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Scalar product for the XXZ spin chain with general integrable boundaries

Mathematical Physics 2021-09-01 v1 Statistical Mechanics High Energy Physics - Theory math.MP

Abstract

We calculate the scalar product of Bethe states of the XXZ spin-12\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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Cite

@article{arxiv.2103.12501,
  title  = {Scalar product for the XXZ spin chain with general integrable boundaries},
  author = {Samuel Belliard and Rodrigo A. Pimenta and Nikita A. Slavnov},
  journal= {arXiv preprint arXiv:2103.12501},
  year   = {2021}
}

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10 pages