GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors

Abstract

We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the GL(3)-based quantum integrable models we prove a formula for the Bethe vectors of composite model. We show that this representation is a particular case of general coproduct property of the weight functions (Bethe vectors) found in the theory of the deformed Knizhnik-Zamolodchikov equation.

The title has been changed to make clearer the connexion with the preprint arXiv:1502.01966

References in corpus (2)

• Zero modes method and form factors in quantum integrable models
• A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)

Cited by in corpus (18)

• Thermal form-factor approach to dynamical correlation functions of integrable lattice models
• GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry
• Form factors of local operators in a one-dimensional two-component Bose gas
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Form factors of local operators in supersymmetric quantum integrable models
• Complete spectrum of quantum integrable lattice models associated to ${\mathcal{U}}_q(\widehat{g{l}_n})$ by separation of variables
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• Thermodynamics, density profiles and correlation functions of the inhomogeneous one-dimensional spinor Bose gas
• Bethe Ansatz and exact form factors of the O(N) Gross Neveu-model
• Correlation functions by Separation of Variables: the XXX spin chain
• Asymptotic behaviour of two-point functions in multi-species models
• Nested Algebraic Bethe Ansatz in integrable models: recent results
• Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry
• One-dimensional two-component Bose gas and the algebraic Bethe ansatz