Inozemtsev's hyperbolic spin model and its related spin chain

Abstract

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.

22 pages, RevTeX, 7 figures

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• One-Dimensional Vertex Models Associated with a Class of Yangian Invariant Haldane-Shastry Like Spin Chains
• Thermodynamics and criticality of supersymmetric spin chains with long-range interactions
• A new perspective on the integrability of Inozemtsev's elliptic spin chain
• Level density distribution for one-dimensional vertex models related to Haldane-Shastry like spin chains
• Appearance of branched motifs in the spectra of $B{C}_N$ type Polychronakos spin chains
• Thermodynamics and criticality of su($m$) spin chains of Haldane-Shastry type
• Supersymmetric $t$-$J$ models with long-range interactions: thermodynamics and criticality
• Generalized Lipkin-Meshkov-Glick models of Haldane-Shastry type