Slavnov and Gaudin-Korepin Formulas for Models without $\mathrm{U}(1)$ Symmetry: the Twisted XXX Chain

Abstract

We consider the XXX spin-$\frac{1}{2}$ Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without $\mathrm{U}(1)$ symmetry characterized by an inhomogenous Baxter T-Q equation.

References in corpus (8)

• Functional relations from the Yang-Baxter algebra: Eigenvalues of the XXZ model with non-diagonal twisted and open boundary conditions
• 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
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Cited by in corpus (19)

• Modified Algebraic Bethe Ansatz: Twisted XXX Case
• Algebraic Bethe Ansatz for the XXZ Gaudin Models with Generic Boundary
• Diagonalization of the Heun-Askey-Wilson operator, Leonard pairs and the algebraic Bethe ansatz
• Scalar product of twisted XXX modified Bethe vectors
• Common framework and quadratic Bethe equations for rational Gaudin magnets in arbitrarily oriented magnetic fields
• Scalar Products in Twisted XXX Spin Chain. Determinant Representation
• Slavnov and Gaudin-Korepin formulas for models without $U(1)$ symmetry: the XXX chain on the segment
• A note on ${\mathfrak{gl}}_2$-invariant Bethe vectors
• 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
• All correlation functions of the open XXX spin 1/2 quantum chains for unparallel boundary magnetic fields with one constraint
• Modified rational six vertex model on the rectangular lattice
• Ground state solutions of inhomogeneous Bethe equations
• Overlap between usual and modified Bethe vectors
• On correlation functions for the open XXZ chain with non-longitudinal boundary fields : the case with a constraint
• Correlation functions of the XXZ spin chain with the twisted boundary condition
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint
• Modified rational six vertex model on a rectangular lattice : new formula, homogeneous and thermodynamic limits