Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble

TL;DR

This paper compares the quench action approach and the generalized Gibbs ensemble in the XXZ spin chain, showing the former accurately predicts steady states while the latter fails for local correlations, with new results on overlaps and correlations.

Contribution

It provides a detailed comparison between quench action and GGE, introduces exact overlaps for q-dimer states, and explains GGE's failure in local correlation predictions.

Findings

Quench action accurately captures steady states.

GGE fails to predict local short-distance correlations.

New exact overlaps for q-dimer states are derived.

Abstract

Following our previous work [PRL 113 (2014) 09020] we present here a detailed comparison of the quench action approach and the predictions of the generalized Gibbs ensemble, with the result that while the quench action formalism correctly captures the steady state, the GGE does not give a correct description of local short-distance correlation functions. We extend our studies to include another initial state, the so-called q-dimer state. We present important details of our construction, including new results concerning exact overlaps for the dimer and q-dimer states, and we also give an exact solution of the quench-action-based overlap-TBA for the q-dimer. Furthermore, we extend our computations to include the xx spin correlations besides the zz correlations treated previously, and give a detailed discussion of the underlying reasons for the failure of the GGE, especially in the light of new developments.