Exact solution and thermodynamics of a spin chain with long-range elliptic interactions



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Finkel Morgenstern, Federico and González López, Artemio (2014) Exact solution and thermodynamics of a spin chain with long-range elliptic interactions. Journal of statistical mechanics : theory and experiment, 2014 . ISSN 1742-5468

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Official URL: http://dx.doi.org/10.1088/1742-5468/2014/12/P12014


We solve in closed form the simplest (su(1 vertical bar 1)) supersymmetric version of Inozemtsev's elliptic spin chain, as well as its infinite (hyperbolic) counterpart. The solution relies on the equivalence of these models to a system of free spinless fermions and on the exact computation of the Fourier transform of the resulting elliptic hopping amplitude. We also compute the thermodynamic functions of the finite (elliptic) chain and their low temperature limit and show that the energy levels become normally distributed in the thermodynamic limit. Our results indicate that at low temperatures the su(1 vertical bar 1) elliptic chain behaves as a critical XX model and deviates in an essential way from the Haldane-Shastry chain.

Item Type:Article
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© IOP Publishing.
This work was supported in part by Spains MINECO under grant no. FIS2011-22566

Uncontrolled Keywords:Inverse-square exchange; Haldane-shastry type; Heisenberg chain; Yangian symmetry; Exact spectrum; Systems; Models; Gas
Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:30699
Deposited On:08 Jun 2015 08:28
Last Modified:10 Dec 2018 15:09

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