Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models

Detalhes bibliográficos
Autor(a) principal: Skrypnyk, T.
Data de Publicação: 2021
Outros Autores: Manojlović, Nenad
Tipo de documento: Artigo
Idioma: eng
Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
Texto Completo: http://hdl.handle.net/10400.1/16335
Resumo: In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2) circle times gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations. (C) 2021 The Author(s). Published by Elsevier B.V.
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spelling Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson modelsYang-baxter equationTriangular boudariesIntegrabilityChainBCSIn the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2) circle times gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations. (C) 2021 The Author(s). Published by Elsevier B.V.0117U000240ElsevierSapientiaSkrypnyk, T.Manojlović, Nenad2021-06-22T08:51:49Z2021-062021-06-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/16335eng10.1016/j.nuclphysb.2021.1154241873-1562info:eu-repo/semantics/openAccessreponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãoinstacron:RCAAP2023-07-24T10:28:04Zoai:sapientia.ualg.pt:10400.1/16335Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:06:28.083124Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informaçãofalse
dc.title.none.fl_str_mv Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
title Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
spellingShingle Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
Skrypnyk, T.
Yang-baxter equation
Triangular boudaries
Integrability
Chain
BCS
title_short Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
title_full Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
title_fullStr Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
title_full_unstemmed Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
title_sort Twisted rational r-matrices and algebraic Bethe ansatz: Application to generalized Gaudin and Richardson models
author Skrypnyk, T.
author_facet Skrypnyk, T.
Manojlović, Nenad
author_role author
author2 Manojlović, Nenad
author2_role author
dc.contributor.none.fl_str_mv Sapientia
dc.contributor.author.fl_str_mv Skrypnyk, T.
Manojlović, Nenad
dc.subject.por.fl_str_mv Yang-baxter equation
Triangular boudaries
Integrability
Chain
BCS
topic Yang-baxter equation
Triangular boudaries
Integrability
Chain
BCS
description In the present paper we develop the algebraic Bethe ansatz approach to the case of non-skew-symmetric gl(2) circle times gl(2)-valued Cartan-non-invariant classical r-matrices with spectral parameters. We consider the two families of these r-matrices, namely, the two non-standard rational r-matrices twisted with the help of second order automorphisms and realize the algebraic Bethe ansatz method for them. We study physically important examples of the Gaudin-type and BCS-type systems associated with these r-matrices and obtain explicitly the Bethe vectors and the spectrum for the corresponding quantum hamiltonians in terms of solutions of Bethe equations. (C) 2021 The Author(s). Published by Elsevier B.V.
publishDate 2021
dc.date.none.fl_str_mv 2021-06-22T08:51:49Z
2021-06
2021-06-01T00:00:00Z
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://hdl.handle.net/10400.1/16335
url http://hdl.handle.net/10400.1/16335
dc.language.iso.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv 10.1016/j.nuclphysb.2021.115424
1873-1562
dc.rights.driver.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Elsevier
publisher.none.fl_str_mv Elsevier
dc.source.none.fl_str_mv reponame:Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
instname:Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron:RCAAP
instname_str Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
instacron_str RCAAP
institution RCAAP
reponame_str Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
collection Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
repository.name.fl_str_mv Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) - Agência para a Sociedade do Conhecimento (UMIC) - FCT - Sociedade da Informação
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