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

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

2009-03-27

arxiv.org/abs/0903.4761v1

Phys. Rev E 79, 060105(R) (2009)

Physics

Mathematical Physics

RevTeX, 5 pages

Scientific paper

10.1103/PhysRevE.79.060105

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 nontrivial modification of the classical central limit theorem, and is especially suited to models whose partition function is explicitly known. In particular, we provide the first 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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