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Inozemtsev's hyperbolic spin model and its related spin chain

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dc.contributor.authorBarba, J. C:
dc.contributor.authorFinkel Morgenstern, Federico
dc.contributor.authorGonzález López, Artemio
dc.contributor.authorRodríguez González, Miguel Ángel
dc.date.accessioned2023-06-20T03:55:24Z
dc.date.available2023-06-20T03:55:24Z
dc.date.issued2010-11-11
dc.description©2010 Elsevier B.V. All rights reserved. This work was partially supported by the Spanish Ministry of Science and Innovation under grant No. FIS2008-00209, and by the Universidad Complutense and Banco Santander under grant No. GR58/08-910556. J.C.B. acknowledges the financial support of the Spanish Ministry of Science and Innovation through an FPU scholarship. The authors would like to thank B. BasuMallick for useful discussions on A_(N−1)-type motifs.
dc.description.abstractIn this paper we study Inozemtsev's su(m) quantum spin model with hyperbolic interactions and the associated spin chain of Haldane-Shastry type introduced by Frahm and Inozemtsev. We compute the spectrum of Inozemtsev's model, and use this result and the freezing trick to derive a simple analytic expression for the partition function of the Frahm-Inozemtsev chain. We show that the energy levels of the latter chain can be written in terms of the usual motifs for the Haldane-Shastry chain, although with a different dispersion relation. The formula for the partition function is used to analyze the behavior of the level density and the distribution of spacings between consecutive unfolded levels. We discuss the relevance of our results in connection with two well-known conjectures in quantum chaos.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipMinistry of Science and Innovation, Spain
dc.description.sponsorshipUCM-Banco Santander
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/31286
dc.identifier.doi10.1016/j.nuclphysb.2010.06.008
dc.identifier.issn0550-3213
dc.identifier.officialurlhttp://dx.doi.org/10.1016/j.nuclphysb.2010.06.008
dc.identifier.relatedurlhttp://www.sciencedirect.com
dc.identifier.relatedurlhttp://arxiv.org/pdf/1005.0487v1.pdf
dc.identifier.urihttps://hdl.handle.net/20.500.14352/44674
dc.issue.number3
dc.journal.titleNuclear physics B
dc.language.isoeng
dc.page.final525
dc.page.initial499
dc.publisherElsevier
dc.relation.projectIDFIS2008-00209
dc.relation.projectIDGR58/08-910556
dc.rightsAtribución 3.0 España
dc.rights.accessRightsopen access
dc.rights.urihttps://creativecommons.org/licenses/by/3.0/es/
dc.subject.cdu51-73
dc.subject.keywordExactly solvable spin models
dc.subject.keywordSpin chains
dc.subject.keywordQuantum chaos
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleInozemtsev's hyperbolic spin model and its related spin chain
dc.typejournal article
dc.volume.number839
