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

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