Symmetry Enriched Phases via Pseudo Anyon Condensation

TL;DR

This paper introduces a framework for understanding symmetry enriched topological phases in 2+1 dimensions through pseudo anyon condensation, embedding them into larger phases with hidden Hopf symmetries, extending the Landau-Ginzburg paradigm.

Contribution

It generalizes the Landau-Ginzburg paradigm to quantum groups and provides a unified classification approach for symmetry enriched topological phases.

Findings

Embedding of symmetry enriched phases into larger phases with hidden Hopf symmetries

Generalization of symmetry breaking to quantum groups and algebras

Potential classification scheme for various topological phases

Abstract

We show that a large class of symmetry enriched (topological) phases of matter in 2+1 dimensions can be embedded in "larger" topological phases- phases describable by larger hidden Hopf symmetries. Such an embedding is analogous to anyon condensation, although no physical condensation actually occurs. This generalizes the Landau-Ginzburg paradigm of symmetry breaking from continuous groups to quantum groups- in fact algebras- and offers a potential classification of the symmetry enriched (topological) phases thus obtained, including symmetry protected trivial phases as well, in a unified framework.