Nonequilibrium symmetry-protected topological order: emergence of semilocal Gibbs ensembles

TL;DR

This paper investigates nonequilibrium dynamics in quantum spin chains, revealing that certain conservation laws with non-quasilocal densities lead to unique stationary states exhibiting symmetry-protected topological features and logarithmic entropy growth.

Contribution

It demonstrates the existence of non-quasilocal conservation laws affecting long-time states and links nonequilibrium behavior to equilibrium topological order in spin chains.

Findings

Stationary states can have non-quasilocal conserved quantities.

Entropy growth in spin blocks is logarithmic at late times.

Symmetry-protected topological order can melt under perturbations.

Abstract

We consider nonequilibrium time evolution in quantum spin chains after a global quench. Usually a nonequilibium quantum many-body system locally relaxes to a (generalised) Gibbs ensemble built from conserved operators with quasilocal densities. Here we exhibit explicit examples of local Hamiltonians that possess conservation laws with densities that are not quasilocal but act as such in the symmetry-restricted space where time evolution occurs. Because of them, the stationary state emerging at infinite time can exhibit exceptional features. We focus on a specific example with a spin-flip symmetry, which is the commonest global symmetry encountered in spin-$1/2$ chains. Among the exceptional properties, we find that, at late times, the excess of entropy of a spin block triggered by a local perturbation in the initial state grows logarithmically with the subsystem's length. We establish a connection with symmetry-protected topological order in equilibrium at zero temperature and study the melting of the order induced either by a (symmetry-breaking) rotation of the initial state or by an increase of the temperature.