Spin chains of Haldane-Shastry type and a generalized central limit theorem
| dc.contributor.author | Enciso, Alberto | |
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.date.accessioned | 2023-06-20T03:55:27Z | |
| dc.date.available | 2023-06-20T03:55:27Z | |
| dc.date.issued | 2009-06 | |
| dc.description | ©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. | |
| dc.description.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. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MICINN (Spain) | |
| dc.description.sponsorship | UCM-Banco Santander | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/31287 | |
| dc.identifier.doi | 10.1103/PhysRevE.79.060105 | |
| dc.identifier.issn | 1539-3755 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevE.79.060105 | |
| dc.identifier.relatedurl | http://journals.aps.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/44675 | |
| dc.issue.number | 6 | |
| dc.journal.title | Physical review E | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | FIS2008-00209 | |
| dc.relation.projectID | GR58/08-910556 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Spin chains of Haldane-Shastry type and a generalized central limit theorem | |
| dc.type | journal article | |
| dc.volume.number | 79 | |
| dcterms.references | [1] F. Haake, Quantum Signatures of Chaos, 2nd ed. SpringerVerlag, Berlin, 2001. [2] M. V. Berry and M. Tabor, Proc. R. Soc. London, Ser. A 356, 375 1977. [3] M. L. Mehta, Random Matrices, 3rd ed. Elsevier, San Diego, 2004. [4] F. D. M. Haldane, Phys. Rev. Lett. 60, 635 1988. [5] B. S. Shastry, Phys. Rev. Lett. 60, 639 1988. [6] A. P. Polychronakos, Phys. Rev. Lett. 70, 2329 1993. [7] H. Frahm, J. Phys. A 26, L473 1993. [8] M. A. Olshanetsky and A. M. Perelomov, Phys. Rep. 94, 313 1983. [9] D. Bernard et al., Europhys. Lett. 30, 301 1995. [10] A. Enciso et al., Nucl. Phys. B 707, 553 2005. [11] T. Yamamoto and O. Tsuchiya, J. Phys. A 29, 3977 1996. [12] B. Basu-Mallick et al., Nucl. Phys. B 812, 402 2009. [13] F. D. M. Haldane, Correlation Effects in Low-dimensional Electron Systems, in Springer Series in Solid-State Sciences Vol. 118, edited by A. Okiji and N. Kawakami Springer, New York, 1994, p. 3. [14] K. Hikami and B. Basu-Mallick, Nucl. Phys. B 566, 511 2000. [15] J. C. Barba et al., Nucl. Phys. B 806, 684 2009. [16] M. Arikawa et al., Phys. Rev. Lett. 86, 3096 2001. [17] M. V. N. Murthy and R. Shankar, Phys. Rev. Lett. 73, 3331 1994. [18] A. P. Polychronakos, J. Phys. A 39, 12793 2006. [19] R. Hernández and E. López, J. High Energy Phys. 11, 2004 079. [20] F. Finkel and A. González-López, Phys. Rev. B 72, 174411 2005. [21] J. C. Barba et al., Phys. Rev. B 77, 214422 2008. [22] J. C. Barba et al., EPL 83, 27005 2008. [23] B. Basu-Mallick and N. Bondyopadhaya, Nucl. Phys. B 757, 280 2006. [24] B. Basu-Mallick and N. Bondyopadhaya, e-print arXiv:0811.3110. [25] A. P. Polychronakos, Nucl. Phys. B 419, 553 1994. [26] R. B. Ash and C. A. Doléans-Dade, Probability and Measure Theory, 2nd ed. Academic Press, San Diego, 2000. [27] For instance, in the case of the su m Haldane-Shastry chain, a relatively simple expression for the partition function is known [20], while there is no such expression for the spectrum (including its degeneracies). Indeed, for a fixed number of sites N, it is possible to compute the levels and their degeneracies using he so-called “motifs” [29] and their associated Young diagrams [30]; but to the best of our knowledge, no general formula expressing these quantities as a function of N is available. [28] B. Basu-Mallick et al., Nucl. Phys. B 795, 596 2008. [29] F. D. M. Haldane et al., Phys. Rev. Lett. 69, 2021 1992. [30] K. Hikami, Nucl. Phys. B 441, 530 1995. | |
| dspace.entity.type | Publication | |
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| relation.isAuthorOfPublication | 7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc | |
| relation.isAuthorOfPublication.latestForDiscovery | 207092a4-0443-4336-a037-15936f8acc25 |
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