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

Abstract

The aim of this paper is studying from an alternative point of view the integrability of the spin chain with long-range elliptic interactions introduced by Inozemtsev. Our analysis relies on some well-established conjectures characterizing the chaotic vs. integrable behavior of a quantum system, formulated in terms of statistical properties of its spectrum. More precisely, we study the distribution of consecutive levels of the (unfolded) spectrum, the power spectrum of the spectral fluctuations, the average degeneracy, and the equivalence to a classical vertex model. Our results are consistent with the general consensus that this model is integrable, and that it is closer in this respect to the Heisenberg chain than to its trigonometric limit (the Haldane-Shastry chain). On the other hand, we present some numerical and analytical evidence showing that the level density of Inozemtsev's chain is asymptotically Gaussian as the number of spins tends to infinity, as is the case with the Haldane-Shastry chain. We are also able to compute analytically the mean and the standard deviation of the spectrum, showing that their asymptotic behavior coincides with that of the Haldane-Shastry chain.

arXiv commentPdflatex, 35 pages, 6 figures. Minor changes, to appear in Annals of Physics

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Cited by in corpus (8)

• Yangian-invariant spin models and Fibonacci numbers
• Elliptic generalization of integrable q-deformed anisotropic Haldane-Shastry long-range spin chain
• Exact solution and thermodynamics of a spin chain with long-range elliptic interactions
• The non-chiral intermediate Heisenberg ferromagnet equation
• How coordinate Bethe ansatz works for Inozemtsev model
• Thermodynamics of Inozemtsev's Elliptic Spin Chain
• A novel class of translationally invariant spin chains with long-range interactions
• Supersymmetric $t$-$J$ models with long-range interactions: partition function and spectrum