Topological-sector fluctuations and ergodicity breaking at the Berezinskii-Kosterlitz-Thouless transition

TL;DR

This paper explores how the Berezinskii-Kosterlitz-Thouless transition involves ergodicity breaking between topological sectors in a 2D Coulomb gas, revealing global topological defect excitations and signatures detectable in experiments.

Contribution

It provides a novel analytical and numerical analysis of topological-sector fluctuations and ergodicity breaking at the BKT transition in a 2D Coulomb gas.

Findings

Ergodicity breaks between topological sectors at the BKT transition.

Global topological defects are excited when local order breaks down.

Quantized topological excitations show global signatures of the transition.

Abstract

The Berezinskii-Kosterlitz-Thouless (BKT) phase transition drives the unbinding of topological defects in many two-dimensional systems. In the two-dimensional Coulomb gas, it corresponds to an insulator-conductor transition driven by charge deconfinement. We investigate the global topological properties of this transition, both analytically and by numerical simulation, using a lattice-field description of the two-dimensional Coulomb gas on a torus. The BKT transition is shown to be an ergodicity breaking between the topological sectors of the electric field, which implies a definition of topological order in terms of broken ergodicity. The breakdown of local topological order at the BKT transition leads to the excitation of global topological defects in the electric field, corresponding to different topological sectors. The quantized nature of these classical excitations, and their strict suppression by ergodicity breaking in the low-temperature phase, afford striking global signatures of topological-sector fluctuations at the BKT transition. We discuss how these signatures could be detected in experiments on, for example, magnetic films and cold-atom systems.