Scalar Products in Twisted XXX Spin Chain. Determinant Representation

Abstract

We consider XXX spin-$1/2$ Heisenberg chain with non-diagonal boundary conditions. We obtain a compact determinant representation for the scalar product of on-shell and off-shell Bethe vectors. In the particular case when both Bethe vectors are on shell, we obtain a determinant representation for the norm of on-shell Bethe vector and prove orthogonality of the on-shell vectors corresponding to the different eigenvalues of the transfer matrix.

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• Scalar product for the XXZ spin chain with general integrable boundaries
• Quantum-classical duality for Gaudin magnets with boundary
• Modified rational six vertex model on the rectangular lattice
• Quantum-classical correspondence for gl(1|1) supersymmetric Gaudin magnet with boundary
• Overlap between usual and modified Bethe vectors
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint