Topological order in the (2+1)D compact lattice superconductor

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