Decay of long-lived oscillations after quantum quenches in gapped interacting quantum systems

TL;DR

This paper investigates the decay of long-lived oscillations in local observables after quantum quenches in gapped interacting systems, revealing a finite decay timescale that increases with smaller quench strengths.

Contribution

It demonstrates that oscillations in such systems decay after a certain time, with the decay time diverging as the quench becomes weaker, using BBGKY hierarchy analysis on spin models mapped to fermions.

Findings

Oscillations decay after a finite time scale.

Decay time increases as quench strength decreases.

Long-lived oscillations are not permanent.

Abstract

The presence of long-lived oscillations in the expectation values of local observables after quantum quenches has recently attracted considerable attention in relation to weak ergodicity breaking. Here we focus on an alternative mechanism that gives rise to such oscillations in a class of systems that support kinematically protected gapped excitations at zero temperature. An open question in this context is whether such oscillations will ultimately decay. We resolve this issue by considering spin models that can be mapped to systems of weakly interacting fermions, which in turn are amenable to an analysis by standard methods based on the BBGKY hierarchy. We find that there is a time scale beyond which the oscillations start to decay, which grows as the strength of the quench is made small.