Supersymmetric Polychronakos Spin Chain: Motif, Distribution Function, and Character

TL;DR

This paper investigates the spectrum degeneracies, motif structures, and distribution functions of the supersymmetric Polychronakos spin chain, providing new representations and character formulas for large system sizes.

Contribution

It introduces a motif representation in terms of supersymmetric skew Young diagrams and analyzes the distribution function and characters for large N.

Findings

Motif representation via supersymmetric skew Young diagrams

Distribution function analysis for quasi-particles

Character formulas for large N limit

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-Szeg{\"o} polynomials which are closely related to the partition function of the $N$ spin chain, we give the representation for motif in terms of the supersymmetric skew Young diagrams. We also study the distribution function for quasi-particles. The character formulae for $N\to \infty$ are briefly discussed.