Supersymmetric Polychronakos spin chain: Motif, distribution function, and character

Abstract

Degeneracy patterns and hyper-multiplet structure in the spectrum of the su( m| n) supersymmetric Polychronakos spin chain are studied by use of the “motif”. Using the recursion relation of the supersymmetric Rogers–Szegö polynomials which are closely related to the partition function of the N spin chain, we give the representation for the motif in terms of the supersymmetric skew Young diagrams. We also study the distribution function for quasi-particles. The character formulae for N→∞ are briefly discussed.