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arXiv:1701.05866 · Journal of Statistical Mechanics Theory and Experiment

Form factors of local operators in supersymmetric quantum integrable models

Jan Fuksa, N. A. Slavnov

Published Apr 1, 2017• 20 citations
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Abstract

Abstract We apply the nested algebraic Bethe ansatz to the models with g l ( 2 | 1 ) and g l ( 1 | 2 ) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the universal form factors. Our derivation is based on the use of the RTT -algebra only. It does not refer to any specific representation of this algebra. We obtain thus determinant representations for form factors of local operators in the cases where an explicit solution of the quantum inverse scattering problem is not known.

DOI
10.1088/1742-5468/aa6686

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Abstract We apply the nested algebraic Bethe ansatz to the models with g l ( 2 | 1 ) and g l ( 1 | 2 ) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the universal form factors. Our derivation is based on the use of the RTT -algebra only. It does not refer to any specific representation of this algebra. We obtain thus determinant representations for form factors of local operators in the cases where an explicit solution of the quantum inverse scattering problem is not known.
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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 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 review the recent results we have obtained in the framework of algebraic Bethe ansatz based on algebras and superalgebras of rank greater than 1 or on their quantum deformation. We present different expressions (explicit, recursive or using the current realization of the algebra) for the Bethe vectors. Then, we provide a general expression (as sum over partitions) for their scalar products. For some particular cases (in the case of gl(3) g l ( 3 ) or its quantum deformation, or of gl(2|1) g l ( 2 | 1 ) ), we provide determinant expressions for the scalar products. We also compute the form factors of the monodromy matrix entries, and give some general methods to relate them. A coproduct formula for Bethe vectors allows to get the form factors of composite models.