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

TL;DR

This paper investigates the topological order in a (2+1)D compact lattice superconductor, linking energy splitting to a new order parameter and analyzing its scaling near the phase transition.

Contribution

It introduces a novel order parameter related to Wilson loops and demonstrates its connection to energy splitting, supporting vortex tunneling theory.

Findings

Energy splitting scales as e^{-L/ξ} near the phase transition

The new order parameter is closely related to large Wilson loops

Supports vortex tunneling scenario in topological order

Abstract

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 $\tilde W$, 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 $\Delta \sim e^{-L/\xi}$, where $L$ is the size of the system, thus giving quantitative support to the vortex tunneling scenario proposed by Wen.