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Symmetry, Integrability and Geometry: Methods and Applications, 2019, Volume 15, 066, 30 pp.
DOI: https://doi.org/10.3842/SIGMA.2019.066 (Mi sigma1502) 		 
This article is cited in 9 scientific papers (total in 9 papers)

Scalar Products in Twisted XXX Spin Chain. Determinant Representation

Samuel Belliarda, Nikita A. Slavnovb

a Institut Denis-Poisson, Université de Tours, Université d'Orléans, Parc de Grammont, 37200 Tours, France
b Steklov Mathematical Institute of Russian Academy of Sciences, 8 Gubkina Str., Moscow, 119991, Russia
Full-text PDF (521 kB) Citations (9)
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DOI: https://doi.org/10.3842/SIGMA.2019.066
Abstract: We consider 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 on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix.
Keywords: XXX chain, non-diagonal boundary conditions, scalar product, determinant.
Funding agency Grant number
Russian Science Foundation 19-11-00062
This work is supported by the Russian Science Foundation under grant 19-11-00062.
Received: June 19, 2019; in final form August 27, 2019; Published online September 3, 2019
Bibliographic databases:
Document Type: Article
MSC: 82B23, 81R50
Language: English
Citation: Samuel Belliard, Nikita A. Slavnov, “Scalar Products in Twisted XXX Spin Chain. Determinant Representation”, SIGMA, 15 (2019), 066, 30 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 9 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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