations and limitations of the generalized Gibbs ensemble in describing these states.

Contribution

It introduces a detailed analysis of inhomogeneous spin correlations after quenches in an XXZ chain, highlighting the failure of the generalized Gibbs ensemble to capture spatial inhomogeneities.

Findings

Magnetization equilibrates to the ground state value at long times.

Two-point correlation functions remain generally inhomogeneous.

Inhomogeneities arise from dephasing of transverse spin components.

Abstract

Results are presented for the nonequilibrium dynamics of a quantum $XXZ$-spin chain whose spins are initially arranged in a domain wall profile via the application of a magnetic field in the $z$-direction which is spatially varying along the chain. The system is driven out of equilibrium in two ways: a). by rapidly turning off the magnetic field, b). by rapidly quenching the interactions at the same time as the magnetic field is turned off. The time-evolution of the domain wall profile as well as various two-point spin correlation functions is studied by the exact solution of the fermionic problem for the $XX$ chain and via a bosonization approach and a mean-field approach for the $XXZ$ chain. At long times the magnetization is found to equilibrate (reach the ground state value), while the two-point correlation functions in general do not. In particular, for quenches within the gapless $XX$ phase, the transverse spin correlation functions acquire a spatially inhomogeneous structure at long times whose details depend on the initial domain wall profile. The spatial inhomogeneity is also recovered for the case of classical spins initially arranged in a domain wall profile and shows that the inhomogeneities arise due to the dephasing of transverse spin components as the domain wall broadens. A generalized Gibbs ensemble approach is found to be inadequate in capturing this spatially inhomogeneous state.