Exact spectrum and partition function of SU(m|n) supersymmetric Polychronakos model

TL;DR

This paper derives the exact spectrum and partition function of the SU(m|n) supersymmetric Polychronakos model, revealing a duality relation and novel q-polynomial expressions, advancing understanding of supersymmetric spin chains.

Contribution

It provides the first exact calculation of the spectrum and partition function for the SU(m|n) supersymmetric Polychronakos model, including a duality relation between models.

Findings

Spectrum is equally spaced, similar to non-supersymmetric case.

Degeneracy factors depend on bosonic (m) and fermionic (n) degrees of freedom.

Partition functions are expressed through novel q-polynomials.

Abstract

By using the fact that Polychronakos-like models can be obtained through the `freezing limit' of related spin Calogero models, we calculate the exact spectrum as well as partition function of SU(m|n) supersymmetric Polychronakos (SP) model. It turns out that, similar to the non-supersymmetric case, the spectrum of SU(m|n) SP model is also equally spaced. However, the degeneracy factors of corresponding energy levels crucially depend on the values of bosonic degrees of freedom (m) and fermionic degrees of freedom (n). As a result, the partition functions of SP models are expressed through some novel q-polynomials. Finally, by interchanging the bosonic and fermionic degrees of freedom, we obtain a duality relation among the partition functions of SP models.