Publication: Inozemtsev's hyperbolic spin model and its related spin chain
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2010-11-11
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In this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.
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©2010 Elsevier B.V. All rights reserved.
This work was partially supported by the Spanish Ministry of Science and Innovation under grant No. FIS2008-00209, and by the Universidad Complutense and Banco Santander under grant No. GR58/08-910556. J.C.B. acknowledges the financial support of the Spanish Ministry of Science and Innovation through an FPU scholarship. The authors would like to thank B. BasuMallick for useful discussions on A_(N−1)-type motifs.
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