Quench of symmetry broken ground states

TL;DR

This paper investigates how different symmetry-broken ground states of quantum spin models lose their local distinguishability after a sudden quench, showing an exponential decay over time regardless of integrability.

Contribution

It introduces a quantitative measure of local distinguishability based on trace distance and demonstrates its exponential decay post-quench in magnetically ordered phases.

Findings

Local distinguishability decays exponentially after a quench

Initial ground states are distinguishable before the quench

Decay behavior is similar across different models

Abstract

We analyze the problem of how different ground states associated to the same set of the Hamiltonian parameters evolve after a sudden quench. To realize our analysis we define a quantitative approach to the local distinguishability between different ground states of a magnetically ordered phase in terms of the trace distance between the reduced density matrices obtained projecting two ground states in the same subset. Before the quench, regardless the particular choice of the subset, any system in a magnetically ordered phase is characterized by ground states that are locally distinguishable. On the other hand, after the quench, the maximum of the distinguishability shows an exponential decay in time. Hence, in the limit of very large time, all the informations about the particular initial ground state are lost even if the systems are integrable. We prove our claims in the framework of the magnetically ordered phases that characterize both the $XY$ model and $N$-cluster Ising models. The fact that we find similar behavior in models within different classes of symmetry makes us confident about the generality of our results.