Exact partition function of SU(m|n) supersymmetric Haldane-Shastry spin chain

TL;DR

This paper derives the exact partition function of the SU(m|n) supersymmetric Haldane-Shastry spin chain from a spin Calogero-Sutherland model, enabling analysis of spectral properties and revealing Gaussian level density distribution.

Contribution

It provides the first exact partition function for the SU(m|n) supersymmetric Haldane-Shastry spin chain, facilitating spectral analysis and duality conjectures.

Findings

Level density distribution follows a Gaussian form for large systems.

Mean and standard deviation of energy levels are exactly calculable.

Partition function likely satisfies a boson-fermion duality relation.

Abstract

By taking the freezing limit of a spin Calogero-Sutherland model containing `anyon like' representation of the permutation algebra, we derive the exact partition function of SU(m|n) supersymmetric Haldane-Shastry (HS) spin chain. This partition function allows us to study global properties of the spectrum like level density distribution and nearest neighbour spacing distribution. It is found that, for supersymmetric HS spin chains with large number of lattice sites, continuous part of the energy level density obeys Gaussian distribution with a high degree of accuracy. The mean value and standard deviation of such Gaussian distribution can be calculated exactly. We also conjecture that the partition function of supersymmetric HS spin chain satisfies a duality relation under the exchange of bosonic and fermionic spin degrees of freedom.