Aviso: para depositar documentos, por favor, inicia sesión e identifícate con tu cuenta de correo institucional de la UCM con el botón MI CUENTA UCM. No emplees la opción AUTENTICACIÓN CON CONTRASEÑA
 

Quasi-exactly solvable n-body spin hamiltonians with short-ange interaction potentials

dc.contributor.authorEnciso, Alberto
dc.contributor.authorFinkel Morgenstern, Federico
dc.contributor.authorGonzález López, Artemio
dc.contributor.authorRodríguez González, Miguel Ángel
dc.date.accessioned2023-06-20T10:57:53Z
dc.date.available2023-06-20T10:57:53Z
dc.date.issued2006-11-03
dc.description©Institute of Mathematics of National Academy of Science of Ukraine. 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.abstractWe review some recent results on quasi-exactly solvable spin models presenting near-neighbors interactions. These systems can be understood as cyclic generalizations of the usual Calogero-Sutherland models. A nontrivial modification of the exchange operator formalism is used to obtain several infinite families of eigenfunctions of these models in closed form.
dc.description.departmentDepto. de Física Teórica
dc.description.facultyFac. de Ciencias Físicas
dc.description.refereedTRUE
dc.description.sponsorshipDGI
dc.description.sponsorshipSpanish Ministry of Education
dc.description.statuspub
dc.eprint.idhttps://eprints.ucm.es/id/eprint/31442
dc.identifier.issn1815-0659
dc.identifier.officialurlhttp://www.emis.ams.org/journals/SIGMA/2006/Paper073/sigma06-073.pdf
dc.identifier.relatedurlhttp://www.emis.ams.org
dc.identifier.urihttps://hdl.handle.net/20.500.14352/51523
dc.journal.titleSIGMA. Symmetry, integrability and geometry: methods and applications
dc.language.isoeng
dc.publisherInstitute of Mathematics of National Academy of Science of Ukraine
dc.relation.projectIDFIS2005-00752
dc.relation.projectIDFPU scholarship
dc.rights.accessRightsopen access
dc.subject.cdu51-73
dc.subject.keywordCalogero–Sutherland models
dc.subject.keywordExchange operators
dc.subject.keywordQuasi-exact solvability
dc.subject.ucmFísica-Modelos matemáticos
dc.subject.ucmFísica matemática
dc.titleQuasi-exactly solvable n-body spin hamiltonians with short-ange interaction potentials
dc.typejournal article
dc.volume.number2
dcterms.references[1] Auberson G., Jain S.R., Khare A., A class of N-body problems with nearest- and next-to- nearest-neighbour interactions, J. Phys. A: Math. Gen., 2001, V.34, 695–724, cond- mat/0004012. [2] Azuma H., Iso S., Explicit relation of the quantum Hall effect and the Calogero–Sutherlan model, Phys. Lett. B, 1994, V.331, 107–113, hep-th/9312001. [3] Baker T.H., Forrester P.J., The Calogero–Sutherland model and generalized classical polynomials, Comm. Math. Phys., 1997, V.188, 175–216, solv-int/9608004. [4] Bogomolny E.B., Gerland U., Schmit C., Models of intermediate statistics, Phys. Rev. E, 1999, V.59, R1315– R1318. [5] Brink L., Turbiner A., Wyllard N., Hidden algebras of the (super) Calogero and Sutherland models, J. Math. Phys., 1998, V.39 1285–1315, hep-th/9705219. [6] Calogero F., Solution of the one-dimensional N-body problem with quadratic and/or inversely quadratic pair potentials, J. Math. Phys., 1971, V.12, 419–436. [7] Deguchi T., Ghosh P.K., Spin chains from super-models, J. Phys. Soc. Japan, 2001, V.70, 3225–3237, hep-th/0012058. [8] Desrosiers P., Lapointe L., Mathieu P., Supersymmetric Calogero–Moser–Sutherland models and Jack superpolynomials, Nucl. Phys. B, 2001, V.606, 547–582, hep-th/0103178. [9] D’Hoker E., Phong D.H., Calogero–Moser systems in SU(N) Seiberg–Witten theory, Nucl. Phys. B, 1998, V.513, 405–444, hep-th/9709053. [10] Dunkl C.F., Dif ferential-dif ference operators associated to reflection groups, Trans. Amer. Math. Soc., 1989, V.311, 167–183. [11] Dunkl C.F., Orthogonal polynomials of types A and B and related Calogero models, Comm. Math. Phys., 1998, V.197, 451–487, q-alg/9710015. [12] Enciso A., Finkel F., González-López A., Rodríguez M.A., Haldane–Shastry spin chains of BCN type, Nucl. Phys. B, 2005, V.707, 553–576, hep-th/0406054. [13] Enciso A., Finkel F., González-López A., Rodríguez M.A., Solvable scalar and spin models with nearneighbors interactions. Phys. Lett. B, 2005, V.605, 214–222, hep-th/0407274. [14] Enciso A., Finkel F., González-López A., Rodríguez M.A., Exchange operator formalism for N-body spin models with near-neighbors interactions, nlin.SI/0604073. [15] Ezung M., Gurappa N., Khare A., Panigrahi P.K., Quantum many-body systems with