Inozemtsev's hyperbolic spin model and its related spin chain

TL;DR

This paper analyzes Inozemtsev's hyperbolic su(m) spin model and its related spin chain, deriving their spectra, partition function, and exploring implications for quantum chaos conjectures.

Contribution

It provides an explicit spectrum calculation and partition function for Inozemtsev's model and the associated spin chain, connecting them to Haldane-Shastry motifs and quantum chaos.

Findings

Spectrum of Inozemtsev's model computed

Partition function of Frahm-Inozemtsev chain derived

Level density and spacing distribution analyzed

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.