Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions

Abstract

We present a certain class of two-dimensional frustrated quantum Heisenberg spin systems with multiple ring exchange interactions which are rigorously demonstrated to have quantum disordered ground states without magnetic long-range order. The systems considered in this paper are s=1/2 antiferromagnets on a honeycomb and square lattices, and an s=1 antiferromagnet on a triangular lattice. We find that for a particular set of parameter values, the ground state is a short-range resonating valence bond state or a valence bond crystal state. It is shown that these systems are closely related to the quantum dimer model introduced by Rokhsar and Kivelson as an effective low-energy theory for valence bond states.

6 pages, 4 figures

References in corpus (2)

• From classical to quantum dynamics at Rokhsar-Kivelson points
• Two-dimensional O(n) model in a staggered field

Cited by in corpus (25)

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• Exotic quantum phases and phase transitions in correlated matter
• Critical Correlations for Short-Range Valence-Bond Wave Functions on the Square Lattice
• 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
• Resonating singlet valence plaquettes
• Correlation functions in SU(2)-invariant RVB spin liquids on nonbipartite lattices
• Devil's staircases, quantum dimer models, and stripe formation in strong coupling models of quantum frustration
• Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
• 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
• Linear independence of nearest-neighbor valence bond states in several two-dimensional lattices
• Exact Realization of a Quantum-Dimer Model in Heisenberg Antiferromagnets on a Diamond-Like Decorated Lattice
• A 2D quantum antiferromagnet with a four-fold degenerate valence-bond-solid ground state
• Proposal of a spin-one chain model with competing dimer and trimer interactions
• Honeycomb antiferromagnet with a triply degenerate dimer ground state
• Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like Decorated Square Lattice
• Quantum dimer model containing Rokhsar-Kivelson point expressed by spin-1/2 Heisenberg antiferromagnets
• Exact Solution and Correlations of a Quantum Dimer Model on the Checkerboard Lattice
• Study of the bilinear biquadratic Heisenberg model on a honeycomb lattice via Schwinger bosons
• Emergence of a Dimer-Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings
• Translation-Invariant Parent Hamiltonians of Valence Bond Crystals
• Vison excitations in near-critical quantum dimer models
• Entanglement studies of resonating valence bonds on the frustrated square lattice