Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz
We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particula...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2013 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2013
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/149364 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz / S. Belliard, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862667415296409600 |
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| author | Belliard, S. Crampé, N. |
| author_facet | Belliard, S. Crampé, N. |
| citation_txt | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz / S. Belliard, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries.
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| first_indexed | 2025-12-07T15:22:52Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-149364 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T15:22:52Z |
| publishDate | 2013 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Belliard, S. Crampé, N. 2019-02-21T07:21:35Z 2019-02-21T07:21:35Z 2013 Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz / S. Belliard, N. Crampé // Symmetry, Integrability and Geometry: Methods and Applications. — 2013. — Т. 9. — Бібліогр.: 39 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B23; 81R12 DOI: http://dx.doi.org/10.3842/SIGMA.2013.072 https://nasplib.isofts.kiev.ua/handle/123456789/149364 We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes the usual form of a product of operators acting on a particular vector except that the number of operators is equal to the length of the chain. We prove this result for the chains with small length. We obtain also an off-shell equation (i.e. satisfied without the Bethe equations) formally similar to the ones obtained in the periodic case or with diagonal boundaries. We would like to thank P. Baseilhac, V. Caudrelier, R.A. Pimenta and E. Ragoucy for discussions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz Article published earlier |
| spellingShingle | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz Belliard, S. Crampé, N. |
| title | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz |
| title_full | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz |
| title_fullStr | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz |
| title_full_unstemmed | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz |
| title_short | Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz |
| title_sort | heisenberg xxx model with general boundaries: eigenvectors from algebraic bethe ansatz |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/149364 |
| work_keys_str_mv | AT belliards heisenbergxxxmodelwithgeneralboundarieseigenvectorsfromalgebraicbetheansatz AT crampen heisenbergxxxmodelwithgeneralboundarieseigenvectorsfromalgebraicbetheansatz |