Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet

TL;DR

This paper derives an effective gauge-like Hamiltonian for the classical ground states of the quantum pyrochlore antiferromagnet, revealing a complex degeneracy structure influenced by order-by-disorder effects.

Contribution

It introduces an approximate effective Hamiltonian resembling a $Z_2$ gauge theory that captures the ground state degeneracy and order-by-disorder phenomena in the pyrochlore antiferromagnet.

Findings

Effective Hamiltonian acts on collinear states.

Ground state entropy is non-extensive, scaling as O(L).

Ground states have larger unit cells than previously considered.

Abstract

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length $S$ is a highly frustrated model with an macroscopic degeneracy of classical ground states. The zero-point energy of (harmonic order) spin wave fluctuations distinguishes a subset of these states. I derive an approximate but illuminating {\it effective Hamiltonian}, acting within the subspace of Ising spin configurations representing the {\it collinear} ground states. It consists of products of Ising spins around loops, i.e has the form of a $Z_2$ lattice gauge theory. The remaining ground state entropy is still infinite but not extensive, being $O(L)$ for system size $O(L^3)$. All these ground states have unit cells bigger than those considered previously.