Spin chains of Haldane-Shastry type and a generalized central limit theorem

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...

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Bibliographic Details
Authors: Enciso, Alberto, Finkel Morgenstern, Federico, González López, Artemio
Format: article
Publication Date:2009
Country:España
Institution:Universidad Complutense de Madrid (UCM)
Repository:Docta Complutense
Language:English
OAI Identifier:oai:docta.ucm.es:20.500.14352/44675
Online Access:https://hdl.handle.net/20.500.14352/44675
Access Level:Open access
Keyword:51-73
Física-Modelos matemáticos
Física matemática
Description
Summary: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.