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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Published in:Symmetry, Integrability and Geometry: Methods and Applications
Date:2019
Main Authors: Belliard, S., Slavnov, N.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2019
Online Access:https://nasplib.isofts.kiev.ua/handle/123456789/210229
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Journal Title:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Cite this: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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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Belliard, S.
Slavnov, N.A.
author_facet Belliard, S.
Slavnov, N.A.
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.
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
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.
first_indexed 2025-12-07T21:24:50Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
issn 1815-0659
language English
last_indexed 2025-12-07T21:24:50Z
publishDate 2019
publisher Інститут математики НАН України
record_format dspace
spelling 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.
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Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Scalar Products in Twisted XXX Spin Chain. Determinant Representation
Article
published earlier
spellingShingle Scalar Products in Twisted XXX Spin Chain. Determinant Representation
Belliard, S.
Slavnov, N.A.
title 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_short Scalar Products in Twisted XXX Spin Chain. Determinant Representation
title_sort scalar products in twisted xxx spin chain. determinant representation
url https://nasplib.isofts.kiev.ua/handle/123456789/210229
work_keys_str_mv AT belliards scalarproductsintwistedxxxspinchaindeterminantrepresentation
AT slavnovna scalarproductsintwistedxxxspinchaindeterminantrepresentation