Condensate induced transitions between topologically ordered phases

TL;DR

This paper develops a theoretical framework for understanding phase transitions between topologically ordered phases in two dimensions caused by bosonic quasiparticle condensation, linking topological quantum field theories with conformal field theory constructions.

Contribution

It extends symmetry breaking theory to topological phases with non-integer quantum dimensions, connecting quantum group symmetry breaking with conformal field theory methods.

Findings

Established a general framework for topological phase transitions via quasiparticle condensation.

Demonstrated connections between quantum group symmetry breaking and conformal field theory constructions.

Provided detailed examples illustrating the theoretical concepts.

Abstract

We investigate transitions between topologically ordered phases in two spatial dimensions induced by the condensation of a bosonic quasiparticle. To this end, we formulate an extension of the theory of symmetry breaking phase transitions which applies to phases with topological excitations described by quantum groups or modular tensor categories. This enables us to deal with phases whose quasiparticles have non-integer quantum dimensions and obey braid statistics. Many examples of such phases can be constructed from two-dimensional rational conformal field theories and we find that there is a beautiful connection between quantum group symmetry breaking and certain well-known constructions in conformal field theory, notably the coset construction, the construction of orbifold models and more general conformal extensions. Besides the general framework, many representative examples are worked out in detail.