Surveying the quantum group symmetries of integrable open spin chains
Autor(a) principal: | |
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Data de Publicação: | 2018 |
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.2018.02.023 http://hdl.handle.net/11449/175978 |
Resumo: | Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices. |
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Repositório Institucional da UNESP |
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Surveying the quantum group symmetries of integrable open spin chainsUsing anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices.Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Physics 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]2018-12-11T17:18:24Z2018-12-11T17:18:24Z2018-05-01info:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/article91-134application/pdfhttp://dx.doi.org/10.1016/j.nuclphysb.2018.02.023Nuclear Physics B, v. 930, p. 91-134.0550-3213http://hdl.handle.net/11449/17597810.1016/j.nuclphysb.2018.02.0232-s2.0-850429092142-s2.0-85042909214.pdfScopusreponame:Repositório Institucional da UNESPinstname:Universidade Estadual Paulista (UNESP)instacron:UNESPengNuclear Physics B1,744info:eu-repo/semantics/openAccess2023-11-04T06:14:23Zoai:repositorio.unesp.br:11449/175978Repositório InstitucionalPUBhttp://repositorio.unesp.br/oai/requestopendoar:29462024-08-05T16:56:01.163850Repositório Institucional da UNESP - Universidade Estadual Paulista (UNESP)false |
dc.title.none.fl_str_mv |
Surveying the quantum group symmetries of integrable open spin chains |
title |
Surveying the quantum group symmetries of integrable open spin chains |
spellingShingle |
Surveying the quantum group symmetries of integrable open spin chains Nepomechie, Rafael I. |
title_short |
Surveying the quantum group symmetries of integrable open spin chains |
title_full |
Surveying the quantum group symmetries of integrable open spin chains |
title_fullStr |
Surveying the quantum group symmetries of integrable open spin chains |
title_full_unstemmed |
Surveying the quantum group symmetries of integrable open spin chains |
title_sort |
Surveying the quantum group symmetries of integrable open spin chains |
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 |
Using anisotropic R-matrices associated with affine Lie algebras gˆ (specifically, A2n (2), A2n−1 (2), Bn (1), Cn (1), Dn (1)) and suitable corresponding K-matrices, we construct families of integrable open quantum spin chains of finite length, whose transfer matrices are invariant under the quantum group corresponding to removing one node from the Dynkin diagram of gˆ. We show that these transfer matrices also have a duality symmetry (for the cases Cn (1) and Dn (1)) and additional Z2 symmetries that map complex representations to their conjugates (for the cases A2n−1 (2), Bn (1) and Dn (1)). A key simplification is achieved by working in a certain “unitary” gauge, in which only the unbroken symmetry generators appear. The proofs of these symmetries rely on some new properties of the R-matrices. We use these symmetries to explain the degeneracies of the transfer matrices. |
publishDate |
2018 |
dc.date.none.fl_str_mv |
2018-12-11T17:18:24Z 2018-12-11T17:18:24Z 2018-05-01 |
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.2018.02.023 Nuclear Physics B, v. 930, p. 91-134. 0550-3213 http://hdl.handle.net/11449/175978 10.1016/j.nuclphysb.2018.02.023 2-s2.0-85042909214 2-s2.0-85042909214.pdf |
url |
http://dx.doi.org/10.1016/j.nuclphysb.2018.02.023 http://hdl.handle.net/11449/175978 |
identifier_str_mv |
Nuclear Physics B, v. 930, p. 91-134. 0550-3213 10.1016/j.nuclphysb.2018.02.023 2-s2.0-85042909214 2-s2.0-85042909214.pdf |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
Nuclear Physics B 1,744 |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.format.none.fl_str_mv |
91-134 application/pdf |
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_ |
1808128723253198848 |