Antiferromagnetic Quantum Spins on the Pyrochlore Lattice

Abstract

The ground state of the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice is theoretically investigated. Starting from the limit of isolated tetrahedra, I include interactions between the tetrahedra and obtain an effective model for the spin-singlet ground state multiplet by third-order perturbation. I determine its ground state using the mean-field approximation and found a dimerized state with a four-sublattice structure, which agrees with the proposal by Harris et al. I also discuss chirality correlations and spin correlations for this state.

4 pages in 2-column format, 5 figures; To appear in J. Phys. Soc. Jpn. (Mar, 2001)

Cited by in corpus (57)

• Quantum Spin Liquids
• Metal-Nonmetal Changeover in Pyrochlore Iridates
• Magnetic transition and orbital degrees of freedom in vanadium spinels
• Ordering in the pyrochlore antiferromagnet due to Dzyaloshinsky-Moriya interactions
• Breathing Pyrochlore Lattice Realized in A-Site Ordered Spinel Oxides LiGaCr4O8 and LiInCr4O8
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Evidence for an unconventional magnetic instability in the spin-tetrahedra system Cu_2Te_2O_5Br_2
• Rank-2 $U(1)$ spin liquid on the breathing pyrochlore lattice
• Experimental Realization of a Quantum Breathing Pyrochlore Antiferromagnet
• Anisotropic exchange within decoupled tetrahedra in the quantum breathing pyrochlore Ba3Yb2Zn5O11
• Orbital and magnetic transitions in geometrically-frustrated vanadium spinels -- Monte Carlo study of an effective spin-orbital-lattice coupled model --
• Competing spin liquids and hidden nematic order in spin ice with frustrated transverse exchange
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Bond order from disorder in the planar pyrochlore magnet
• Novel Phase Transitions in the Breathing Pyrochlore Lattice: 7Li-NMR on LiInCr4O8 and LiGaCr4O8
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• Flat bands and Dirac cones in breathing lattices
• Quantum spin ice on the breathing pyrochlore lattice
• Magnetic Phase Diagram of the Breathing Pyrochlore Antiferromagnet LiGa1-xInxCr4O8
• Ground-state selection and spin-liquid behaviour in the classical Heisenberg model on the breathing pyrochlore lattice
• Mott transition and heavy fermion state in the pyrochlore Hubbard model
• Symmetry Breaking on the Three-Dimensional Hyperkagome Lattice of Na_4Ir_3O_8
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Low-energy excitations of the Hubbard model on the Kagomé lattice
• Geometrical frustration induced (semi-)metal to insulator transition
• The planar pyrochlore antiferromagnet: A large-N analysis
• Quantum dimer models and effective Hamiltonians on the pyrochlore lattice
• Quantum Disordered Ground States in Frustrated Antiferromagnets with Multiple Ring Exchange Interactions
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Metal-to-Insulator Transition, Spin Gap Generation, and Charge Ordering in Geometrically Frustrated Electron Systems
• On the valence-bond solid phase of the crossed-chain quantum spin model
• Spin ordering induced by lattice distortions in classical Heisenberg antiferromagnets on the breathing pyrochlore lattice
• Projective symmetry group classification of chiral ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice: application to the spin-$1/2$ XXZ Heisenberg model
• Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice
• Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet
• The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study
• Competing quantum spin liquids, gauge fluctuations, and anisotropic interactions in a breathing pyrochlore lattice
• Low-energy properties of two-dimensional quantum triangular antiferromagnets: Non-perturbative renormalization group approach
• Effective Hamiltonian of Three-orbital Hubbard Model on Pyrochlore Lattice: Application to LiV_2O_4
• Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Magnetic properties of a capped kagome molecule with 60 quantum spins
• Magnetization process and ordering of the $S=1/2$ pyrochlore magnet in a field
• Role of orbital degrees of freedom in investigating the magnetic properties of geometrically frustrated vanadium spinels
• Parity-broken ground state for the spin-1 pyrochlore antiferromagnet
• Order, Disorder and Monopole Confinement in the Spin-$1/2$ XXZ Model on a Pyrochlore Tube
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• The quantum spin quadrumer
• Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model
• Non-Fermi liquid, unscreened scalar chirality and parafermions in a frustrated tetrahedron Anderson model
• Hole-doping effects on a frustrated spin ladder
• Adiabatic Continuity of the Spinful Quantum Hall States
• Nematicity Liquid in a Trimerized-Kagome Antiferromagnet