Abstract
We study antiferromagnetic systems with enhanced “nearly-SU(N)” symmetry, which can be realized in systems of ultracold spinor atoms in optical lattices. Examples of N = 3 (for S = 1 bosons) and N = 4 (for S=32 fermions) are considered. Near the SU(N) point, the low-energy physics can be described by the CPN−1 model with an additional symmetry-breaking term lowering the symmetry down to SU(2) and favoring the Néel ordering. We show that the effective theory of such systems can be cast in the form of a nonlinear sigma model with the SO(3) matrix-valued field, which is typically obtained for frustrated magnets with non-collinear order. Further, we show that those systems possess a peculiar effect of topological binding: for a system with the underlying spin S, lowering of the symmetry from SU(2S + 1) to SU(2) leads to binding of topological unit-charge excitations of the CP2S model (skyrmions for space dimension d = 2, instantons for d = 1, and hedgehogs for d = 3) into 2S-multiplets.
Highlights
Through the past several decades, low-dimensional quantum magnets have steadily attracted attention of researchers, in particular as a convenient playground for effects involving topologically nontrivial excitations
We study antiferromagnetic systems with enhanced “nearly-SU(N)” symmetry, which can be realized in systems of ultracold spinor atoms in optical lattices
We show that the effective theory of such systems can be cast in the form of a nonlinear sigma model with the SO(3) matrix-valued field, which is typically obtained for frustrated magnets with non-collinear order
Summary
Through the past several decades, low-dimensional quantum magnets have steadily attracted attention of researchers, in particular as a convenient playground for effects involving topologically nontrivial excitations. The low-energy physics of SU(N) antiferromagnets is captured by the CPN−1 model, with topological terms playing a crucial role in the case of low spatial dimensionality d < 3 For such highly symmetric systems, even weak additional interactions might become important if they break the enhanced symmetry. If such a perturbation favors the Néel order, it is natural to assume that the resulting physics will be described by the standard O(3) nonlinear sigma model (NLSM) that is well-known to be the effective theory of “common” Heisenberg antiferromagnets. Quite generally, the SU(2S + 1) ↦ SU(2) perturbation leads to binding of unit-charge topological configurations of the CP2S model into 2S multiplets
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