Resonating valence bond states in the PEPS formalism

TL;DR

This paper explores resonating valence bond states within the PEPS framework, establishing their relation to known models and demonstrating their realization as ground states of local Hamiltonians on the kagome lattice.

Contribution

It proves the equivalence between the toric code, dimer, and RVB states in PEPS, and constructs a continuous Hamiltonian path connecting them.

Findings

RVB states are the ground states of local Hamiltonians on kagome lattice.

No phase transition signs observed during interpolation.

Established relations between toric code, dimer, and RVB states.

Abstract

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.