Time reversal invariant gapped boundaries of twisted Z2 gauge theory

Abstract

The boundary of a fractionalized topological phase can be gapped by condensing a proper set of bosonic quasiparticles. Interestingly, in the presence of a global symmetry, such a boundary can exhibit different symmetry transformation properties, depending on the details of the condensation. In this talk, I discuss an explicit example of this kind - the double semion state with time reversal symmetry. We find two distinct cases where the semionic excitations on the boundary can transform either as time reversal singlets or as time reversal doublets, depending on the coherent phase factor of the boson condensate. The existence of these two possibilities are demonstrated using both field theory argument and exactly solvable lattice models. Furthermore, we study the domain walls between these two types of gapped boundaries. We find that they carry symmetry protected degeneracies and applying time reversal symmetry tunnels a semion between them.