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



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Finkel Morgenstern, Federico and González López, Artemio (2014) A new perspective on the integrability of Inozemtsev's elliptic spin chain. Annals of physics, 351 . pp. 797-827. ISSN 0003-4916

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Official URL: http://dx.doi.org/10.1016/j.aop.2014.10.006


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.

Item Type:Article
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© 2014 Elsevier Inc. All rights reserved.
This work was supported in part by Spain's MINECO under grant no. FIS2011-22566.

Uncontrolled Keywords:Inverse-square exchange; Long-range interactions; Yangian symmetry; Heisenberg chain; Lie-algebras; Bcn type; N-type; Systems; Model; Spectrum
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30700
Deposited On:08 Jun 2015 08:34
Last Modified:10 Dec 2018 15:09

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