Correlations and diagonal entropy after quantum quenches in XXZ chains

TL;DR

This paper investigates quantum quenches in XXZ chains, demonstrating that the complete GGE accurately predicts correlations and entropy, and highlighting differences from the local GGE, especially for ferromagnetic initial states.

Contribution

It provides the first comprehensive calculation of short-range correlators and diagonal entropy using the complete GGE in XXZ chains, validating the ensemble with exact methods.

Findings

Complete GGE matches exact diagonalization results.

Diagonal entropy equals half the Yang-Yang entropy.

Differences between complete and local GGE are significant for ferromagnetic states.

Abstract

We study quantum quenches in the XXZ spin-$1/2$ Heisenberg chain from families of ferromagnetic and antiferromagnetic initial states. Using Bethe ansatz techniques, we compute short-range correlators in the complete generalized Gibbs ensemble (GGE), which takes into account all local and quasi-local conservation laws. We compare our results to exact diagonalization and numerical linked cluster expansion calculations for the diagonal ensemble finding excellent agreement and thus providing a very accurate test for the validity of the complete GGE. Furthermore, we compute the diagonal entropy in the post-quench steady state. By careful finite-size scaling analyses of the exact diagonalization results, we show that the diagonal entropy is equal to one half the Yang-Yang entropy corresponding to the complete GGE. Finally, the complete GGE is quantitatively contrasted with the GGE built using only the local conserved charges (local GGE). The predictions of the two ensembles are found to differ significantly in the case of ferromagnetic initial states. Such initial states are better suited than others considered in the literature to experimentally test the validity of the complete GGE and contrast it to the failure of the local GGE.