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

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.