Recurrence relations for off-shell Bethe vectors in trigonometric integrable models

Abstract

The zero modes method is applied in order to get action of the monodromy matrix entries onto off-shell Bethe vectors in quantum integrable models associated with $U_q({\mathfrak{gl}}_N)$-invariant $R$-matrices. The action formulas allow to get recurrence relations for off-shell Bethe vectors and for highest coefficients of the Bethe vectors scalar product.

References in corpus (12)

• How Algebraic Bethe Ansatz works for integrable model
• Combinatorial Formulae for Nested Bethe Vectors
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Bethe Ansatz for the Universal Weight Function
• Bethe vectors of quantum integrable models based on Uq(gl(N))
• Introduction to the nested algebraic Bethe ansatz
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Actions of the monodromy matrix elements onto $\mathfrak{gl}(m|n)$-invariant Bethe vectors
• On the supersymmetric XXX spin chains associated to ${\mathfrak{gl}}_{1|1}$
• On the R-matrix realization of quantum loop algebras

Cited by in corpus (3)

• On exact overlaps for $\mathfrak{gl}(N)$ symmetric spin chains
• Scalar products and norm of Bethe vectors in ${\mathfrak{o}}_{2n+1}$ invariant integrable models
• Multiple commutation relations of the quantum affine algebra $U_q({\widehat{\mathfrak{gl}}}_N)$, nested Bethe vector and the Gelfand-Tsetlin basis