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Scalar product for the XXZ spin chain with general integrable boundaries

Samuel Belliard 1 Rodrigo A. Pimenta Nikita A. Slavnov
1 IDP - Institut Denis Poisson
Abstract : We calculate the scalar product of Bethe states of the XXZ spin- 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.
Keywords : determinant integrability boundary condition off-shell transfer matrix spin: chain
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https://hal.archives-ouvertes.fr/hal-03191129
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Submitted on : Tuesday, April 6, 2021 - 10:02:51 PM
Last modification on : Friday, April 1, 2022 - 3:57:01 AM

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Samuel Belliard, Rodrigo A. Pimenta, Nikita A. Slavnov. Scalar product for the XXZ spin chain with general integrable boundaries. J.Phys.A, 2021, 54 (34), pp.344001. ⟨10.1088/1751-8121/ac1482⟩. ⟨hal-03191129⟩

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