Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet

Abstract

We study the effect of quantum fluctuations on the half-polarized magnetization plateau of a pyrochlore antiferromagnet. We argue that an expansion around the easy axis limit is appropriate for discussing the ground state selection amongst the classically degenerate manifold of collinear states with a 3:1 ratio of spins parallel/anti-parallel to the magnetization axis. A general approach to the necessary degenerate perturbation theory is presented, and an effective quantum dimer model within this degenerate manifold is derived for arbitrary spin $s$. We also generalize the existing semiclassical analysis of Hizi and Henley [Phys. Rev. B {\bf 73}, 054403 (2006)] to the easy axis limit, and show that both approaches agree at large $s$. We show that under rather general conditions, the first non-constant terms in the effective Hamiltonian for $s\ge 1$ occur only at {\sl sixth} order in the transverse exchange coupling. For $s\ge 3/2$, the effective Hamiltonian predicts a magnetically ordered state. For $s\le 1$ more exotic possibilities may be realized, though an analytical solution of the resulting quantum dimer model is not possible.

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• Quantum Spin Ice and dimer models with Rydberg atoms
• Quantum Selection of Order in an $XXZ$ Antiferromagnet on a Kagomé Lattice
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Nematic, vector-multipole, and plateau-liquid states in the classical O(3) pyrochlore antiferromagnet with biquadratic interactions in applied magnetic field
• Quantum order by disorder in the Kitaev model on a triangular lattice
• Topological degeneracy and vortex manipulation in Kitaev's honeycomb model
• Real-space perturbation theory for frustrated magnets: application to magnetization plateaus
• Topological Color Codes and Two-Body Quantum Lattice Hamiltonians
• Magnetization plateaus and sublattice ordering in easy axis Kagome lattice antiferromagnets
• Semiclassical spin liquid state of easy axis Kagome antiferromagnets
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Magnon interactions in the quantum paramagnetic phase of CoNb${}_2$O${}_6$
• Topological spin liquids in the ruby lattice with anisotropic Kitaev interactions
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Tunneling-induced restoration of classical degeneracy in quantum kagome ice
• Ising nematic fluid phase of hard-core dimers on the square lattice
• Quantum order by disorder in a semiclassical spin ice
• Strong-coupling expansion and effective hamiltonians
• Depleted pyrochlore antiferromagnets
• Quantum selection of order and dynamic properties of Kitaev-Heisenberg ferromagnet on a triangular lattice
• Topological phases of the compass ladder model