The spectrum of quantum-group-invariant transfer matrices
Autor(a) principal: | |
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Data de Publicação: | 2019 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UNESP |
Texto Completo: | http://dx.doi.org/10.1016/j.nuclphysb.2018.11.017 http://hdl.handle.net/11449/188407 |
Resumo: | Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions. |
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Repositório Institucional da UNESP |
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The spectrum of quantum-group-invariant transfer matricesIntegrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Stony Brook UniversityPhysics Department University of Miami, P.O. Box 248046Instituto de Física Teórica-UNESP, Rua Dr. Bento Teobaldo Ferraz 271, Bloco IIInstituto de Física Teórica-UNESP, Rua Dr. Bento Teobaldo Ferraz 271, Bloco IIFAPESP: 2015/00025-9FAPESP: 2017/03072-3University of MiamiUniversidade Estadual Paulista (Unesp)Nepomechie, Rafael I.Retore, Ana L. [UNESP]2019-10-06T16:07:05Z2019-10-06T16:07:05Z2019-01-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article266-297http://dx.doi.org/10.1016/j.nuclphysb.2018.11.017Nuclear Physics B, v. 938, p. 266-297.0550-3213http://hdl.handle.net/11449/18840710.1016/j.nuclphysb.2018.11.0172-s2.0-85057181774Scopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNuclear Physics Binfo:eu-repo/semantics/openAccess2021-10-23T15:55:12Zoai:repositorio.unesp.br:11449/188407Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T21:02:08.438030Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
The spectrum of quantum-group-invariant transfer matrices |
title |
The spectrum of quantum-group-invariant transfer matrices |
spellingShingle |
The spectrum of quantum-group-invariant transfer matrices Nepomechie, Rafael I. |
title_short |
The spectrum of quantum-group-invariant transfer matrices |
title_full |
The spectrum of quantum-group-invariant transfer matrices |
title_fullStr |
The spectrum of quantum-group-invariant transfer matrices |
title_full_unstemmed |
The spectrum of quantum-group-invariant transfer matrices |
title_sort |
The spectrum of quantum-group-invariant transfer matrices |
author |
Nepomechie, Rafael I. |
author_facet |
Nepomechie, Rafael I. Retore, Ana L. [UNESP] |
author_role |
author |
author2 |
Retore, Ana L. [UNESP] |
author2_role |
author |
dc.contributor.none.fl_str_mv |
University of Miami Universidade Estadual Paulista (Unesp) |
dc.contributor.author.fl_str_mv |
Nepomechie, Rafael I. Retore, Ana L. [UNESP] |
description |
Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras gˆ, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown there that these transfer matrices have quantum group symmetry corresponding to removing the pth node from the gˆ Dynkin diagram. Here we determine the spectrum of these transfer matrices by using analytical Bethe ansatz, and we determine the dependence of the corresponding Bethe equations on p. We propose formulas for the Dynkin labels of the Bethe states in terms of the numbers of Bethe roots of each type. We also briefly study how duality transformations are implemented on the Bethe ansatz solutions. |
publishDate |
2019 |
dc.date.none.fl_str_mv |
2019-10-06T16:07:05Z 2019-10-06T16:07:05Z 2019-01-01 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.uri.fl_str_mv |
http://dx.doi.org/10.1016/j.nuclphysb.2018.11.017 Nuclear Physics B, v. 938, p. 266-297. 0550-3213 http://hdl.handle.net/11449/188407 10.1016/j.nuclphysb.2018.11.017 2-s2.0-85057181774 |
url |
http://dx.doi.org/10.1016/j.nuclphysb.2018.11.017 http://hdl.handle.net/11449/188407 |
identifier_str_mv |
Nuclear Physics B, v. 938, p. 266-297. 0550-3213 10.1016/j.nuclphysb.2018.11.017 2-s2.0-85057181774 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Nuclear Physics B |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
266-297 |
dc.source.none.fl_str_mv |
Scopus reponame:Repositório Institucional da UNESP instname:Universidade Estadual Paulista (UNESP) instacron:UNESP |
instname_str |
Universidade Estadual Paulista (UNESP) |
instacron_str |
UNESP |
institution |
UNESP |
reponame_str |
Repositório Institucional da UNESP |
collection |
Repositório Institucional da UNESP |
repository.name.fl_str_mv |
Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP) |
repository.mail.fl_str_mv |
|
_version_ |
1808129276569976832 |