Topological R\'enyi entropy after a quantum quench

TL;DR

This paper analytically investigates the robustness of topological order in a quantum system after a quench, showing that topological Renyi entropy remains stable over time, indicating resilience of topological order.

Contribution

It provides an analytical study of topological order dynamics post-quench, demonstrating its resilience using exact and perturbative solutions in the toric-code model.

Findings

Topological Renyi entropy remains unchanged after long-term evolution.

Topological order shows resilience against various quantum quenches.

Abstract

We present an analytical study on the resilience of topological order after a quantum quench. The system is initially prepared in the ground state of the toric-code model, and then quenched by switching on an external magnetic field. During the subsequent time evolution, the variation in topological order is detected via the topological Renyi entropy of order 2. We consider two different quenches: the first one has an exact solution, while the second one requires perturbation theory. In both cases, we find that the long-term time average of the topological Renyi entropy in the thermodynamic limit is the same as its initial value. Based on our results, we argue that topological order is resilient against a wide range of quenches.