SU(N)→ SU(2) symmetry breaking in quantum antiferromagnets

Abstract

We study a SU(2)-symmetric spin-3/2 system on a bipartite lattice close to the antiferromagnetic SU(4)-symmetric point, which can be described by the CP3 model with a perturbation breaking the symmetry from SU(4) down to SU(2) and favoring the Néel ordering. We show that the effective theory of the perturbed model is not the usual O(3) nonlinear sigma model (NLSM), but rather the O(3) x O(2) NLSM. We show that in the presence of perturbation, the topological charge q of the CP3 field is connected to the O(3)-NLSM type topological charge of the spin texture Q (defined in a usual way via the unit Néel vector) by the relation q=3Q, thus under the influence of the perturbation unit-charge skyrmions of CP^3 model bind into triplets. We also show that in the general spin-S case, symmetry breaking from SU(2S+1) to SU(2) results in the general relation 2S Q_O(3)=q_CP^2S between CP^2S and O(3) charges, so one can expect 2S-multiplet binding of skyrmions.

Keywords

• frustrated magnets
• skyrmions
• cold gases in optical lattices