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oai:docta.ucm.es:20.500.14352/446752023-08-25T13:51:21Zcom_20.500.14352_14col_20.500.14352_15

Spin chains of Haldane-Shastry type and a generalized central limit theorem Enciso, Alberto Finkel Morgenstern, Federico González López, Artemio 51-73 Física-Modelos matemáticos Física matemática ©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. 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. MICINN (Spain) UCM-Banco Santander Depto. de Física Teórica Fac. de Ciencias Físicas TRUE pub 2023-06-20T03:55:27Z 2023-06-20T03:55:27Z 2009-06 journal article https://hdl.handle.net/20.500.14352/44675 1539-3755 10.1103/PhysRevE.79.060105 eng FIS2008-00209 GR58/08-910556 open access application/pdf American Physical Society