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Scalar Products in Twisted XXX Spin Chain. Determinant Representation

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.
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https://hal.archives-ouvertes.fr/hal-02178562
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Submitted on : Wednesday, July 10, 2019 - 4:07:53 AM
Last modification on : Friday, November 25, 2022 - 4:15:26 AM

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Samuel Belliard, Nikita A. Slavnov. Scalar Products in Twisted XXX Spin Chain. Determinant Representation. SIGMA, 2019, 15, pp.066. ⟨10.3842/SIGMA.2019.066⟩. ⟨hal-02178562⟩

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