  We study resonating valence bond (RVB) states in the Projected Entangled Pair
States (PEPS) formalism. Based on symmetries in the PEPS description, we
establish relations between the toric code state, the orthogonal dimer state,
and the SU(2) singlet RVB state on the kagome lattice: We prove the equivalence
of toric code and dimer state, and devise an interpolation between the dimer
state and the RVB state. This interpolation corresponds to a continuous path in
Hamiltonian space, proving that the RVB state is the four-fold degenerate
ground state of a local Hamiltonian on the (finite) kagome lattice. We
investigate this interpolation using numerical PEPS methods, studying the decay
of correlation functions, the change of overlap, and the entanglement spectrum,
none of which exhibits signs of a phase transition.
