Global properties of the spectrum of the Haldane-Shastry spin chain
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.date.accessioned | 2023-06-20T10:56:56Z | |
| dc.date.available | 2023-06-20T10:56:56Z | |
| dc.date.issued | 2005-11 | |
| dc.description | ©2005 The American Physical Society. This work was partially supported by the Spanish DGI under Grant No. BFM2002-02646. The authors would like to thank J. Retamosa for several helpful discussions. | |
| dc.description.abstract | We derive an exact expression for the partition function of the su(m) Haldane-Shastry spin chain, which we use to study the density of levels and the distribution of the spacing between consecutive levels. Our computations show that when the number of sites N is large enough, the level density is Gaussian to a very high degree of approximation. More surprisingly, we also find that the nearest-neighbor spacing distribution is not Poissonian, so that this model departs from the typical behavior for an integrable system. We show that the cumulative spacing distribution of the model can be well approximated by a simple functional law involving only three parameters. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | DGI, Spain | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/31360 | |
| dc.identifier.doi | 10.1103/PhysRevB.72.174411 | |
| dc.identifier.issn | 1098-0121 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1103/PhysRevB.72.174411 | |
| dc.identifier.relatedurl | http://journals.aps.org | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51498 | |
| dc.issue.number | 17 | |
| dc.journal.title | Physical review B | |
| dc.language.iso | eng | |
| dc.publisher | American Physical Society | |
| dc.relation.projectID | BFM2002-02646 | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Global properties of the spectrum of the Haldane-Shastry spin chain | |
| dc.type | journal article | |
| dc.volume.number | 72 | |
| dcterms.references | 1F. D. M. Haldane, Phys. Rev. Lett. 60, 635 1988. 2B. S. Shastry, Phys. Rev. Lett. 60, 639 1988. 3M. C. Gutzwiller, Phys. Rev. Lett. 10, 159 1963. 4F. Gebhard and D. Vollhardt, Phys. Rev. Lett. 59, 1472 1987. 5C. Gros, R. Joynt, and T. M. Rice, Phys. Rev. B 36, 381 1987. 6P. W. Anderson, G. Baskaran, Z. Zou, and T. Hsu, Phys. Rev. Lett. 58, 2790 1987. 7M. Fowler and J. A. Minahan, Phys. Rev. Lett. 70, 2325 1993. 8F. D. M. Haldane, Phys. Rev. Lett. 66, 1529 1991. 9N. Kawakami, Phys. Rev. B 46, 1005 1992. 10Z. N. C. Ha and F. D. M. Haldane, Phys. Rev. B 47, 12459 1993. 11F. D. M. Haldane, Phys. Rev. Lett. 67, 937 1991. 12F. D. M. Haldane, Z. N. C. Ha, J. C. Talstra, D. Bernard, and V. Pasquier, Phys. Rev. Lett. 69, 2021 1992. 13D. Bernard, M. Gaudin, F. D. M. Haldane, and V. Pasquier, J. Phys. A 26, 5219 1993. 14C. F. Dunkl, Trans. Am. Math. Soc. 311, 167 1989. 15A. P. Polychronakos, Phys. Rev. Lett. 69, 703 1992. 16B. Sutherland, Phys. Rev. A 4, 2019 1971. 17B. Sutherland, Phys. Rev. A 5, 1372 1972. 18K. Hikami and B. Basu-Mallick, Nucl. Phys. B 566, 511 2000. 19K. Hikami and M. Wadati, J. Math. Phys. 44, 3569 2003. 20H. Frahm, J. Phys. A 26, L473 1993. 21A. P. Polychronakos, Phys. Rev. Lett. 70, 2329 1993. 22A. Enciso, F. Finkel, A. González-López, and M. A. Rodríguez, Nucl. Phys. B 707, 553 2005. 23A. P. Polychronakos, Nucl. Phys. B 419, 553 1994. 24B. Basu-Mallick, Nucl. Phys. B 482, 713 1996. 25F. Calogero and A. M. Perelomov, Commun. Math. Phys. 59, 109 1978. 26K. K. Mon and J. B. French, Ann. Phys. 95, 90 1975. 27V. K. B. Kota, Phys. Rep. 347, 223 2001. 28M. V. Berry and M. Tabor, Proc. R. Soc. London 356, 375 1977. 29D. Poilblanc, T. Ziman, J. Bellissard, F. Mila, and J. Montambaux, Europhys. Lett. 22, 537 1993. 30 J-C. A. d’Auriac, J-M. Maillard, and C. M. Viallet, J. Phys. A 35, 4801 2002. 31F. Haake, Quantum Signatures of Chaos, 2nd ed. SpringerVerlag, Berlin, 2001. 32N. Rosenzweig and C. E. Porter, Phys. Rev. 120, 1698 1960. 33K. Kudo and T. Deguchi, J. Phys. Soc. Jpn. 74, 1992 2005. 34A. Relaño, J. Dukelsky, J. M. G. Gómez, and J. Retamosa, Phys. Rev. E 70, 026208 5 2004. 35Our computations show that the number of levels, and hence of different spacings, increases monotonically with N of a fixed parity, but decreases when N jumps from 2j to 2j+1. | |
| dspace.entity.type | Publication | |
| relation.isAuthorOfPublication | 207092a4-0443-4336-a037-15936f8acc25 | |
| relation.isAuthorOfPublication | 7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc | |
| relation.isAuthorOfPublication.latestForDiscovery | 207092a4-0443-4336-a037-15936f8acc25 |
Download
Original bundle
1 - 1 of 1
