Semiclassical degeneracies and ordering for highly frustrated magnets in a field

TL;DR

This paper investigates how quantum fluctuations influence the ground states of highly frustrated magnets in strong magnetic fields, revealing symmetries and topological effects that partially lift classical degeneracies, especially in kagome magnets.

Contribution

It introduces dynamical symmetries that preserve classical degeneracies and connects frustrated magnet problems to gauge theories, showing how magnetic fields can tune these systems.

Findings

Quantum fluctuations cause small energy differences except near specific collinear states.

Presence of a topological flux-sensitive term in the effective Hamiltonian.

Magnetic field can tune the physical sector of the associated gauge theories.

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.