IQI Weekly Seminar

Symmetrization of topologically ordered wavefunctions is a powerful method for constructing new topological models. We study wavefunctions obtained by symmetrizing quantum double models of a group G in the Projected Entangled Pair States (PEPS) formalism. Using the fact that PEPS characterize topological phases through a local symmetry, we can show that symmetrization naturally gives rise to a larger symmetry group H which is always non-abelian. We prove that by symmetrizing on sufficiently large blocks, one can always construct wavefunctions in the same phase as the double model of H. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we identify a number of different possible phases obtained by anyon condensation from the non-abelian double of H, and find strong evidence that symmetrizing on individual spins gives rise to a critical model.