Study of anyon condensation and topological phase transitions from a $\mathbb{Z}_4$ topological phase using Projected Entangled Pair States

TL;DR

This paper employs PEPS to analyze topological phase transitions in a $ ext{Z}_4$ model, introducing order parameters for anyon condensation and deconfinement, revealing a rich phase diagram with various transition types.

Contribution

It introduces a PEPS-based framework with novel order parameters to characterize topological phases and transitions in $ ext{Z}_4$ models, including direct transitions between distinct topological phases.

Findings

Identified diverse phase transitions, including first and second order.

Characterized direct transitions between toric code and double semion phases.

Developed order parameters for anyon condensation and deconfinement.

Abstract

We use Projected Entangled Pair States (PEPS) to study topological quantum phase transitions. The local description of topological order in the PEPS formalism allows us to set up order parameters which measure condensation and deconfinement of anyons, and serve as a substitute for conventional order parameters. We apply these order parameters, together with anyon-anyon correlation functions and some further probes, to characterize topological phases and phase transitions within a family of models based on a $\mathbb Z_4$ symmetry, which contains $\mathbb Z_4$ quantum double, toric code, double semion, and trivial phases. We find a diverse phase diagram which exhibits a variety of different phase transitions of both first and second order which we comprehensively characterize, including direct transitions between the toric code and the double semion phase.