Semiclassical analysis of two- and three-spin antiferromagnets and anyons on a sphere

Details Semiclassical analysis of two- and three-spin antiferromagnets and anyons on a sphere Semiclassical analysis of two- and three-spin antiferromagnets and anyons on a sphere

1993-04-28

arxiv.org/abs/hep-th/9304151v1

Mod.Phys.Lett.A8:1805-1814,1993

Physics

High Energy Physics

High Energy Physics - Theory

16 pages, plain tex, 1 figure available on request, IISc-CTS-93-3

Scientific paper

10.1142/S0217732393001525

We do a semiclassical analysis for two or three spins which are coupled antiferromagnetically to each other. The semiclassical wave functions transform correctly under permutations of the spins if one takes into account the Wess-Zumino term present in the path integral for spins. The Wess-Zumino term here is a total derivative which has no effect on the energy spectrum. The semiclassical problem is related to that of anyons moving on a sphere with the statistics parameter $\theta$ being $2 \pi S$ for two spins and $3 \pi S$ for three spins. Finally, we present a novel way of deriving the semiclassical wave functions from the spin wave functions.

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