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Scalar product for the XXZ spin chain with general integrable boundaries

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arxiv 2103.12501 v1 pith:GUN4CI7B submitted 2021-03-23 math-ph cond-mat.stat-mechhep-thmath.MP

Samuel Belliard , Rodrigo A. Pimenta , Nikita A. Slavnov This is my paper · ORCID
classification math-phcond-mat.stat-mechhep-thmath.MP
keywords betheoff-shellproductscalarboundarychaingeneralintegrable
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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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  1. The $q$-Racah polynomials from scalar products of Bethe states II

    math-ph 2025-01 conditional novelty 6.0 of 10

    The paper derives normalized scalar products of on-shell and off-shell Bethe states using Leonard triples, obtains explicit solutions of Belliard-Slavnov systems, and gives a determinant formula for q-Racah polynomials.

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