Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos) |
Texto Completo: | http://hdl.handle.net/10400.1/13816 |
Resumo: | In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model. |
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Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundaryGaudin modelAlgebraic bethe ansatzNon-unitary r-matrixIn this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model.MDPISapientiaManojlovic, NenadSalom, Igor2020-04-30T10:49:22Z20202020-01-01T00:00:00Zinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10400.1/13816eng2073-899410.3390/sym12030352info: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:RCAAP2023-07-24T10:26:01Zoai:sapientia.ualg.pt:10400.1/13816Portal AgregadorONGhttps://www.rcaap.pt/oai/openaireopendoar:71602024-03-19T20:04:56.230748Repositório 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 |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
title |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
spellingShingle |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary Manojlovic, Nenad Gaudin model Algebraic bethe ansatz Non-unitary r-matrix |
title_short |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
title_full |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
title_fullStr |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
title_full_unstemmed |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
title_sort |
Algebraic bethe ansatz for the trigonometric sℓ(2) Gaudin model with triangular boundary |
author |
Manojlovic, Nenad |
author_facet |
Manojlovic, Nenad Salom, Igor |
author_role |
author |
author2 |
Salom, Igor |
author2_role |
author |
dc.contributor.none.fl_str_mv |
Sapientia |
dc.contributor.author.fl_str_mv |
Manojlovic, Nenad Salom, Igor |
dc.subject.por.fl_str_mv |
Gaudin model Algebraic bethe ansatz Non-unitary r-matrix |
topic |
Gaudin model Algebraic bethe ansatz Non-unitary r-matrix |
description |
In this paper we deal with the trigonometric Gaudin model, generalized using a nontrivial triangular reflection matrix (corresponding to non-periodic boundary conditions in the case of anisotropic XXZ Heisenberg spin-chain). In order to obtain the generating function of the Gaudin Hamiltonians with boundary terms we follow an approach based on Sklyanin’s derivation in the periodic case. Once we have the generating function, we obtain the corresponding Gaudin Hamiltonians with boundary terms by taking its residues at the poles. As the main result, we find the generic form of the Bethe vectors such that the off-shell action of the generating function becomes exceedingly compact and simple. In this way—by obtaining Bethe equations and the spectrum of the generating function—we fully implement the algebraic Bethe ansatz for the generalized trigonometric Gaudin model. |
publishDate |
2020 |
dc.date.none.fl_str_mv |
2020-04-30T10:49:22Z 2020 2020-01-01T00:00:00Z |
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/10400.1/13816 |
url |
http://hdl.handle.net/10400.1/13816 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
2073-8994 10.3390/sym12030352 |
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 |
MDPI |
publisher.none.fl_str_mv |
MDPI |
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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1799133287806926848 |