The exactly solvable spin Sutherland model of B-N type and its related spin chain
| dc.contributor.author | Basu-Mallick,, B. | |
| dc.contributor.author | Finkel Morgenstern, Federico | |
| dc.contributor.author | González López, Artemio | |
| dc.date.accessioned | 2023-06-19T14:55:04Z | |
| dc.date.available | 2023-06-19T14:55:04Z | |
| dc.date.issued | 2013-01-21 | |
| dc.description | ©2012 Elsevier B.V. All rights reserved. This work was supported in part by Spain’s MEC, under grant No. FIS2011-22566. | |
| dc.description.abstract | We compute the spectrum of the su(m) spin Sutherland model of B-N type, including the exact degeneracy of all energy levels. By studying the large coupling constant limit of this model and of its scalar counterpart, we evaluate the partition function of their associated spin chain of Haldane-Shastry type in closed form. With the help of the formula for the partition function thus obtained we study the chain's spectrum, showing that it cannot be obtained as a limiting case of its BCN counterpart. The structure of the partition function also suggests that the spectrum of the Haldane-Shastry spin chain of BN type is equivalent to that of a suitable vertex model, as is the case for its A(N-1) counterpart, and that the density of its eigenvalues is normally distributed when the number of sites N tends to infinity. We analyze this last conjecture numerically using again the explicit formula for the partition function, and check its validity for several values of N and at. | |
| dc.description.department | Depto. de Física Teórica | |
| dc.description.faculty | Fac. de Ciencias Físicas | |
| dc.description.refereed | TRUE | |
| dc.description.sponsorship | MEC (Spain) | |
| dc.description.status | pub | |
| dc.eprint.id | https://eprints.ucm.es/id/eprint/31228 | |
| dc.identifier.doi | 10.1016/j.nuclphysb.2012.09.008 | |
| dc.identifier.issn | 0550-3213 | |
| dc.identifier.officialurl | http://dx.doi.org/10.1016/j.nuclphysb.2012.09.008 | |
| dc.identifier.relatedurl | http://www.sciencedirect.com | |
| dc.identifier.relatedurl | http://arxiv.org/pdf/1207.5941v1 | |
| dc.identifier.uri | https://hdl.handle.net/20.500.14352/34762 | |
| dc.issue.number | 3 | |
| dc.journal.title | Nuclear physics B | |
| dc.language.iso | eng | |
| dc.page.final | 413 | |
| dc.page.initial | 391 | |
| dc.publisher | Elsevier | |
| dc.relation.projectID | FIS2011-22566 | |
| dc.rights | Atribución 3.0 España | |
| dc.rights.accessRights | open access | |
| dc.rights.uri | https://creativecommons.org/licenses/by/3.0/es/ | |
| dc.subject.cdu | 51-73 | |
| dc.subject.keyword | Calogero–sutherland spin models | |
| dc.subject.keyword | Haldane–shastry spin chains | |
| dc.subject.keyword | Dunkl operators | |
| dc.subject.ucm | Física-Modelos matemáticos | |
| dc.subject.ucm | Física matemática | |
| dc.title | The exactly solvable spin Sutherland model of B-N type and its related spin chain | |
| dc.type | journal article | |
| dc.volume.number | 866 | |
| dcterms.references | [1] F. Calogero, J. Math. Phys. 12 (1971) 419–436. [2] B. Sutherland, Phys. Rev. A 4 (1971) 2019–2021. [3] B. Sutherland, Phys. Rev. A 5 (1972) 1372–1376. [4] M.A. Olshanetsky, A.M. Perelomov, Phys. Rep. 94 (1983) 313–404. [5] G.J. Heckman, E.M. Opdam, Compos. Math. 64 (1987) 329–352. [6] E.M. Opdam, Compos. Math. 67 (1988) 191–209. [7] L. Fehér, B.G. Pusztai, Rev. Math. Phys. 22 (2010) 699–732. [8] F.D.M. Haldane, Phys. Rev. Lett. 60 (1988) 635–638. [9] B.S. Shastry, Phys. Rev. Lett. 60 (1988) 639–642. [10] Z.N.C. Ha, F.D.M. Haldane, Phys. Rev. B 