$SU(N)\to SU(2)$ 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 $C{P}^3$ 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 $O(3)\times O(2)$ NLSM. We show that in the presence of perturbation, the topological charge $q$ of the $C{P}^3$ 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 $C{P}^3$ 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 $2S{Q}_{O(3)}=q_{C{P}^{2S}}$ between $C{P}^{2S}$ and $O(3)$ charges, so one can expect $2S$-multiplet binding of skyrmions.

8 pages

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