Inozemtsev's hyperbolic spin model and its related spin chain

2010/05/04 by J. C. Barba, Federico Finkel, F. Finkel +4 · 1 citation
Chemistry · Mathematics · Physics and Astronomy · #Chain (unit) #Combinatorics #Mathematical physics #Mathematics #Molecular spectroscopy and chirality #Partition (number theory) #Partition function (quantum field theory) #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Spectroscopy and Quantum Chemical Studies #Spin (aerodynamics) #Statistical physics #cond-mat.str-el #hep-th #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2010.06.008

published as Nucl.Phys.B839:499-525,2010 · 22 pages, RevTeX, 7 figures

arxiv created 2010/05/04 · openalex publication_date 2010/06/12 · arxiv updated 2014/11/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

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.

Citations

• Random Matrix Theories in Quantum Physics: Common Concepts
• Exchange operator formalism for integrable systems of particles
• Invariants of the Haldane-Shastry SU(N) chain
• On the Sutherland Spin Model of B N Type and Its Associated Spin Chain
• Global properties of the spectrum of the Haldane-Shastry spin chain
• Yangian symmetry of integrable quantum chains with long-range interactions and a new description of states in conformal field theory
• Solution of the One-Dimensional N-Body Problems with Quadratic and/or Inversely Quadratic Pair Potentials
• A N -Type Dunkl Operators and New Spin Calogero-Sutherland Models
• Integrable systems for particles with internal degrees of freedom
• Differential-difference operators associated to reflection groups
• Level clustering in the regular spectrum
• Electron correlations in narrow energy bands

Cited by

• A new perspective on the integrability of Inozemtsev’s elliptic spin chain

Related

• The deformed Inozemtsev spin chain
• The open supersymmetric Haldane-Shastry spin chain and its associated motifs
• Conservation laws of the Haldane-Shastry type spin chains
• Landscapes of integrable long-range spin chains
• The trigonometric counterpart of the Haldane Shastry Model