Thermalization of Topological Entropy after a Quantum Quench

TL;DR

This paper demonstrates that topological order in two-dimensional systems thermalizes after a quantum quench, with residual topological entropy preserved under gauge symmetry, analyzed through exact analytical methods.

Contribution

It provides an exact analytical study of the time evolution of topological entropy post-quench, revealing conditions for residual topological order.

Findings

Topological order thermalizes after a quantum quench.

Residual topological entropy persists if gauge symmetry is preserved.

Methodology applicable to disordered systems to explore many-body localization.

Abstract

In two spatial dimensions, topological order is robust for static deformations at zero temperature, while it is fragile at any finite temperature. How robust is topological order after a quantum quench? In this paper we show that topological order thermalizes under the unitary evolution after a quantum quench. If the quench preserves gauge symmetry, there is a residual topological entropy exactly like in the finite temperature case. We obtain this result by studying the time evolution of the topological 2-R\'enyi entropy in a fully analytical, exact way. These techniques can be then applied to systems with strong disorder to show whether a many-body localization phenomenon appears in topologically ordered systems.