Universality and robustness of revivals in the transverse field XY model

TL;DR

This paper investigates the universal and robust revival phenomena in the transverse field XY model after a quantum quench, linking revival times to quasiparticle velocities and demonstrating their persistence under perturbations.

Contribution

It establishes the universal nature of revival times in the XY model and shows their robustness against non-integrable perturbations, connecting revivals to local dynamics and Lieb-Robinson bounds.

Findings

Revival times are integer multiples of T_rev   L / v_max.

Revivals are independent of initial state and quench size.

Revivals persist under non-integrable perturbations, linked to Lieb-Robinson velocity.

Abstract

We study the structure of the revivals in an integrable quantum many-body system, the transverse field XY spin chain, after a quantum quench. The time evolutions of the Loschmidt echo, the magnetization, and the single spin entanglement entropy are calculated. We find that the revival times for all of these observables are given by integer multiples of T_rev \sim L / v_max where L is the linear size of the system and v_max is the maximal group velocity of quasiparticles. This revival structure is universal in the sense that it does not depend on the initial state and the size of the quench. Applying non-integrable perturbations to the XY model, we observe that the revivals are robust against such perturbations: they are still visible at time scales much larger than the quasiparticle lifetime. We therefore propose a generic connection between the revival structure and the locality of the dynamics, where the quasiparticle speed v_max generalizes into the Lieb$-$Robinson speed v_LR.