Projected Entangled Pair States with continuous virtual symmetries

TL;DR

This paper investigates PEPS models with continuous SU(2) virtual symmetries, revealing their unique entanglement properties and ground state degeneracies, which suggest they are not typical gapped topological phases.

Contribution

It introduces a class of PEPS models with continuous symmetries, constructs their parent Hamiltonians, and analyzes their entanglement and degeneracy properties.

Findings

Logarithmic correction to entanglement entropy

Extensive ground state degeneracy on periodic systems

Models likely represent critical or exotic phases

Abstract

We study Projected Entangled Pair States (PEPS) with continuous virtual symmetries, i.e., symmetries in the virtual degrees of freedom, through an elementary class of models with SU(2) symmetry. Discrete symmetries of that kind have previously allowed for a comprehensive explanation of topological order in the PEPS formalism. We construct local parent Hamiltonians whose ground space with open boundaries is exactly parametrized by the PEPS wavefunction, and show how the ground state can be made unique by a suitable choice of boundary conditions. We also find that these models exhibit a logarithmic correction to the entanglement entropy and an extensive ground space degeneracy on systems with periodic boundaries, which suggests that they do not describe conventional gapped topological phases, but either critical models or some other exotic phase.