Extended string-net models with all anyons at finite temperature

TL;DR

This paper investigates how thermal fluctuations affect topological order in extended string-net models with all anyons, revealing a finite-temperature phase transition in finite systems and providing exact spectral and partition function calculations.

Contribution

It extends the string-net model to include all anyon excitations and computes exact spectral degeneracies and partition functions at finite temperature.

Findings

Topological order is destroyed at any nonzero temperature in the thermodynamic limit.

Finite-size systems retain topological order up to a finite temperature.

Scaling behavior similar to the 1D classical Ising model is observed.

Abstract

The string-net model describes a vast family of topological orders in two spatial dimensions. Here, we consider the effect of thermal fluctuations on these topological phases. In the original string-net model, the description of charge (vertex) excitations can be problematic. Therefore, in order to describe all anyon excitations, we study an extended model [Y. Hu et al., Phys. Rev. B 97, 195154 (2018)]. Building on recent methods, we compute the spectral degeneracies of excited states and obtain the exact partition function. In the thermodynamic limit, the latter is dominated by the trivial (vacuum) anyon, so that topological order is destroyed at any nonzero temperature. In contrast, in a finite-size system, order survives up to a finite temperature, revealing a nontrivial scaling between temperature and size similar to that of the one-dimensional classical Ising model. We confirm this scaling by computing the thermal average of several observables such as Wegner-Wilson loops and topological mutual information.