Scalar product for the XXZ spin chain with general integrable boundaries

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.

10 pages

References in corpus (10)

• Correlation functions of the open XXZ chain I
• Modified algebraic Bethe ansatz for XXZ chain on the segment - I - triangular cases
• Modified algebraic Bethe ansatz for XXZ chain on the segment - II - general cases
• Correlation functions of the open XXZ chain II
• Bethe states of the XXZ spin-1/2 chain with arbitrary boundary fields
• Partial domain wall partition functions
• Why scalar products in the algebraic Bethe ansatz have determinant representation
• Algebraic Bethe ansatz for the XXX chain with triangular boundaries and Gaudin model
• Algebraic Bethe ansatz for the totally asymmetric simple exclusion process with boundaries
• Determinant representations of scalar products for the open XXZ chain with non-diagonal boundary terms

Cited by in corpus (4)

• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Modified rational six vertex model on the rectangular lattice
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint