A Family of Non-Abelian Kitaev Models on a Lattice: Topological Confinement and Condensation

TL;DR

This paper investigates a family of non-Abelian lattice models derived from Kitaev's model, revealing how modifications lead to symmetry breaking, topological charge confinement, and partial or complete loss of topological order.

Contribution

It introduces a new class of non-Abelian models with explicit symmetry breaking, analyzing their topological properties and charge dynamics using ribbon operator algebras.

Findings

Topological order is partially or fully destroyed in modified models.

Confinement and condensation of topological charges are observed.

The models demonstrate how symmetry breaking affects topological phases.

Abstract

We study a family of non-Abelian topological models in a lattice that arise by modifying the Kitaev model through the introduction of single-qudit terms. The effect of these terms amounts to a reduction of the discrete gauge symmetry with respect to the original systems, which corresponds to a generalized mechanism of explicit symmetry breaking. The topological order is either partially lost or completely destroyed throughout the various models. The new systems display condensation and confinement of the topological charges present in the standard non-Abelian Kitaev models, which we study in terms of ribbon operator algebras.