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

Abstract

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 $θ$ being $2 πS$ for two spins and $3 πS$ for three spins. Finally, we present a novel way of deriving the semiclassical wave functions from the spin wave functions.