The Berry-Tabor conjecture for spin chains of Haldane-Shastry typeJ. C. Barba, F. Finkel, A. González-López and M. A. Rodríguez
Departamento de Física Teórica II, Universidad Complutense - 28040 Madrid, Spain, EU
received 23 April 2008; accepted in final form 28 May 2008; published July 2008
published online 27 June 2008
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.
75.10.Pq - Spin chain models.
05.45.Mt - Quantum chaos; semiclassical methods.
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