dcterms.references[1] F. Calogero, J. Math. Phys. 12 (1971) 419. [2] B. Sutherland, Phys. Rev. A 4 (1971) 2019. [3] B. Sutherland, Phys. Rev. A 5 (1972) 1372. [4] F.D.M. Haldane, Phys. Rev. Lett. 60 (1988) 635. [5] B.S. Shastry, Phys. Rev. Lett. 60 (1988) 639. [6] J. Hubbard, Proc. R. Soc. London Ser. A 276 (1963) 238. [7] M.C. Gutzwiller, Phys. Rev. Lett. 10 (1963) 159. [8] F. Gebhard, D. Vollhardt, Phys. Rev. Lett. 59 (1987) 1472. [9] F. Gebhard, A.E. Ruckenstein, Phys. Rev. Lett. 68 (1992) 244. [10] F.D.M. Haldane, Z.N.C. Ha, J.C. Talstra, D. Bernard, V. Pasquier, Phys. Rev. Lett. 69 (1992) 2021. [11] M. Fowler, J.A. Minahan, Phys. Rev. Lett. 70 (1993) 2325. [12] A.P. Polychronakos, Phys. Rev. Lett. 69 (1992) 703. [13] D. Bernard, M. Gaudin, F.D.M. Haldane, V. Pasquier, J. Phys. A: Math. Gen. 26 (1993) 5219. [14] Z.N.C. Ha, F.D.M. Haldane, Phys. Rev. B 46 (1992) 9359. [15] A.P. Polychronakos, Phys. Rev. Lett. 70 (1993) 2329. [16] J.A. Minahan, A.P. Polychronakos, Phys. Lett. B 302 (1993) 265. [17] H. Frahm, J. Phys. A: Math. Gen. 26 (1993) L473. [18] M.A. Olshanetsky, A.M. Perelomov, Phys. Rep. 94 (1983) 313. [19] T. Yamamoto, Phys. Lett. A 208 (1995) 293. [20] F. Finkel, D. Gómez-Ullate, A. González-López, M.A. Rodríguez, R. Zhdanov, Commun. Math. Phys. 221 (2001) 477. [21] F. Finkel, D. Gómez-Ullate, A. González-López, M.A. Rodríguez, R. Zhdanov, Commun. Math. Phys. 233 (2003) 191. [22] A. Enciso, F. Finkel, A. González-López, M.A. Rodríguez, Nucl. Phys. B 707 (2005) 553. [23] B. Basu-Mallick, F. Finkel, A. González-López, Nucl. Phys. B 812 (2009) 402. [24] B. Basu-Mallick, F. Finkel, A. González-López, New exactly solvable quantum spin models of DN type, arXiv:0909.2968v2 [math-ph]. [25] V.I. Inozemtsev, D.V. Meshcheryakov, Phys. Scr. 33 (1986) 99. [26] V.I. Inozemtsev, Phys. Scr. 53 (1996) 516. [27] H. Frahm, V.I. Inozemtsev, J. Phys. A: Math. Gen. 27 (1994) L801. [28] T. Yamamoto, O. Tsuchiya, J. Phys. A: Math. Gen. 29 (1996) 3977. [29] A.P. Polychronakos, Nucl. Phys. B 419 (1994) 553. [30] F. Finkel, A. González-López, Phys. Rev. B 72 (2005) 174411. [31] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Phys. Rev. B 77 (2008) 214422. [32] A. Enciso, F. Finkel, A. González-López, Phys. Rev. E 79 (2009) 060105. [33] T. Guhr, A. Müller-Groeling, H.A. Weidenmüller, Phys. Rep. 299 (1998) 189. [34] M.V. Berry, M. Tabor, Proc. R. Soc. London Ser. A 356 (1977) 375. [35] O. Bohigas, M.J. Giannoni, C. Schmit, Phys. Rev. Lett. 52 (1984) 1. [36] D. Poilblanc, T. Ziman, J. Bellissard, F. Mila, J. Montambaux, Europhys. Lett. 22 (1993) 537. [37] J.-Ch. Anglès d’Auriac, J.-M. Maillard, C.M. Viallet, J. Phys. A: Math. Gen. 35 (2002) 4801. [38] B. Basu-Mallick, N. Bondyopadhaya, Nucl. Phys. B 757 (2006) 280. [39] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Europhys. Lett. 83 (2008) 27005. [40] J.C. Barba, F. Finkel, A. González-López, M.A. Rodríguez, Nucl. Phys. B 806 (2009) 684. [41] C.F. Dunkl, Trans. Am. Math. Soc. 311 (1989) 167. [42] I. Cherednik, Adv. Math. 106 (1994) 65. [43] B. Basu-Mallick, N. Bondyopadhaya, K. Hikami, D. Sen, Nucl. Phys. B 782 (2007) 276. [44] B. Basu-Mallick, N. Bondyopadhaya, D. Sen, Nucl. Phys. B 795 (2008) 596. [45] G. Szegö, Orthogonal Polynomials, 4th edition, Amer. Math. Soc., Providence, RI, 1975. [46] F.D.M. Haldane, in: A. Okiji, N. Kawakami (Eds.), Correlation Effects in Low-dimensional Electron Systems, in: Springer Series in Solid-state Sciences, vol. 118, 1994, pp. 3–20. [47] B. Basu-Mallick, N. Bondyopadhaya, Phys. Lett. A 373 (2009) 2831. [48] E. Corrigan, R. Sasaki, J. Phys. A: Math. Gen. 35 (2002) 7017. [49] S. Ahmed, Lett. Nuovo Cimento 22 (1978) 371. [50] S. Ahmed, M.E. Muldoon, SIAM J. Math. Anal. 14 (1983) 372.
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