Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment

Abstract

We consider the isotropic spin$-\frac{1}{2}$ Heisenberg chain with the most general integrable boundaries. The scalar product between the on-shell Bethe vector and its off-shell dual, obtained by means of the modified algebraic Bethe ansatz, is given by a modified Slavnov formula. The corresponding Gaudin-Korepin formula, \textit{i.e.}, the square of the norm, is also obtained.

v2, published version, 13 pages

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Cited by in corpus (10)

• The open XXX spin chain in the SoV framework: scalar product of separate states
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Scalar products of Bethe vectors in the 8-vertex model
• Correlation functions by Separation of Variables: the XXX spin chain
• Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
• Scalar product for the XXZ spin chain with general integrable boundaries
• An inhomogeneous Lax representation for the Hirota equation
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• A tale of two Bethe ansätze
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint