Topological Order in the (2+1)D Compact Lattice Superconductor

Abstract

We study topological aspects of a compact lattice superconductor, and show that the characteristic energy splitting, $Δ$, between almost degenerate ground states, is simply related to a novel order parameter $\tilde W$, which is closely related to large Wilson loops. Using Monte Carlo methods, we study the scaling properties of $\tilde W$ close to the deconfining phase transition, and conclude that $Δ\sim e^{-L/ξ}$, where $L$ is the size of the system, thus giving quantitative support to the vortex tunneling scenario proposed by Wen.