Global properties of the spectrum of the Haldane-Shastry spin chain

TL;DR

This paper derives an exact partition function for the su(m) Haldane-Shastry spin chain, revealing Gaussian level density and non-Poissonian spacing distribution, indicating unique spectral properties among integrable models.

Contribution

It provides the first exact expression for the partition function and analyzes spectral properties, showing deviations from typical integrable system behavior.

Findings

Level density approaches a Gaussian distribution for large N.

Nearest-neighbor spacing distribution is not Poissonian.

Cumulative spacing distribution fits a simple three-parameter law.

Abstract

We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when the number of sites N is large enough the level density is Gaussian to a very high degree of approximation. More surprisingly, we also find that the nearest-neighbor spacing distribution is not Poissonian, so that this model departs from the typical behavior for an integrable system. We show that the cumulative spacing distribution of the model can be well approximated by a simple functional law involving only three parameters.