SU(2)-invariant spin-1/2 Hamiltonians with RVB and other valence bond phases

Abstract

We construct a family of rotationally invariant, local, S=1/2 Klein Hamiltonians on various lattices that exhibit ground state manifolds spanned by nearest-neighbor valence bond states. We show that with selected perturbations such models can be driven into phases modeled by well understood quantum dimer models on the corresponding lattices. Specifically, we show that the perturbation procedure is arbitrarily well controlled by a new parameter which is the extent of decoration of the reference lattice. This strategy leads to Hamiltonians that exhibit i) $Z_2$ RVB phases in two dimensions, ii) U(1) RVB phases with a gapless ``photon'' in three dimensions, and iii) a Cantor deconfined region in two dimensions. We also construct two models on the pyrochlore lattice, one model exhibiting a $Z_2$ RVB phase and the other a U(1) RVB phase.

arXiv comment16 pages, 15 figures; 1 figure and some references added; some minor typos fixed

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• Exotic quantum phases and phase transitions in correlated matter
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• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• Correlated phases of bosons in tilted, frustrated lattices
• Quantum magnetism on the Cairo pentagonal lattice
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• Spin Hamiltonians with resonating-valence-bond ground states
• Entanglement in gapless resonating valence bond 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
• Resonating singlet valence plaquettes
• Fermionic spin excitations in two and three-dimensional antiferromagnets
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• A resonant valence bond spin liquid in the dilute limit of doped frustrated Mott insulators
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• Engineering SU(2) invariant spin models to mimic quantum dimer physics on the square lattice
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• Classical and quantum spin liquids
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• Detecting non-magnetic excitations in quantum magnets
• Vison excitations in near-critical quantum dimer models
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• Entanglement studies of resonating valence bonds on the frustrated square lattice
• Quantum dimer models and exotic orders