Topological phase diagram of $\mathcal{D}(S_3)$ induced by forbidding charges and fluxes

Abstract

We analyze phase transitions induced by forbidding charges and fluxes in $\mathcal{D}(S_3)$, the simplest non-Abelian model among quantum doubles, a class of 2D spin lattice topological models introduced by Kitaev. Contrary to a topological quantum field theory, the lattice degrees of freedom allow to forbid charges and fluxes independently, resulting in a non-trivial effect on dyons. Forbidding charges and fluxes leads to only a subset of the original anyons remaining, forming a new theory. We interpret the processes the theory undergoes in terms of condensation, spontaneous symmetry breaking, splitting of particles. Mapping the complete phase diagram of $\mathcal{D}(S_3)$, we find two distinct groups of phases: quantum doubles of subgroups of $S_3$, and a non-trivial emergent chiral phase, $SU(2)_4$.