Constructing topological models by symmetrization: A PEPS study

Abstract

Symmetrization of topologically ordered wavefunctions is a powerful method for constructing new topological models. Here, we study wavefunctions obtained by symmetrizing quantum double models of a group $G$ in the Projected Entangled Pair States (PEPS) formalism. We show that symmetrization naturally gives rise to a larger symmetry group $\tilde{G}$ 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 $\tilde{G}$. In order to understand the effect of symmetrization on smaller patches, we carry out numerical studies for the toric code model, where we find strong evidence that symmetrizing on individual spins gives rise to a critical model which is at the phase transitions of two inequivalent toric codes, obtained by anyon condensation from the double model of $\tilde{G}$.

10 pages. v2: accepted version

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Cited by in corpus (11)

• Entanglement phases as holographic duals of anyon condensates
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Parton construction of particle-hole-conjugate Read-Rezayi parafermion fractional quantum Hall states and beyond
• Gauging permutation symmetries as a route to non-Abelian fractons
• Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in $\nu =1/2+1/2$ Bilayers
• Characterization of topological phase transitions from a non-Abelian topological state and its Galois conjugate through condensation and confinement order parameters
• Complete characterization of non-Abelian topological phase transitions and detection of anyon splitting with projected entangled pair states
• Determining non-Abelian topological order from infinite projected entangled pair states
• Determining topological order from infinite projected entangled pair states
• Variational methods for characterizing matrix product operator symmetries
• Topological phase diagram of $\mathcal{D}(S_3)$ induced by forbidding charges and fluxes