Quantum relaxation and finite size effects in the XY chain in a transverse field after global quenches

TL;DR

This paper investigates the nonequilibrium dynamics of the quantum XY chain after global quenches, analyzing relaxation, correlations, and entanglement in finite systems, and compares exact results with semiclassical and generalized Gibbs ensemble predictions.

Contribution

It provides a detailed comparison of exact, semiclassical, and generalized Gibbs ensemble descriptions of relaxation phenomena in the quantum XY chain after quenches.

Findings

Semiclassical theory accurately describes relaxation in finite systems.

Generalized Gibbs ensemble captures stationary correlations.

Exact solutions validate semiclassical and GGE approaches.

Abstract

We consider global quenches in the quantum XY chain in a transverse field and study the nonequilibrium relaxation of the magnetization and the correlation function as well as the entanglement entropy in finite systems. For quenches in the ordered phase, the exact results are well described by a semiclassical theory (SCT) in terms of ballistically moving quasiparticles. In the thermodynamic limit the SCT is exact for the entanglement entropy and its modified version following the method of Calabrese, Essler and Fagotti: arXiv:1204.3911 is exact for the magnetization and the correlation function, too. The stationary correlation function is shown to be described by a generalized Gibbs ensemble.