Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$

Abstract

We obtain recursion formulas for the Bethe vectors of models with periodic boundary conditions solvable by the nested algebraic Bethe ansatz and based on the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_n)$. We also present a sum formula for their scalar products. This formula describes the scalar product in terms of a sum over partitions of the Bethe parameters, whose factors are characterized by two highest coefficients. We provide different recursions for these highest coefficients. In addition, we show that when the Bethe vectors are on-shell, their norm takes the form of a Gaudin determinant.

29 pages. arXiv admin note: text overlap with arXiv:1704.08173. v2: version to appear in SciPost Phys

References in corpus (8)

• Algebraic Bethe ansatz approach to the asymptotic behavior of correlation functions
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Bethe Ansatz and Bethe Vectors Scalar Products
• Norm of Bethe vectors in models with $\mathfrak{gl}(m|n)$ symmetry
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation
• Colour-independent partition functions in coloured vertex models
• Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry

Cited by in corpus (9)

• Dual Separated Variables and Scalar Products
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• Recurrence relations for off-shell Bethe vectors in trigonometric integrable models
• Cutting the cylinder into squares: The square form factor
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint