Partition function of the Levin-Wen model

TL;DR

This paper calculates the energy level degeneracies of the Levin-Wen model for anyon theories and graphs, enabling the derivation of partition functions and demonstrating the absence of thermal phase transitions.

Contribution

It provides a general method to compute the partition function of the Levin-Wen model for arbitrary input theories and surface embeddings.

Findings

Degeneracy of energy levels computed for anyon theories

Partition function derived for finite sizes and temperatures

No thermal phase transitions observed

Abstract

Using a description of the Levin-Wen model excitations in terms of Wilson lines, we compute the degeneracy of the energy levels for any input anyon theory and for any trivalent graph embedded on any (orientable) compact surface. This result allows one to obtain the finite-size and finite-temperature partition function and to show that there are no thermal phase transitions.