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The Berry-Tabor conjecture for spin chains of Haldane-Shastry type

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Barba, J. C. and Finkel Morgenstern, Federico and González López, Artemio and Rodríguez González, Miguel Ángel (2008) The Berry-Tabor conjecture for spin chains of Haldane-Shastry type. EPL, 83 (2). ISSN 0295-5075

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Official URL: http://dx.doi.org/10.1209/0295-5075/83/27005




Abstract

According to a long-standing conjecture of Berry and Tabor, the distribution of the spacings between consecutive levels of a "generic" integrable model should follow Poisson's law. In contrast, the spacings distribution of chaotic systems typically follows Wigner's law. An important exception to the Berry-Tabor conjecture is the integrable spin chain with long-range interactions introduced by Haldane and Shastry in 1988, whose spacings distribution is neither Poissonian nor of Wigner's type. In this letter we argue that the cumulative spacings distribution of this chain should follow the "square root of a logarithm" law recently proposed by us as a characteristic feature of all spin chains of Haldane-Shastry type. We also show in detail that the latter law is valid for the rational counterpart of the Haldane-Shastry chain introduced by Polychronakos.


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©EPLA, 2008.
This work was partially supported by the DGI under grant no. FIS2005-00752, and by the Complutense University and the DGUI under grant no. GR74/07-910556. JCB acknowledges the financial support of the Spanish Ministry of Education and Science through an FPU scholarship.

Subjects:Sciences > Physics > Physics-Mathematical models
Sciences > Physics > Mathematical physics
ID Code:31355
Deposited On:14 Jul 2015 18:11
Last Modified:10 Dec 2018 15:09

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