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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| Дата: | 2013 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2013
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/149364 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1493642019-02-22T01:23:24Z Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz Belliard, S. Crampé, N. 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. 2013 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/149364 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Belliard, S. Crampé, N. |
| spellingShingle |
Belliard, S. Crampé, N. Heisenberg XXX Model with General Boundaries: Eigenvectors from Algebraic Bethe Ansatz Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Belliard, S. Crampé, N. |
| author_sort |
Belliard, S. |
| title |
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_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_sort |
heisenberg xxx model with general boundaries: eigenvectors from algebraic bethe ansatz |
| publisher |
Інститут математики НАН України |
| publishDate |
2013 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/149364 |
| 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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:32:49Z |
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2023-05-20T17:32:49Z |
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