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

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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 W, which is closely related to large Wilson loops. Using Monte Carlo methods, we study the scaling properties of W close to the deconfining phase transition, and conclude that Δ e⁻ˡ/ξ, where L is the size of the system, thus giving quantitative support to the vortex tunneling scenario proposed by Wen.