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...
| Authors: | , , |
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| 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 |
| 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. |
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