Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1412.6037 · Nuclear Physics B

Zero modes method and form factors in quantum integrable models

Stanislav Zdislavovich Pakuliak, E. Ragoucy, N. A. Slavnov

Published Feb 19, 2015• 32 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1016/j.nuclphysb.2015.02.006

Related papers

GL(3) -Based Quantum Integrable Composite Models. II. Form Factors of Local Operators

Stanislav Zdislavovich Pakuliak, E. Ragoucy, Université de Savoie, France +1 more

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.

arXiv:1502.01966•Symmetry Integrability and Geometry Methods and Applications•Jul 31, 2015•41 citations

Form factors in quantum integrable models with GL(3) -invariant R-matrix

Stanislav Zdislavovich Pakuliak, E. Ragoucy, N. A. Slavnov

We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL(3)-invariant R-matrix. We obtain determinant representations for form factors of off-diagonal entries of the monodromy matrix. These representations can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

arXiv:1312.1488•Nuclear Physics B•Feb 18, 2014•53 citations

Form factors of local operators in the algebraic Bethe ansatz

Stanislav Zdislavovich Pakuliak, E. Ragoucy, N. A. Slavnov

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.

•Feb 6, 2015•5 citations

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

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

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.

•Jan 1, 2015•5 citations

Form factors in SU(3)-invariant integrable models

S. Belliard, Stanislav Zdislavovich Pakuliak, E. Ragoucy +1 more

We study SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain determinant representations for form factors of diagonal entries of the monodromy matrix. This representation can be used for the calculation of form factors and correlation functions of the XXX SU(3)-invariant Heisenberg chain.

•Aug 17, 2016•55 citations

Form factors of the monodromy matrix entries in gl(2|1) -invariant integrable models

Arthur Hutsalyuk, Andrii Nikolaevich Liashyk, Stanislav Zdislavovich Pakuliak +2 more

We study integrable models solvable by the nested algebraic Bethe ansatz and described by gl ( 2 | 1 ) or gl ( 1 | 2 ) superalgebras. We obtain explicit determinant representations for form factors of the monodromy matrix entries. We show that all form factors are related to each other at special limits of the Bethe parameters. Our results allow one to obtain determinant formulas for form factors of local operators in the supersymmetric t – J model.

arXiv:1607.04978•Nuclear Physics B•Sep 5, 2016•22 citations
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.
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 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.