Description
Symmetry-enriched topological (SET) phases combine intrinsic topological order with global symmetries, giving rise to novel symmetry phenomena. While SET phases with Abelian anyons are relatively well understood, those involving nonabelian anyons remain elusive. This obscurity stems from the multi-dimensional internal gauge spaces intrinsic to nonabelian anyons. We will introduce a systematic framework for constructing exactly solvable lattice models of SET phases based on an enlarged version of the string-net model. Using these explicitly constructed models, we will then focus on how the internal gauge spaces of nonabelian anyons transform under these symmetries. This framework uncovers a universal phenomenon: global symmetry fragmentation (GSF). We will introduce how symmetry-invariant anyons exhibit internal Hilbert space decompositions into eigensubspaces that are labeled by generally fractional symmetry charges. Furthermore, we will see how symmetry-permuted anyons hybridize and fragment their internal spaces in accordance with their symmetry behavior.
