Condensation-Driven Phase Transitions in Perturbed String Nets

TL;DR

This paper investigates topological phase transitions in perturbed Fibonacci string nets, revealing how non-Abelian anyon condensation leads to symmetry breaking beyond traditional Landau theory, using tensor network methods.

Contribution

It introduces a novel approach to analyze topological phase transitions through tensor networks and matrix-product-operator symmetries in non-solvable models.

Findings

Topological phase transition involves non-Abelian anyon condensation.

Symmetry breaking occurs in the entanglement structure of the transfer matrix.

Method generalizes the Landau paradigm to topological phases.

Abstract

We develop methods to probe the excitation spectrum of topological phases of matter in two spatial dimensions. Applying these to the Fibonacci string nets perturbed away from exact solvability, we analyze a topological phase transition driven by the condensation of non-Abelian anyons. Our numerical results illustrate how such phase transitions involve the spontaneous breaking of a topological symmetry, generalizing the traditional Landau paradigm. The main technical tool is the characterization of the ground states using tensor networks and the topological properties using matrix-product-operator symmetries. The topological phase transition manifests itself by symmetry breaking in the entanglement degrees of freedom of the quantum transfer matrix.