Persistent oscillations after quantum quenches in $d$ dimensions

TL;DR

This paper analytically studies the dynamics of local observables after quantum quenches in $d$-dimensional systems, revealing conditions for persistent oscillations and their dependence on system size and quench region.

Contribution

It provides analytical insights into the conditions for undamped oscillations post-quench in $d$-dimensional systems, including the role of quasiparticle modes and quench region size.

Findings

Undamped oscillations occur when the initial state includes single-quasiparticle modes.

In $d>1$, a quench within the ferromagnetic phase of the Ising model causes persistent order parameter oscillations.

Oscillations inside a quenched subregion spread as a light cone, with persistence depending on the volume of the quenched region.

Abstract

We obtain analytical results for the time evolution of local observables in systems undergoing quantum quenches in $d$ spatial dimensions. For homogeneous systems we show that oscillations undamped in time occur when the state produced by the quench includes single-quasiparticle modes and the observable couples to those modes. In particular, a quench of the transverse field within the ferromagnetic phase of the Ising model produces undamped oscillations of the order parameter when $d>1$. For the more general case in which the quench is performed only in a subregion of the whole $d$-dimensional space occupied by the system, the time evolution occurs inside a light cone spreading away from the boundary of the quenched region as time increases. The additional condition for undamped oscillations is that the volume of the quenched region is extensive in all dimensions.