Spin-dependent extension of Calogero-Sutherland model through anyon-like representations of permutation operators

Abstract

We consider a A N−1 type of spin-dependent Calogero-Sutherland model, containing an arbitrary representation of the permutation operators on the combined internal space of all particles, and find that such a model can be solved as easily as its standard su( M) invariant counterpart through the diagonalisation of Dunkl operators. A class of novel representations of the permutation operator P ij , which pick up non-trivial phase factors along with interchanging the spins of the ith and jth particles, are subsequently constructed. These ‘anyon-like’ representations interestingly lead to different variants of the spin Calogero-Sutherland model with highly non-local interactions. We also explicitly derive some exact eigenfunctions as well as energy eigenvalues of these models and observe that the related degeneracy factors crucially depend on the choice of a few discrete parameters which characterise such anyon-like representations.