Spin Hamiltonians with resonating-valence-bond ground states

Abstract

Quantum dimer models exhibit quantum critical points and liquid states when the ground state is the resonating-valence bond (RVB) state. We construct SU(2)-invariant spin-1/2 Hamiltonians with the same RVB ground state. The main technical obstacle overcome is the fact that different "dimer" configurations in the spin model are not orthogonal to each other. We show that the physics depends on how dimers are related to the spins, and find a Hamiltonian that may be quantum critical.

v3: major revision, with new results and new title

References in corpus (5)

• Evidence for deconfined quantum criticality in a two-dimensional Heisenberg model with four-spin interactions
• Antiferromagnetic to valence-bond-soild transitions in two-dimensional SU(N) Heisenberg models with multi-spin interactions
• Topological order from quantum loops and nets
• Generalized Hardcore Dimer Models approach to low-energy Heisenberg frustrated antiferromagnets: general properties and application to the kagome antiferromagnet
• 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

Cited by in corpus (32)

• Quantum Spin Liquid States
• Resonating valence bond states in the PEPS formalism
• Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
• Finite-size scaling and boundary effects in two-dimensional valence-bond-solids
• Properties of Resonating-Valence-Bond Spin Liquids and Critical Dimer Models
• Entanglement scaling in two-dimensional gapless systems
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Interfaces, Strings, and a Soft Mode in the Square Lattice Quantum Dimer Model
• Confinement and Deconfinement of Spinons in Two Dimensions
• Entanglement in gapless resonating valence bond states
• Resonating valence bond wavefunctions and classical interacting dimer models
• Topological ${\mathbb{Z}}_2$ Resonating-Valence-Bond Spin Liquid on the Square Lattice
• Finite-Volume Energy Spectrum, Fractionalized Strings, and Low-Energy Effective Field Theory for the Quantum Dimer Model on the Square Lattice
• Characterizing Genuine Multisite Entanglement in Isotropic Spin Lattices
• Coexistence of long-range and algebraic correlations for short-range valence-bond wave functions in three dimensions
• Correlation functions in SU(2)-invariant RVB spin liquids on nonbipartite lattices
• Dynamical stability of the quantum Lifshitz theory in 2+1 Dimensions
• Resonating valence bond trial wave functions with both static and dynamically determined Marshall sign structure
• Ground state uniqueness of the twelve site RVB spin-liquid parent Hamiltonian on the kagome lattice
• Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice
• Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices
• Correlated valence-bond states
• The frustration-free fully packed loop model
• Resonating valence-bond physics on the honeycomb lattice
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
• Exact ground states with deconfined gapless excitations for the 3 leg spin-1/2 tube
• Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
• Classical and quantum spin liquids
• Vison excitations in near-critical quantum dimer models
• Entanglement studies of resonating valence bonds on the frustrated square lattice
• Triplet resonating valence bond theory and transition metal chalcogenides