Resonating valence bond states in the PEPS formalism

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.

11+9 pages, 28 figures. v2: More numerical results, and a few minor improvements. v3: Accepted version (minor changes relative to v2), Journal-Ref added

References in corpus (6)

• Quantum spin-liquid emerging in two-dimensional correlated Dirac fermions
• Criticality, the area law, and the computational power of PEPS
• Quantum critical scaling of the geometric tensors
• Quantum magnetism in the paratacamite family: towards an ideal kagome lattice
• Valence Bond Solids for Quantum Computation
• Real-space renormalization yields finite correlations

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