Inozemtsevs hyperbolic spin model and its related spin chain

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.

💡 Research Summary

The paper investigates Inozemtsev’s su(m) quantum spin model with hyperbolic (1/ sinh²) interactions and the associated Frahm‑Inozemtsev (FI) spin chain, which belongs to the Haldane‑Shastry family. The authors first derive the exact spectrum of the Inozemtsev model by employing a Bethe‑Ansatz–type construction. The Hamiltonian contains a coupling constant g and a hyperbolic parameter α that controls the range of the interaction; the two‑body potential is V_{ij}=g²/ sinh²