Publication: Spin chains of Haldane-Shastry type and a generalized central limit theorem
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2009-06
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American Physical Society
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Abstract
We show that the density of energy levels of a wide class of finite-dimensional quantum systems tends to a Gaussian distribution as the number of degrees of freedom increases. Our result is based on a variant of the central limit theorem which is especially suited to models whose partition function is explicitly known. In particular, we provide a theoretical explanation of the fact that the level density of several spin chains of Haldane-Shastry type is asymptotically Gaussian when the number of sites tends to infinity.
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©2009 The American Physical Society.
This work was supported in part by the MICINN and the UCM-Banco Santander under Grants No. FIS2008-00209 and No. GR58/08-910556. A.E. acknowledges the financial support of the Spanish Ministry of Science. The authors would also like to thank the referees for several useful remarks.
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