Scalar products in models with GL(3) trigonometric R-matrix. Highest coefficient

Abstract

We study quantum integrable models with GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of the highest coefficients. We show that in the models with GL(3) trigonometric R-matrix there exist two different highest coefficients. We obtain various representations for them in terms of sums over partitions. We also prove several important properties of the highest coefficients, which are necessary for the evaluation of the scalar products.

27 pages

References in corpus (2)

• The dynamical spin structure factor for the anisotropic spin-1/2 Heisenberg chain
• Bethe Ansatz and Bethe Vectors Scalar Products

Cited by in corpus (10)

• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Three-Point Functions and su(1|1) Spin Chains
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Bethe vectors for models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$
• Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• New symmetries of $\mathfrak{gl}(N)$-invariant Bethe vectors
• Asymptotic behaviour of two-point functions in multi-species models
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Scalar products in models with $GL(3)$ trigonometric $R$-matrix. General case