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.

arXiv comment11+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 (21)

• Fault-tolerant quantum computation by anyons
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• An RVB phase in the triangular lattice quantum dimer model
• Ground state overlap and quantum phase transitions
• 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
• Topological quantum order: stability under local perturbations
• Valence Bond Solids for Quantum Computation
• Entanglement spectrum and boundary theories with projected entangled-pair states
• PEPS as ground states: degeneracy and topology
• Quantum dimer model on the kagome lattice: solvable dimer liquid and Ising gauge theory
• Topological and Entanglement Properties of Resonating Valence Bond wavefunctions
• Ground-state phase diagram of the quantum J1-J2 model on the honeycomb lattice
• SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases
• Microscopic Models of 2D Magnets with Fractionalized Excitations
• Spin Hamiltonians with resonating-valence-bond ground states
• Linear independence of nearest neighbor valence bond states on the kagome lattice and construction of SU(2)-invariant spin-1/2-Hamiltonian with a Sutherland-Rokhsar-Kivelson quantum liquid ground state
• Real-space renormalization yields finite correlations
• Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices

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