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Teoreticheskaya i Matematicheskaya Fizika, 2023, Volume 217, Number 1, Pages 179–203
DOI: https://doi.org/10.4213/tmf10572 (Mi tmf10572) 		 
Scalar products of Bethe vectors in the generalized algebraic Bethe ansatz

G. Kulkarnia, N. A. Slavnovb

a Université de Lyon, ENS de Lyon, Université Claude Bernard Lyon 1, CNRS, Laboratoire de Physique, Lyon, France
b Steklov Mathematical Institute, Russian Academy of Sciences, Moscow, Russia
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DOI: https://doi.org/10.4213/tmf10572
Abstract: We consider an $XYZ$ spin chain within the framework of the generalized algebraic Bethe ansatz. We study scalar products of the transfer matrix eigenvectors and arbitrary Bethe vectors. In the particular case of free fermions, we obtain explicit expressions for the scalar products with different number of parameters in two Bethe vectors.
Keywords: generalized algebraic Bethe ansatz, Bethe vectors, gauge transformed monodromy matrix, scalar products.
Funding agency Grant number
Ministry of Science and Higher Education of the Russian Federation
Russian Science Foundation 19-11-00062
The work of G. Kulkarni was supported by the SIMC postdoctoral grant of the Steklov Mathematical Institute. Section 4 of the paper represents the work of N. A. Slavnov. The work of N. A. Slavnov was supported by the Russian Science Foundation under grant no. 19-11-00062, https://rscf.ru/en/project/19-11-00062/, and performed at the Steklov Mathematical Institute, Russian Academy of Sciences.
Received: 21.06.2023
Revised: 21.06.2023
English version:
Theoretical and Mathematical Physics, 2023, Volume 217, Issue 1, Pages 1574–1594
DOI: https://doi.org/10.1134/S0040577923100100
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: G. Kulkarni, N. A. Slavnov, “Scalar products of Bethe vectors in the generalized algebraic Bethe ansatz”, TMF, 217:1 (2023), 179–203; Theoret. and Math. Phys., 217:1 (2023), 1574–1594
Citation in format AMSBIB
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\paper Scalar products of Bethe vectors in the~generalized algebraic
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\pages 179--203
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\jour Theoret. and Math. Phys.
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\issue 1
\pages 1574--1594
\crossref{https://doi.org/10.1134/S0040577923100100}
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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