# Disorder-protected topological entropy after a quantum quench

## TL;DR

This paper investigates how disorder can protect topological entropy in quantum systems after a sudden quench, demonstrating that Anderson localization enhances the robustness of topological phases.

## Contribution

It introduces an analytical method to study the time evolution of topological entropy post-quench and shows disorder-induced localization preserves topological order.

## Key findings

- Disorder in the Hamiltonian couplings enhances topological entropy resilience.
- Anderson localization prevents the decay of topological order after a quantum quench.
- Topological phases can be protected by disorder even out of equilibrium.

## Abstract

Topological phases of matter are considered the bedrock of novel quantum materials as well as ideal candidates for quantum computers that possess robustness at the physical level. The robustness of the topological phase at finite temperature or away from equilibrium is therefore a very desirable feature. Disorder can improve the lifetime of the encoded topological qubits. Here we tackle the problem of the survival of the topological phase as detected by topological entropy, after a sudden quantum quench. We introduce a method to study analytically the time evolution of the system after a quantum quench and show that disorder in the couplings of the Hamiltonian of the toric code and the resulting Anderson localization can make the topological entropy resilient.