Tensor-network approach to phase transitions in string-net models

TL;DR

This paper employs tensor-network states to analyze phase transitions in string-net models, successfully capturing known second-order and novel first-order transitions, thereby advancing understanding of topological phases.

Contribution

Introduces a tensor-network approach to study phase transitions in string-net models, revealing new first-order transition behavior in Fibonacci string nets.

Findings

Captured second-order phase transition in $ ext{Z}_2$ string nets

Identified first-order phase transition in Fibonacci string nets

Validated approach against known models and results

Abstract

We use a recently proposed class of tensor-network states to study phase transitions in string-net models. These states encode the genuine features of the string-net condensate such as, e.g., a nontrivial perimeter law for Wilson loops expectation values, and a natural order parameter detecting the breakdown of the topological phase. In the presence of a string tension, a quantum phase transition occurs between the topological phase and a trivial phase. We benchmark our approach for $\mathbb{Z}_2$ string nets and capture the second-order phase transition which is well known from the exact mapping onto the transverse-field Ising model. More interestingly, for Fibonacci string nets, we obtain first-order transitions in contrast with previous studies but in qualitative agreement with mean-field results.