46 (1992) 9359–9368. [11] K. Hikami, M. Wadati, J. Phys. Soc. Jpn. 62 (1993) 469–472. [12] J.A. Minahan, A.P. Polychronakos, Phys. Lett. B 302 (1993) 265–270. [13] A.P. Polychronakos, Phys. Rev. Lett. 70 (1993) 2329–2331. [14] B. Sutherland, B.S. Shastry, Phys. Rev. Lett. 71 (1993) 5–8. [15] H. Frahm, J. Phys. A: Math. Gen. 26 (1993) L473–L479. [16] A.P. Polychronakos, Nucl. Phys. B 419 (1994) 553–566. [17] F. Finkel, A. González-López, Phys. Rev. B 72 (2005) 174411(6). [18] Z.N.C. Ha, Quantum Many-body Systems in One Dimension, Advances in Statistical Mechanics, vol. 12, World Scientific, Singapore, 1996. [19] M.V.N. Murthy, R. Shankar, Phys. Rev. Lett. 73 (1994) 3331–3334. [20] A.P. Polychronakos, J. Phys. A: Math. Gen. 39 (2006) 12793–12845. [21] H. Azuma, S. Iso, Phys. Lett. B 331 (1994) 107–113. [22] C.W.J. Beenakker, B. Rajaei, Phys. Rev. B 49 (1994) 7499–7510. [23] M. Caselle, Phys. Rev. Lett. 74 (1995) 2776–2779. [24] N. Beisert, C. Kristjansen, M. Staudacher, Nucl. Phys. B 664 (2003) 131–184. [25] N. Beisert, Nucl. Phys. B 682 (2004) 487–520. [26] T. Bargheer, N. Beisert, F. Loebbert, J. Phys. A: Math. Theor. 42 (2009) 285205(58). [27] A. Rej, Lett. Math. Phys. 99 (2012) 85–102. [28] N. Taniguchi, B.S. Shastry, B.L. Altshuler, Phys. Rev. Lett. 75 (1995) 3724–3727. [29] P.J. Forrester, Nucl. Phys. B 416 (1994) 377–385. [30] J.F. van Diejen, Commun. Math. Phys. 188 (1997) 467–497. [31] C.F. Dunkl, Commun. Math. Phys. 197 (1998) 451–487. [32] F. Finkel, D. Gómez-Ullate, A. González-López, M.A. Rodríguez, R. Zhdanov, Commun. Math. Phys. 221 (2001) 477–497. [33] D. Bernard, M. Gaudin, F.D.M. Haldane, V. Pasquier, J. Phys. A: Math. Gen. 26 (1993) 5219–5236. [34] K. Hikami, Nucl. Phys. B 441 (1995) 530–548. [35] B. Basu-Mallick, N. Bondyopadhaya, K. Hikami, D. Sen, Nucl. Phys. B 782 (2007) 276–295. [36] N. Beisert, D. Erkal, J. Stat. Mech. 0803 (2008) P03001. [37] D. Bernard, V. Pasquier, D. Serban, Europhys. Lett. 30 (1995) 301–306. [38] T. Yamamoto, Phys. Lett. A 208 (1995) 293–302. [39] T. Yamamoto, O. Tsuchiya, J. Phys. A: Math. Gen. 29 (1996) 3977–3984. [40] E. Corrigan, R. Sasaki, J. Phys. A: Math. Gen. 35 (2002) 7017–7061. [41] F. Finkel, D. Gómez-Ullate, A. González-López, M.A. Rodríguez, R. Zhdanov, Commun. Math. Phys. 233 (2003) 191–209. [42] A. Enciso, F. Finkel, A. González-López, M.A. Rodríguez, Nucl. Phys. B 707 (2005) 553–576. [43] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Phys. Rev. B 77 (2008) 214422(10). [44] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Nucl. Phys. B 806 (2009) 684–714. [45] S.P. Khastgir, A.J. Pocklington, R. Sasaki, J. Phys. A: Math. Gen. 33 (2000) 9033–9064. [46] I. Loris, R. Sasaki, J. Phys. A: Math. Gen. 37 (2004) 211–237. [47] B. Basu-Mallick, F. Finkel, A. González-López, Nucl. Phys. B 812 (2009) 402–423. [48] B. Basu-Mallick, F. Finkel, A. González-López, Nucl. Phys. B 843 (2011) 505–553. [49] B. Simon, Ann. Inst. H. Poincaré Sect. A (N. S.) 38 (1983) 295–308. [50] S. Ahmed, M. Bruschi, F. Calogero, M.A. Olshanetsky, A.M. Perelomov, Nuovo Cimento B 49 (1979) 173–199. [51] F.D.M. Haldane, Z.N.C. Ha, J.C. Talstra, D. Bernard, V. Pasquier, Phys. Rev. Lett. 69 (1992) 2021–2025. [52] A. Enciso, F. Finkel, A. González-López, Phys. Rev. E 82 (2010) 051117(6). [53] A. Enciso, F. Finkel, A. González-López, Thermodynamics of spin chains of Haldane–Shastry type and onedimensional vertex models, Ann. Phys. New York 327 (2012) 2627–2665, arXiv:1204.3805v1 [cond-mat.statmech]. | |
| 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
