Semiclassical ordering in the large-N pyrochlore antiferromagnet

Abstract

We study the semiclassical limit of the $Sp(N)$ generalization of the pyrochlore lattice Heisenberg antiferromagnet by expanding about the $N\to \infty$ saddlepoint in powers of a generalized inverse spin. To leading order, we write down an effective Hamiltonian as a series in loops on the lattice. Using this as a formula for calculating the energy of any classical ground state, we perform Monte-Carlo simulations and find a unique collinear ground state. This state is not a ground state of linear spin-wave theory, and can therefore not be a physical (N=1) semiclassical ground state.

4 pages, 4 eps figures; published version

References in corpus (5)

• Large N expansion for frustrated and doped quantum antiferromagnets
• The planar pyrochlore antiferromagnet: A large-N analysis
• Effective Hamiltonians and dilution effects in kagome and related antiferromagnets
• Quantum spin liquids: a large-S route
• U(1) spin liquids and valence bond solids in a large-N three-dimensional Heisenberg model

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• Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Order by disorder in classical kagome antiferromagnets with chiral interactions
• Effective Hamiltonians for large-S pyrochlore antiferromagnet
• A Theorem on Extensive Spectral Degeneracy for Systems with Higher Symmetries in General Dimensions
• Depleted pyrochlore antiferromagnets