Scalar product for the XXZ spin chain with general integrable boundaries * *Dedicated to the memory of Omar Foda.

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.