Publication: Global properties of the spectrum of the Haldane-Shastry spin chain
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2005-11
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American Physical Society
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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.
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©2005 The American Physical Society.
This work was partially supported by the Spanish DGI under Grant No. BFM2002-02646. The authors would like to thank J. Retamosa for several helpful discussions.
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35Our computations show that the number of levels, and hence of different spacings, increases monotonically with N of a fixed parity, but decreases when N jumps from 2j to 2j+1.