Symmetry-enriched phases obtained via pseudo anyon condensation

Abstract

We propose a framework to describe topological phases with global internal symmetries. This involves embedding the phase of interest into an intrinsic topological-order. Such an embedding is related to the physics of anyon condensation, although no physical condensation actually occurs here. Crucial physical properties of the symmetric phase, such as edge states and global charges of anyons are easily recovered from the embedding. The framework naturally reproduces all phases that are currently known in 2+1 d, and potentially provides a complete classification of symmetric topological phases in 2+1 d. We illustrate our idea with simple examples.