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.
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.
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