Resonating valence bond states in the PEPS formalism

Understand

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.