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arXiv · 2103.12501

Scalar product for the XXZ spin chain with general integrable boundaries

Samuel Belliard·Rodrigo A. Pimenta·Nikita A. Slavnov
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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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Samuel Belliard, Rodrigo A. Pimenta, Nikita A. Slavnov. 2021-03-23. Scalar product for the XXZ spin chain with general integrable boundaries. https://doi.org/10.1088/1751-8121%2Fac1482

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