Scalar Products in Twisted XXX Spin Chain. Determinant Representation
We consider the XXX spin-1/2 Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors are on shell, we obtain a determinant representation for...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2019 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2019
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/210229 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Scalar Products in Twisted XXX Spin Chain. Determinant Representation / S. Belliard, N.A. Slavnov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 33 назв. — англ. |
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Belliard, S. Slavnov, N.A. 2025-12-04T13:03:39Z 2019 Scalar Products in Twisted XXX Spin Chain. Determinant Representation / S. Belliard, N.A. Slavnov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 33 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 82B23; 81R50 arXiv: 1906.06897 https://nasplib.isofts.kiev.ua/handle/123456789/210229 https://doi.org/10.3842/SIGMA.2019.066 We consider the XXX spin-1/2 Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors are on shell, we obtain a determinant representation for the norm of the on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix. The work was performed at the Steklov Mathematical Institute of the Russian Academy of Sciences, Moscow. This work is supported by the Russian Science Foundation under grant 19-11-00062. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Scalar Products in Twisted XXX Spin Chain. Determinant Representation Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation |
| spellingShingle |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation Belliard, S. Slavnov, N.A. |
| title_short |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation |
| title_full |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation |
| title_fullStr |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation |
| title_full_unstemmed |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation |
| title_sort |
scalar products in twisted xxx spin chain. determinant representation |
| author |
Belliard, S. Slavnov, N.A. |
| author_facet |
Belliard, S. Slavnov, N.A. |
| publishDate |
2019 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
We consider the XXX spin-1/2 Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors are on shell, we obtain a determinant representation for the norm of the on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/210229 |
| citation_txt |
Scalar Products in Twisted XXX Spin Chain. Determinant Representation / S. Belliard, N.A. Slavnov // Symmetry, Integrability and Geometry: Methods and Applications. — 2019. — Т. 15. — Бібліогр.: 33 назв. — англ. |
| work_keys_str_mv |
AT belliards scalarproductsintwistedxxxspinchaindeterminantrepresentation AT slavnovna scalarproductsintwistedxxxspinchaindeterminantrepresentation |
| first_indexed |
2025-12-07T21:24:50Z |
| last_indexed |
2025-12-07T21:24:50Z |
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1850886261360820224 |