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.

arXiv comment16 pages, no figures

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Cited by in corpus (13)

• Density Matrices of Seniority-Zero Geminal Wavefunctions
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• Scalar products of Bethe vectors in the 8-vertex model
• Correlation functions by Separation of Variables: the XXX spin chain
• Scalar product for the XXZ spin chain with general integrable boundaries
• Thermal form-factor expansion of the dynamical two-point functions of local operators in integrable quantum chains
• Modified rational six vertex model on the rectangular lattice
• Determinant Form of Correlators in High Rank Integrable Spin Chains via Separation of Variables
• Separation of variables for higher rank integrable models: review of recent progress
• Overlap between usual and modified Bethe vectors
• Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin
• Transition density matrices of Richardson-Gaudin states
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint