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GL(3)-based quantum integrable composite models: 1. Bethe vectors

S. Pakuliak, E. Ragoucy, N. A. Slavnov

Published Jan 1, 2015• 5 citations
OpenAlex

Abstract

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

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We consider a composite generalized quantum integrable model solvable by thenested algebraic Bethe ansatz. Using explicit formulas of the action of themonodromy matrix elements onto Bethe vectors in the GL(3)-based quantumintegrable models we prove a formula for the Bethe vectors of composite model.We show that this representation is a particular case of general coproductproperty of the weight functions (Bethe vectors) found in the theory of thedeformed Knizhnik-Zamolodchikov equation.
We study integrable models solvable by the nested algebraic Bethe ansatz andpossessing the GL(3)-invariant R-matrix. We consider a composite model wherethe total monodromy matrix of the model is presented as a product of twopartial monodromy matrices. Assuming that the last ones can be expanded intoseries with respect to the inverse spectral parameter we calculate matrixelements of the local operators in the basis of the transfer matrixeigenstates. We obtain determinant representations for these matrix elements.Thus, we solve the inverse scattering problem in a weak sense.
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix.We consider a composite model where the total monodromy matrix of the model is presented as a product of two partial monodromy matrices.Assuming that the last ones can be expanded into series with respect to the inverse spectral parameter we calculate matrix elements of the local operators in the basis of the transfer matrix eigenstates.We obtain determinant representations for these matrix elements.Thus, we solve the inverse scattering problem in a weak sense.