Exchange operator formalism for N-body spin models with near-neighbours interactions
| dc.contributor.author | Enciso, Alberto | |
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.contributor.author | Rodríguez González, Miguel Ángel | |
| dc.date.accessioned | 2023-06-20T10:56:54Z | |
| dc.date.available | 2023-06-20T10:56:54Z | |
| dc.date.issued | 2007-02-23 | |
| dc.description | ©IOP Publishing Ltd. This work was partially supported by the DGI under grant no. FIS2005-00752. A.E. acknowledges the financial support of the Spanish Ministry of Education through an FPU scholarship | |
| dc.description.abstract | We present a detailed analysis of the spin models with near-neighbours interactions constructed in our previous paper (Enciso et al 2005 Phys. Lett. B 605 214) by a suitable generalization of the exchange operator formalism. We provide a complete description of a certain flag of finite-dimensional spaces of spin functions preserved by the Hamiltonian of each model. By explicitly diagonalizing the Hamiltonian in the latter spaces, we compute several infinite families of eigenfunctions of the above models in closed form in terms of generalized Laguerre and Jacobi polynomials. | |
| 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.sponsorship | Spanish Ministry of Education | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/31356 | |
| dc.identifier.doi | doi.org/10.1088/1751-8113/40/8/012 | |
| dc.identifier.issn | 1751-8113 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1088/1751-8113/40/8/012 | |
| dc.identifier.relatedurl | http://iopscience.iop.org | |
| dc.identifier.relatedurl | http://arxiv.org/pdf/nlin/0604073v2.pdf | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/51497 | |
| dc.issue.number | 8 | |
| dc.journal.title | Journal of physics A: Mathematical and theoretical | |
| dc.language.iso | eng | |
| dc.page.final | 1883 | |
| dc.page.initial | 1857 | |
| dc.publisher | IOP Publishing Ltd | |
| dc.relation.projectID | FIS2005-00752 | |
| dc.relation.projectID | FPU scholarship | |
| dc.rights.accessRights | open access | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Calogero–Sutherland models | |
| dc.subject.keyword | Exchange operators | |
| dc.subject.keyword | Quasi-exact solvability | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | Exchange operator formalism for N-body spin models with near-neighbours interactions | |
| dc.type | journal article | |
| dc.volume.number | 40 | |
| dcterms.references | [1] Enciso A, Finkel F, González-López A and Rodríguez MA 2005 Phys. Lett. B 605 214 [2] Calogero F 1971 J. Math. Phys. 12 419 [3] Sutherland B 1971 Phys. Rev. A 4 2019 [4] Sutherland B 1972 Phys. Rev. A 5 1372 [5] Fernández Núñez J, García Fuertes W and Perelomov AM 2005 J. Math. Phys. 46 103505(27) [6] Sergeev AN and Veselov AP 2004 Commun. Math. Phys. 245 249 [7] Baker TH and Forrester PJ 1997 Commun. Math. Phys. 188 175 [8] Dunkl CF 1998 Commun. Math. Phys. 197 451 [9] Takemura K 2003 Commun. Math. Phys. 235 467 [10] Takemura K 2005 Commun. Math. Phys. 258 367. [11] Polychronakos AP 1995 Phys. Rev. Lett. 74 5153 [12] Simons BD, Lee PA and Altshuler BL 1994 Phys. Rev. Lett. 72 64 [13] Stöckmann HJ 2004 J. Phys. A: Math. Gen. 37 137 [14] Taniguchi N, Shastry BS and Altshuler BL 1995 Phys. Rev. Lett. 75 3724 [15] Carey AL and Langmann E 1999 Commun. Math. Phys. 201 1 [16] D’Hoker E and Phong DH 1998 Nucl. Phys. B 513 405 [17] Sakamoto R, Shiraishi J, Arnaudon D, Frappat L and Ragoucy E 2005 Nucl. Phys. B 704 490 [18] Olshanetsky MA and Perelomov AM 1983 Phys. Rep. 94 313 [19] Gómez-Ullate D, González-López A and Rodríguez MA 2000 J. Phys. A: Math. Gen. 33 7305 [20] Gómez-Ullate D, González-López A and Rodríguez MA 2001 Phys. Lett. B 511 112 [21] Hou X and Shifman M 1999 Int. J. Mod. Phys. A 14 2993 [22] Minzoni A, Rosenbaum M and Turbiner A 1996 Mod. Phys. Lett. A 11 1977 [23] Haldane FDM 1988 Phys. Rev. Lett. 60 635 [24] Shastry BS 1988 Phys. Rev. Lett. 60 639 [25] Freedman DZ and Mende PF 1990 Nucl. Phys. B 344 317 [26] Brink L, Turbiner A and Wyllard N 1998 J. Math. Phys. 39 1285 [27] Desrosiers P, Lapointe L and Mathieu P 2001 Nucl. Phys. B 606 547 [28] Desrosiers P, Lapointe L and Mathieu P 2003 Commun. Math. Phys. 242 331 [29] Ghosh PK 2004 Nucl. Phys. B 681 359 [30] Basu-Mallick B 1996 Nucl. Phys. B 482 713 [31] Dunkl CF 1989 Trans. Am. Math. Soc. 311 167 [32] Finkel F, Gómez-Ullate D, González-López A, Rodríguez MA and Zhdanov R 2003 Commun. Math. Phys. 233 191 [33] Polychronakos AP 1992 Phys. Rev. Lett. 69 703 [34] Yamamoto T 1995 Phys. Lett. A 208 293 [35] Finkel F, Gómez-Ullate D, González-López A, Rodríguez MA and Zhdanov R 2001 Commun. Math. Phys. 221 477 [36] Finkel F, Gómez-Ullate D, González-López A, Rodríguez MA and Zhdanov R 2001 Nucl. Phys. B 613 472 [37] Polychronakos AP 1993 Phys. Rev. Lett. 70 2329 [38] Polychronakos AP 1994 Nucl. Phys. B 419 553 [39] Enciso A, Finkel F, González-López A and Rodríguez MA 2005 Nucl. Phys. B 707 553 [40] Finkel F and González-López A 2005 Phys. Rev. B 72 174411(6) [41] Jain SR and Khare A 1999 Phys. Lett. A 262 35 [42] Auberson G, Jain SR and Khare A 2001 J. Phys. A: Math. Gen. 34 695 [43] Deguchi T and Ghosh PK 2001 J. Phys. Soc. Jpn. 70 3225 [44] Ha ZNC and Haldane FDM 1992 Phys. Rev. B 46 9359 [45] Minahan JA and Polychronakos AP 1993 Phys. Lett. B 302 265 [46] Bernard D, Gaudin M, Haldane FDM and Pasquier V 1993 J. Phys. A: Math. Gen. 26 5219 [47] Gradshteyn IS and Ryzhik IM 2000 Table of Integrals, Series, and Products (San Diego: Academic Press) sixth edition [48] Ezung M, Gurappa N, Khare A and Panigrahi PK 2005 Phys. Rev. B 71 125121(8) | |
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