# Scalar product for the XXZ spin chain with general integrable boundaries

Abstract : We calculate the scalar product of Bethe states of the XXZ spin-$\frac{1}{2}$ chain with general integrable boundary conditions. The off-shell equations satisfied by the transfer matrix and the off-shell Bethe vectors allow one to derive a linear system for the scalar product of off-shell and on-shell Bethe states. We show that this linear system can be solved in terms of a compact determinant formula that involves the Jacobian of the transfer matrix eigenvalue and certain q-Pochhammer polynomials of the boundary couplings.
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Preprints, Working Papers, ...
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https://hal.archives-ouvertes.fr/hal-03191129
Contributor : Inspire Hep <>
Submitted on : Tuesday, April 6, 2021 - 10:02:51 PM
Last modification on : Tuesday, April 13, 2021 - 10:01:56 PM

### Citation

Samuel Belliard, Rodrigo A. Pimenta, Nikita A. Slavnov. Scalar product for the XXZ spin chain with general integrable boundaries. 2021. ⟨hal-03191129⟩

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