The spectrum of quantum-group-invariant transfer matrices
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Elsevier
2019-01-01
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| Series: | Nuclear Physics B |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S055032131830333X |
| _version_ | 1818152420693245952 |
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| author | Rafael I. Nepomechie Ana L. Retore |
| author_facet | Rafael I. Nepomechie Ana L. Retore |
| author_sort | Rafael I. Nepomechie |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-12-11T13:54:26Z |
| format | Article |
| id | doaj.art-052a89111af54c6294045bfed733cc4b |
| institution | Directory Open Access Journal |
| issn | 0550-3213 |
| language | English |
| last_indexed | 2024-12-11T13:54:26Z |
| publishDate | 2019-01-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Nuclear Physics B |
| spelling | doaj.art-052a89111af54c6294045bfed733cc4b2022-12-22T01:04:06ZengElsevierNuclear Physics B0550-32132019-01-01938266297The spectrum of quantum-group-invariant transfer matricesRafael I. Nepomechie0Ana L. Retore1Physics Department, P.O. Box 248046, University of Miami, Coral Gables, FL 33124, USA; Corresponding author.Physics Department, P.O. Box 248046, University of Miami, Coral Gables, FL 33124, USA; Instituto de Física Teórica-UNESP, Rua Dr. Bento Teobaldo Ferraz 271, Bloco II 01140-070, São Paulo, BrazilIntegrable 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.http://www.sciencedirect.com/science/article/pii/S055032131830333X |
| spellingShingle | Rafael I. Nepomechie Ana L. Retore The spectrum of quantum-group-invariant transfer matrices Nuclear Physics B |
| title | 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_short | The spectrum of quantum-group-invariant transfer matrices |
| title_sort | spectrum of quantum group invariant transfer matrices |
| url | http://www.sciencedirect.com/science/article/pii/S055032131830333X |
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