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

Abstract

We study an Abelian compact gauge theory minimally coupled to bosonic matter with charge $q$, which may undergo a confinement-deconfinement transition in $2+1$ dimensions. The transition is analyzed using a nonlocal order parameter $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$, 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 $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ corresponds to the domain wall energy of that model. $\stackrel{\ifmmode \tilde{}\else \~{}\fi{}}{W}$ 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.