Finite-temperature properties of string-net models

TL;DR

This paper analyzes the finite-temperature behavior of a refined string-net model, revealing how excitations and topological properties like confinement and mutual information evolve with temperature.

Contribution

It introduces a refined string-net model with variable plaquette energies and provides exact calculations of thermodynamic quantities and topological mutual information at finite temperature.

Findings

Partition function dominated by pure fluxons at large size

Wegner-Wilson loops obey an area law indicating confinement

Topological mutual information exhibits nontrivial size-temperature scaling

Abstract

We consider a refined version of the string-net model which assigns a different energy cost to each plaquette excitation. Using recent exact calculations of the energy-level degeneracies we compute the partition function of this model and investigate several thermodynamical quantities. In the thermodynamic limit, we show that the partition function is dominated by the contribution of special particles, dubbed pure fluxons, which trivially braid with all other (product of) fluxons. We also analyze the behavior of Wegner-Wilson loops associated to excitations and show that they obey an area law, indicating confinement, for any finite temperature except for pure fluxons that always remain deconfined. Finally, using a recently proposed conjecture, we compute the topological mutual information at finite temperature, which features a nontrivial scaling between system size and temperature, similar to the one-dimensional classical Ising model.