Bethe vectors of GL(3)-invariant integrable models

Abstract

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. Different formulas are given for the Bethe vectors and the actions of the generators of the Yangian Y(sl(3)) on Bethe vectors are considered. These actions are relevant for the calculation of correlation functions and form factors of local operators of the underlying quantum models.

22 pages, typos corrected

References in corpus (4)

• Highest coefficient of scalar products in SU(3)-invariant integrable models
• Bethe Ansatz and Bethe Vectors Scalar Products
• A computation of an universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)
• On the universal weight function for the quantum affine algebra U_q(\hat{\mathfrak{gl}}_N)

Cited by in corpus (36)

• New Construction of Eigenstates and Separation of Variables for SU(N) Quantum Spin Chains
• Form factors in quantum integrable models with GL(3)-invariant R-matrix
• Current presentation for the double super-Yangian $DY(\mathfrak{gl}(m|n))$ and Bethe vectors
• 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
• GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Why scalar products in the algebraic Bethe ansatz have determinant representation
• Zero modes method and form factors in quantum integrable models
• Form factors of local operators in a one-dimensional two-component Bose gas
• On Bethe vectors in ${\mathfrak{gl}}_3$-invariant integrable models
• Bethe Vectors of Quantum Integrable Models with GL(3) Trigonometric $R$-Matrix
• Multiple Actions of the Monodromy Matrix in $\mathfrak{gl}(2|1)$-Invariant Integrable Models
• Multiple integral formulae for the scalar product of on-shell and off-shell Bethe vectors in SU(3)-invariant models
• Bethe vectors of quantum integrable models based on Uq(gl(N))
• New Compact Construction of Eigenstates for Supersymmetric Spin Chains
• Modified Algebraic Bethe Ansatz: Twisted XXX Case
• Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• On Scalar Products in Higher Rank Quantum Separation of Variables
• Reflection algebra and functional equations
• Colour-independent partition functions in coloured vertex models
• Determinant representations for form factors in quantum integrable models with GL(3)-invariant R-matrix
• Multiple commutation relations in the models with gl(2|1) symmetry
• Separation of variables bases for integrable $g{l}_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Introduction to the nested algebraic Bethe ansatz
• Scalar products and norm of Bethe vectors for integrable models based on $U_q({\widehat{\mathfrak{gl}}}_n)$
• A note on ${\mathfrak{gl}}_2$-invariant Bethe vectors
• 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
• Modified rational six vertex model on the rectangular lattice
• Scalar product of Bethe vectors from functional equations
• One-dimensional two-component Bose gas and the algebraic Bethe ansatz
• New approach to scalar products of Bethe vectors
• Master equation for correlation functions in algebra symmetry $\mathfrak{gl}(2|1)$ related models
• Bethe vectors and form factors for two-component Bose gas