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arXiv:1503.00546 · Journal of Physics A Mathematical and Theoretical

Form factors of local operators in a one-dimensional two-component Bose gas

Stanislav Zdislavovich Pakuliak, E. Ragoucy, N A Slavnov

Published Oct 5, 2015• 39 citations
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Abstract

We consider a one-dimensional model of a two-component Bose gas and study form factors of local operators in this model. For this aim, we use an approach based on the algebraic Bethe ansatz. We show that the form factors under consideration can be reduced to those of the monodromy matrix entries in a generalized GL (3)-invariant model. In this way we derive determinant representations for the form factors of local operators.

DOI
10.1088/1751-8113/48/43/435001

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We consider a one-dimensional model of a two-component Bose gas and study form factors of local operators in this model. For this aim, we use an approach based on the algebraic Bethe ansatz. We show that the form factors under consideration can be reduced to those of the monodromy matrix entries in a generalized GL (3)-invariant model. In this way we derive determinant representations for the form factors of local operators.
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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.
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