Effective Hamiltonian for the Pyrochlore antiferromagnet: semiclassical derivation and degeneracy

TL;DR

This paper derives an effective Hamiltonian for the pyrochlore antiferromagnet in the semiclassical limit, revealing a highly degenerate set of ground states and providing insights into flux configurations and magnetization plateaus.

Contribution

It introduces a real-space loop expansion method to derive an effective Hamiltonian that captures the degeneracy and flux states in the pyrochlore antiferromagnet.

Findings

Identifies a family of degenerate collinear ground states.

Provides bounds on the degeneracy of these states.

Demonstrates applicability to related lattices and magnetization plateaus.

Abstract

In the classical pyrochlore lattice Heisenberg antiferromagnet, there is a macroscopic continuous ground state degeneracy. We study semiclassical limit of large spin length $S$, keeping only the lowest order (in 1/S) correction to the classical Hamiltonian. We perform a detailed analysis of the spin-wave modes, and using a real-space loop expansion, we produce an effective Hamiltonian, in which the degrees of freedom are Ising variables representing fluxes through loops in the lattice. We find a family of degenerate collinear ground states, related by gauge-like $Z_2$ transformations and provide bounds for the order of the degeneracy. We further show that the theory can readily be applied to determine the ground states of the Heisenberg Hamiltonian on related lattices, and to field-induced collinear magnetization plateau states.