Semiclassical eigenstates of four-sublattice antiferromagnets

Applying Bohr-Sommerfeld quantization and the topological phase of spin path integrals, one can determine the multiplicities, lattice symmetries, and eigenvalue clustering pattern of the low-lying singlet eigenstates of the triangular and fee antiferromagnets with four-sublattice classical ground states. In the triangular case, the clustering pattern agrees with numerical results of Lecheminant et al. [Phys. Rev. B 52, 6647 (1995)].