  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.
