Topological Order Following a Quantum Quench

TL;DR

This paper investigates the stability of topological order in quantum spin systems after a rapid quench, analyzing how topological features evolve when the system is driven out of equilibrium.

Contribution

It provides analytical and numerical insights into the conditions under which topological order persists or is destroyed following a quantum quench.

Findings

Topological order can survive certain quenches depending on the Hamiltonian.

Topological entropy decreases or remains stable after specific quenches.

A new dynamical measure effectively detects topological order in non-equilibrium states.

Abstract

We determine the conditions under which topological order survives a rapid quantum quench. Specifically, we consider the case where a quantum spin system is prepared in the ground state of the Toric Code Model and, after the quench, it evolves with a Hamiltonian that does not support topological order. We provide analytical results supported by numerical evidence for a variety of quench Hamiltonians. The robustness of topological order under non-equilibrium situations is tested by studying the topological entropy and a novel dynamical measure, which makes use of the similarity between partial density matrices obtained from different topological sectors.