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

Christopher L. Henley
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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.

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Christopher L. Henley. 2005-08-31. Order by disorder and gauge-like degeneracy in quantum pyrochlore antiferromagnet. https://doi.org/10.1103/physrevlett.96.047201

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