Degenerate perturbation theory of quantum fluctuations in a pyrochlore antiferromagnet

TL;DR

This paper develops a degenerate perturbation theory approach to analyze quantum fluctuations in a pyrochlore antiferromagnet, revealing how different spin magnitudes influence ground state selection and magnetic ordering.

Contribution

It introduces a general degenerate perturbation theory framework and an effective quantum dimer model for pyrochlore antiferromagnets, extending semiclassical analysis to the easy axis limit.

Findings

Effective Hamiltonian terms appear at sixth order for s≥1.

For s≥3/2, predicts magnetically ordered states.

For s≤1, potential for exotic ground states.

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 $s\geq 1$ occur only at {\sl sixth} order in the transverse exchange coupling. For $s\geq 3/2$, the effective Hamiltonian predicts a magnetically ordered state. For $s\leq 1$ more exotic possibilities may be realized, though an analytical solution of the resulting quantum dimer model is not possible.