Kibble-Zurek Scaling and String-Net Coarsening in Topologically Ordered Systems

TL;DR

This paper investigates the non-equilibrium dynamics of topologically ordered systems during phase transitions, revealing Kibble-Zurek scaling and slow string-net coarsening as signatures of topological order.

Contribution

It introduces the concept of Kibble-Zurek scaling and coarsening dynamics in topologically ordered systems without symmetry breaking, expanding understanding of non-equilibrium topological phenomena.

Findings

Demonstrates Kibble-Zurek scaling in topological phase transitions

Identifies slow string-net coarsening as a signature of topological order

Applies analysis to both abelian and non-abelian topological phases

Abstract

We consider the non-equilibrium dynamics of topologically ordered systems driven across a continuous phase transition into proximate phases with no, or reduced, topological order. This dynamics exhibits scaling in the spirit of Kibble and Zurek but now {\it without} the presence of symmetry breaking and a local order parameter. The late stages of the process are seen to exhibit a slow, coarsening dynamics for the string-net that underlies the physics of the topological phase, a potentially interesting signature of topological order. We illustrate these phenomena in the context of particular phase transitions out of the abelian Z_2 topologically ordered phase of the toric code/Z_2 gauge theory, and the non-abelian SU(2)$_k$ ordered phases of the relevant Levin-Wen models.