Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy

Abstract

In the classical pyrochlore lattice Heisenberg antiferromagnet, there is a macroscopic continuous ground state degeneracy. We study semiclassical limit of large spin length $S$, keeping only the lowest order (in 1/S) correction to the classical Hamiltonian. We perform a detailed analysis of the spin-wave modes, and using a real-space loop expansion, we produce an effective Hamiltonian, in which the degrees of freedom are Ising variables representing fluxes through loops in the lattice. We find a family of degenerate collinear ground states, related by gauge-like $Z_2$ transformations and provide bounds for the order of the degeneracy. We further show that the theory can readily be applied to determine the ground states of the Heisenberg Hamiltonian on related lattices, and to field-induced collinear magnetization plateau states.

20 pages, 15 figures. Minor additions to text. Added some references

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Cited by in corpus (23)

• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Mechanisms of degeneracy breaking in pyrochlore antiferromagnets
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Lattice gas description of pyrochlore and checkerboard antiferromagnets in a strong magnetic field
• Linear independence of localized magnon states
• Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
• Long range order in the classical kagome antiferromagnet: effective Hamiltonian approach
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Magnetization plateaus and sublattice ordering in easy axis Kagome lattice antiferromagnets
• Semiclassical degeneracies and ordering for highly frustrated magnets in a field
• Semiclassical spin liquid state of easy axis Kagome antiferromagnets
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Mott-Hubbard transition and spin-liquid state on the pyrochlore lattice
• Order by disorder in classical kagome antiferromagnets with chiral interactions
• Effective Hamiltonians for large-S pyrochlore antiferromagnet
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Color ice states, weathervane modes, and order by disorder in the bilinear-biquadratic pyrochlore Heisenberg antiferromagnet
• Effective Hamiltonians for some highly frustrated magnets
• Magnetic Order and Mott Transition on the Checkerboard Lattice
• Spin-nematic order in the frustrated pyrochlore-lattice quantum rotor model
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Depleted pyrochlore antiferromagnets
• Incoherent transport in a classical spin liquid