Constructing topological models by symmetrization: A PEPS study

TL;DR

This paper explores how symmetrizing topologically ordered wavefunctions within the PEPS framework can generate larger symmetry groups and new phases, including critical models at phase transitions between toric codes.

Contribution

It demonstrates that symmetrization of quantum double models produces larger non-abelian symmetry groups and can generate wavefunctions in the same phase as the double model of the enlarged group.

Findings

Symmetrization leads to a larger non-abelian symmetry group \( ilde G\).

Sufficiently large block symmetrization preserves the original phase.

Single-spin symmetrization results in a critical model at phase transitions.

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 $\tilde G$.