Wegner-Wilson loops in string nets

TL;DR

This paper investigates the behavior of Wegner-Wilson loops in the string-net model of Levin and Wen under string tension, revealing a phase transition from topological to trivial phases and characterizing loop laws in each phase.

Contribution

It provides a perturbative analysis of Wegner-Wilson loops in the string-net model with string tension, detailing their behavior across the phase transition.

Findings

Wegner-Wilson loops follow a perimeter law in the topological phase.

In the trivial phase, loops obey a modified area law.

The analysis covers arbitrary input theories of the string-net model.

Abstract

We study the Wegner-Wilson loops in the string-net model of Levin and Wen in the presence of a string tension. The latter is responsible for a phase transition from a topological deconfined phase (weak tension) to a trivial confined phase (strong tension). We analyze the behavior of all Wegner-Wilson loops in both limiting cases for an arbitrary input theory of the string-net model. Using a fluxon picture, we compute perturbatively the first contributions to a perimeter law in the topological phase as a function of the quantum dimensions. In the trivial phase, we find that Wegner-Wilson loops obey a modified area law, in agreement with a recent mean-field approach.