Effective Hamiltonians forlarge-S pyrochlore antiferromagnets

Abstract

The pyrochlore lattice Heisenberg antiferromagnet has a massive classical ground-statedegeneracy. We summarize three approximation schemes, valid for large spin lengthS, to capture the (partial) lifting of this degeneracy when zero-point quantum fluctuationsare taken into account; all three are related to analytic loop expansions. The first isharmonic-order spin waves; at this order, there remains an infinite manifold of degeneratecollinear ground states, related by a gauge-like symmetry. The second is anharmonic (quarticorder) spin waves, using a self-consistent approximation; the harmonic-order degeneracy issplit, but (within numerical precision) some degeneracy may remain, with entropy still of orderL in a systemof L3 sites. Thethird is a large-N approximation, a standard and convenient approach for frustrated antiferromagnets; however, thelarge-N result contradicts the harmonic order atO(S) and hence mustbe wrong (for large S).