A model of symmetry enriched topological phases and its symmetry breaking gapped boundaries

We present a model of symmetry enriched topological phases (SET) based on the toric code model, with symmetry group being the tensor product of translation and a Z₂ onsite unitary symmetry. The symmetry does not permute anyon types and the model is in a nontrivial symmetry fractionalization class. We also discuss a gapped boundary with spontaneous symmetry breaking (SSB). This boundary condenses e anyon in the usual way, and the excitations at the boundary are domain walls. A domain containing an even number of effective spins could be created locally and a domain with an odd number of effective spins carry m charge. On a cylinder with an odd circumference, the Z₂ symmetry permutes the minimal entangled states (MESs). A boundary with odd circumference could absorb an m by flipping all its effective spins. This leads to a correlation of symmetry breaking sectors at the boundary to the bulk MES sectors.