nearest and next-tonearest neighbor long-range interactions, Phys. Rev. B, 2005, V.71, 125121(8), cond-mat/0007005. [16] Finkel F., Gómez-Ullate D., González-López A., Rodríguez M.A., Zhdanov R., AN -type Dunkl operators and new spin Calogero–Sutherland models, Comm. Math. Phys., 2001, V.221, 477– 497, hep-th/0102039. [17] Finkel F., Gómez-Ullate D., González-López A., Rodríguez M.A., Zhdanov R., New spin Calogero–Sutherland models related to BN -type Dunkl operators, Nucl. Phys. B, 2001, V.613, 472–496, hep-th/0103190. [18] Gorsky A., Nekrasov N., Hamiltonian systems of Calogero type, and two dimensional Yang–Mills theory, Nucl. Phys. B, 1994, V.414, 213–238, hep-th/9304047. [19] Haldane F.D.M., O(3) nonlinear σ model and the topological distinction between integer- and half-integerspin antiferromagnets in two dimensions, Phys. Rev. Lett., 1988, V.60, 635– 638. [20] Heckman G.J., Dunkl operators, Astérisque, 1997, V.245, 223–246. [21] Hitchin N., Stable bundles and integrable systems, Duke Math. J., 1987, V.54, 91–114. [22] Jain S.R., Khare A., An exactly solvable many-body problem in one dimension and the short-range Dyson model, Phys. Lett. A, 1999, V.262, 35–39, cond-mat/9904121. [23] Kasman, A., Bispectral KP solutions and linearization of Calogero–Moser particle systems, Comm. Math. Phys., 1995, V.172, 427–448, hep-th/9412124. [24] Kirillov A.A., Jr., Lectures on affine Hecke algebras and Macdonald’s conjectures, Bull. Amer. Math. Soc. (N.S.), 1997, V.34, 251–292, math.QA/9501219. [25] Moser J., Three integrable Hamiltonian systems connected to isospectral deformations, Adv. Math., 1975, V.16, 197–220. [26] Olshanetsky M.A., Perelomov A.M., Quantum integrable systems related to Lie algebras, Phys. Rep., 1983, V.94, 313–403. [27] Perelomov A.M., Remark on the completeness of the coherent state system, Theor. Math. Phys., 1971, V.6, 213–224. [28] Polychronakos A.P., Nonrelativistic bosonization and fractional statistics, Nucl. Phys. B, 1989, V.324, 597– 622. [29] Polychronakos A.P., Exchange operator formalism for integrable systems of particles, Phys. Rev. Lett., 1992, V.69, 703–706, hep-th/9202057. [30] Polychronakos A.P., Lattice integrable systems of Haldane–Shastry type, Phys. Rev. Lett., 1993, V.70, 2329–2332, hep-th/9210109. [31] Polychronakos A.P., Exact spectrum of an SU(N) spin chain with inverse-square exchange, Nucl. Phys. B, 1994, V.419, 553–566. [32] Polychronakos A.P., Waves and solitons in the continuum limit of the Calogero–Sutherland model, 1995, Phys. Rev. Lett., 1995, V.74, 5153–5156, hep-th/9411054. [33] Rühl W., Turbiner A.V., Exact solvability of the Calogero and Sutherland models, Mod. Phys. Lett. A, 1995, V.10, 2213–2221, hep-th/9506105. [34] Shastry B.S., Exact solution of an S = 1/2 Heisemberg antiferromagnetic chain with long- ranged interactions, Phys. Rev. Lett., 1988, V.60, 639–642. [35] Shifman M.A., Turbiner A.V., Quantal problems with partial algebraization of the spectrum, Comm. Math. Phys., 1989, V.126, 347–365. [36] Shukla P., Non-hermitian random matrices and the Calogero–Sutherland model, Phys. Rev. Lett., 2001, V.87, 194102(5). [37] Sutherland B., Exact results for a quantum many-body problem in one dimension, I, II, Phys. Rev. A, 1971, V.4, 2019–2021, 1972, V.5, 1372–1376. [38] Turbiner A.V., Quasi-exactly solvable problems and sl(2) algebra, Comm. Math. Phys., 1988, V.118, 467– 474. [39] Turbiner A.V., Lie algebras and polynomials in one variable, J. Phys. A: Math. Gen., 1992, V.25, L1087– L1093. [40] Turbiner A.V., Lie algebras and linear operators with invariant subspaces, in Lie Algebras, Cohomologies and New Findings in Quantum Mechanics, Editors N. Kamran and P.J. Olver, Contemporary Mathematics, Vol. 160, Providence, AMS, 1994, 263–310, funct-an/9301001. [41] Weyl H., The classical groups, Princeton, Princeton University Press, 1997. [42] Yamamoto T., Multicomponent Calogero model of BN -type confined in a harmonic potential, Phys. Lett. A, 1995, V.208, 293–302, cond-mat/9508012.
dspace.entity.typePublication
relation.isAuthorOfPublication207092a4-0443-4336-a037-15936f8acc25
relation.isAuthorOfPublication7f260dbe-eebb-4d43-8ba9-d8fbbd5b32fc
relation.isAuthorOfPublicationd781a665-7ef6-44e0-a0da-81f722f1b8ad
relation.isAuthorOfPublication.latestForDiscovery207092a4-0443-4336-a037-15936f8acc25

Download

Original bundle

Now showing 1 - 1 of 1
Loading...
Thumbnail Image
Name:
Finkel15.pdf
Size:
256.53 KB
Format:
Adobe Portable Document Format

Collections