Light-cone velocities after a global quench in a non-interacting model

TL;DR

This paper investigates how the initial state influences the speed at which correlations and entanglement spread in a non-interacting XY chain after a global quench, revealing state-dependent light-cone velocities.

Contribution

It demonstrates that initial state translation invariance affects the maximal correlation spreading speed, a novel effect in non-interacting systems, supported by numerical and analytical results.

Findings

Light-cone velocity depends on initial state properties.

Translation invariance of initial states influences correlation spread.

Entanglement entropy evolution shows similar state-dependent behavior.

Abstract

We study the light-cone velocity for global quenches in the non-interacting XY chain starting from a class of initial states that are eigenstates of the local $z$-component of the spin. We point out how translation invariance of the initial state can affect the maximal speed at which correlations spread. As a consequence the light-cone velocity can be state-dependent also for non-interacting systems: a new effect of which we provide clear numerical evidence and analytic predictions. Analogous considerations, based on numerical results, are drawn for the evolution of the entanglement entropy.