Quantum dimer models and effective Hamiltonians on the pyrochlore lattice

Abstract

We study a large-N deformation of the S=1/2 pyrochlore Heisenberg antiferromagnet which leads to a soluble quantum dimer model at leading non-trivial order. In this limit, the ground state manifold -- while extensively degenerate -- breaks the inversion symmetry of the lattice, which implies a finite temperature Ising transition without translational symmetry breaking. At lower temperatures and further in the 1/N expansion, we discuss an effective Hamiltonian within the degenerate manifold, which has a transparent physical interpretation as representing dimer potential energies. We find mean-field ground states of the effective Hamiltonian which exhibit translational symmetry breaking. The entire scenario offers a new perspective on previous treatments of the SU(2) problem not controlled by a small parameter, in particular showing that a mean-field state considered previously encodes the physics of a maximally flippable dimer configuration. We also comment on the difficulties of extending our results to the SU(2) case, and note implications for classical dimer models.

9 pages

References in corpus (3)

• Emergent excitations in a geometrically frustrated magnet
• Coulomb and Liquid Dimer Models in Three Dimensions
• Singlet Excitations in Pyrochlore: A Study of Quantum Frustration

Cited by in corpus (24)

• Magnetic Pyrochlore Oxides
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Experimental Realization of a Quantum Breathing Pyrochlore Antiferromagnet
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Monopole Flux State on the Pyrochlore Lattice
• Quantum spin ice with frustrated transverse exchange: from pi-flux phase to nematic quantum spin liquid
• 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
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Bond order wave instabilities in doped frustrated antiferromagnets: "Valence bond solids" at fractional filling
• The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study
• Dynamical stability of the quantum Lifshitz theory in 2+1 Dimensions
• Thermodynamics of the pyrochlore Heisenberg ferromagnet with arbitrary spin $S$
• Exact entropy of dimer coverings for a class of lattices in three or more dimensions
• Deconfined quantum criticality driven by Dirac fermions in SU(2) antiferromagnets
• Structural and spin-glass properties of single crystal $J_{eff}$ = 1/2 pyrochlore antiferromagnet NaCdCo${}_2$F${}_7$ : correlating $T_f$ with magnetic-bond-disorder
• Higher-order Topological States in Chiral Split Magnons of Honeycomb Altermagnets
• Broken-Symmetry Ground States of the Heisenberg model on the Pyrochlore Lattice
• Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model
• Doped resonating-valence-bond states: Robustness of the spin-ice phases in three-dimensional Rydberg arrays