Semiclassical degeneracies and ordering for highly frustrated magnets in a field

Abstract

We discuss ground state selection by quantum fluctuations in frustrated magnets in a strong magnetic field. We show that there exist dynamical symmetries -- one a generalisation of Henley's gauge-like symmetry for collinear spins, the other the quantum relict of non-collinear weathervane modes -- which ensure a partial survival of the classical degeneracies. We illustrate these for the case of the kagome magnet, where we find zero-point energy differences to be rather small everywhere except near the collinear `up-up-down` configurations, where there is rotational but not translational symmetry breaking. In the effective Hamiltonian, we demonstrate the presence of a term sensitive to a topological `flux'. We discuss the connection of such problems to gauge theories by casting the frustrated lattices as medial lattices of appropriately chosen simplex lattices, and in particular we show how the magnetic field can be used to tune the physical sector of the resulting gauge theories.

10 pages, 8 figures

References in corpus (8)

• Pyrochlore Photons: The U(1) Spin Liquid in a S=1/2 Three-Dimensional Frustrated Magnet
• Why spin ice obeys the ice rules
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Exact low-temperature behavior of kagome antiferromagnet at high fields
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order
• Bond order from disorder in the planar pyrochlore magnet
• Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy
• Quantum spin liquids: a large-S route

Cited by in corpus (14)

• Anderson localisation in tight-binding models with flat bands
• Highly Frustrated Magnetic Clusters: The kagome on a sphere
• Magnetic phase diagrams of classical triangular and kagome antiferromagnets
• Non-monotonic zero point entropy in diluted spin ice
• Dipolar order by disorder in the classical Heisenberg antiferromagnet on the kagome lattice
• Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet
• Real-space perturbation theory for frustrated magnets: application to magnetization plateaus
• Magnetization plateaus and sublattice ordering in easy axis Kagome lattice antiferromagnets
• Hierarchy of energy scales and field-tunable order by disorder in dipolar-octupolar pyrochlores
• Anharmonic Ground state selection in the pyrochlore antiferromagnet
• Ground state selection by magnon interactions in the fcc antiferromagnet
• Effective Hamiltonians for large-S pyrochlore antiferromagnet
• Unconventional magnets in external magnetic fields
• Inhomogeneous quantum antiferromagnetism on periodic lattices