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SIGMA, 2019, Volume 15, 066, 30 pages (Mi sigma1502)  

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

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.


DOI: https://doi.org/10.3842/SIGMA.2019.066

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Full text: https://www.imath.kiev.ua/~sigma/2019/066/
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Bibliographic databases:

ArXiv: 1906.06897
MSC: 82B23, 81R50
Received: June 19, 2019; in final form August 27, 2019; Published online September 3, 2019
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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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\paper Scalar Products in Twisted XXX Spin Chain. Determinant Representation
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\vol 15
\papernumber 066
\totalpages 30
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