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GL(3)-based quantum integrable composite models: 2. Form factors of local operators

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

Published Jan 1, 2015• 5 citations
OpenAlex

Abstract

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.

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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.
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. Assuming that the monodromy matrix of the model can be expanded into series with respect to the inverse spectral parameter, we define zero modes of the monodromy matrix entries as the first nontrivial coefficients of this series. Using these zero modes we establish new relations between form factors of the elements of the monodromy matrix. We prove that all of them can be obtained from the form factor of a diagonal matrix element in special limits of Bethe parameters. As a result we obtain determinant representations for form factors of all the entries of the monodromy matrix.