Order by Disorder and Gaugelike Degeneracy in a Quantum Pyrochlore Antiferromagnet

The (three-dimensional) pyrochlore lattice antiferromagnet with Heisenberg spins of large spin length S is a highly frustrated model with a 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 effective Hamiltonian, acting within the subspace of Ising spin configurations representing the collinear ground states. It consists of products of Ising spins around loops, i.e., has the form of a Z₂ lattice gauge theory. The remaining ground-state entropy is still infinite but not extensive, being O(L) for system size O(L³). All these ground states have unit cells bigger than those considered previously.