Why scalar products in the algebraic Bethe ansatz have determinant representation

Abstract

We show that the scalar products of on-shell and off-shell Bethe vectors in the algebra1ic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also apply our method to the XXX spin chain with broken $U(1)$ symmetry.

16 pages, no figures

References in corpus (4)

• 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
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation

Cited by in corpus (2)

• Overlap between usual and modified Bethe vectors
• Transition density matrices of Richardson-Gaudin states