Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble

TL;DR

This paper investigates the long-time behavior of the XXZ spin chain after quantum quenches, revealing that the generalized Gibbs ensemble fails to predict local observables, whereas the quench-action formalism succeeds.

Contribution

It demonstrates the failure of the GGE in describing local observables after quenches in the XXZ chain and validates the quench-action approach as a more accurate method.

Findings

GGE predictions deviate from numerical data for local correlators

Quench-action formalism accurately predicts steady states

GGE cannot fully describe local observables in this context

Abstract

We study the nonequilibrium time evolution of the spin-1/2 anisotropic Heisenberg (XXZ) spin chain, with a choice of dimer product and Neel states as initial states. We investigate numerically various short-ranged spin correlators in the long-time limit and find that they deviate significantly from predictions based on the generalized Gibbs ensemble (GGE) hypotheses. By computing the asymptotic spin correlators within the recently proposed quench-action formalism [Phys. Rev. Lett. 110, 257203 (2013)], however, we find excellent agreement with the numerical data. We, therefore, conclude that the GGE cannot give a complete description even of local observables, while the quench-action formalism correctly captures the steady state in this case.