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

References in corpus (7)

• Criticality, the area law, and the computational power of PEPS
• Topological Order with a Twist: Ising Anyons from an Abelian Model
• Condensate induced transitions between topologically ordered phases
• Valence Bond Solids for Quantum Computation
• Genons, twist defects, and projective non-Abelian braiding statistics
• Resonating valence bond states in the PEPS formalism
• Explicit tensor network representation for the ground states of string-net models

Cited by in corpus (1)

• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry