Topological order and the deconfinement transition in the (2+1) dimensional compact Abelian Higgs model

TL;DR

This paper investigates the confinement-deconfinement transition in a (2+1)D Abelian gauge theory coupled to bosonic matter, introducing a nonlocal order parameter linked to topological order and analyzing the transition via Monte Carlo simulations.

Contribution

It introduces a nonlocal order parameter related to Wilson loops for fractional charges and maps the model to a dual clock symmetry, providing new insights into topological order and phase transitions.

Findings

Identification of a nonlocal order parameter $ ilde W$ for the transition

Mapping to a dual clock model with global symmetry

Monte Carlo results elucidate the nature of the deconfinement transition

Abstract

We study an Abelian compact gauge theory minimally coupled to bosonic matter with charge q, which may undergo a confinement--deconfinement transition in (2+1)D. The transition is analyzed using a nonlocal order parameter $\tilde W$, which is related to large Wilson loops for fractional charges. We map the model to a dual representation with no gauge field but only a global q-state clock symmetry and show that $\tilde W$ correspond to the domain wall energy of that model. $\tilde W$ is also directly connected to the concept of topological order. We exploit these facts in Monte Carlo simulations to study the detailed nature of the deconfinement transition.