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SIGMA, 2015, Volume 11, 063, 20 pages (Mi sigma1044)  

This article is cited in 13 scientific papers (total in 13 papers)

$GL(3)$-Based Quantum Integrable Composite Models. I. Bethe Vectors

Stanislav Pakuliakabc, Eric Ragoucyd, Nikita A. Slavnove

a Institute of Theoretical & Experimental Physics, 117259 Moscow, Russia
b Moscow Institute of Physics and Technology, 141700, Dolgoprudny, Moscow reg., Russia
c Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow reg., Russia
d Laboratoire de Physique Théorique LAPTH, CNRS and Université de Savoie, BP 110, 74941 Annecy-le-Vieux Cedex, France
e Steklov Mathematical Institute, Moscow, Russia

Abstract: We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors in the $GL(3)$-based quantum integrable models we prove a formula for the Bethe vectors of composite model. We show that this representation is a particular case of general coproduct property of the weight functions (Bethe vectors) found in the theory of the deformed Knizhnik–Zamolodchikov equation.

Keywords: Bethe ansatz; quantum affine algebras, composite models.

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-90405-ukr-a
15-31-20484-mol_a_ved
Russian Academy of Sciences - Federal Agency for Scientific Organizations
The work of S.P. was supported in part by RFBR-Ukraine grant 14-01-90405-ukr-a. N.A.S. was supported by the Program of RAS "Nonlinear Dynamics in Mathematics and Physics" and by the grant RFBR-15-31-20484-mol_a_ved.


DOI: https://doi.org/10.3842/SIGMA.2015.063

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Bibliographic databases:

ArXiv: 1501.07566
Document Type: Article
MSC: 17B37; 81R50
Received: February 18, 2015; in final form July 22, 2015; Published online July 31, 2015
Language: English

Citation: Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “$GL(3)$-Based Quantum Integrable Composite Models. I. Bethe Vectors”, SIGMA, 11 (2015), 063, 20 pp.

Citation in format AMSBIB
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\by Stanislav~Pakuliak, Eric~Ragoucy, Nikita~A.~Slavnov
\paper ${\rm GL}(3)$-Based Quantum Integrable Composite Models. I.~Bethe Vectors
\jour SIGMA
\yr 2015
\vol 11
\papernumber 063
\totalpages 20
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\crossref{https://doi.org/10.3842/SIGMA.2015.063}
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Stanislav Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “$GL(3)$-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators”, SIGMA, 11 (2015), 064, 18 pp.  mathnet  crossref  mathscinet  elib
    2. S. Pakuliak, E. Ragoucy, N. A. Slavnov, “Form factors of local operators in a one-dimensional two-component Bose gas”, J. Phys. A-Math. Theor., 48:43 (2015), 435001  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. O. I. Patu, A. Kluemper, “Thermodynamics, density profiles, and correlation functions of the inhomogeneous one-dimensional spinor Bose gas”, Phys. Rev. A, 92:4 (2015), 043631  crossref  adsnasa  isi  elib  scopus
    4. H. M. Babujian, A. Foerster, M. Karowski, “Bethe ansatz and exact form factors of the $O(N)$ Gross–Neveu model”, J. High Energy Phys., 2016, no. 2, 042  crossref  mathscinet  isi  elib  scopus
    5. K. K. Kozlowski, E. Ragoucy, “Asymptotic behaviour of two-point functions in multi-species models”, Nucl. Phys. B, 906 (2016), 241–288  crossref  mathscinet  zmath  isi  elib  scopus
    6. Jan Fuksa, “Bethe Vectors for Composite Models with $\mathfrak{gl}(2|1)$ and $\mathfrak{gl}(1|2)$ Supersymmetry”, SIGMA, 13 (2017), 015, 17 pp.  mathnet  crossref
    7. J. Fuksa, N. A. Slavnov, “Form factors of local operators in supersymmetric quantum integrable models”, J. Stat. Mech.-Theory Exp., 2017, 043106  crossref  mathscinet  isi  scopus
    8. F. Goehmann, M. Karbach, A. Kluemper, K. K. Kozlowski, J. Suzuki, “Thermal form-factor approach to dynamical correlation functions of integrable lattice models”, J. Stat. Mech.-Theory Exp., 2017, 113106  crossref  mathscinet  isi
    9. N. Gromov, F. Levkovich-Maslyuk, G. Sizov, “New construction of eigenstates and separation of variables for $\mathrm{SU}(N)$ quantum spin chains”, J. High Energy Phys., 2017, no. 9, 111  crossref  mathscinet  zmath  isi
    10. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in the models with $\mathfrak{gl}(m|n)$ symmetry”, Nucl. Phys. B, 923 (2017), 277–311  crossref  zmath  isi
    11. E. Ragoucy, “Bethe vectors and form factors for two-component Bose gas”, Phys. Part. Nuclei Lett., 14:2 (2017), 336–340  crossref  isi
    12. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_n)$”, SciPost Phys., 4:1 (2018), 006  crossref  isi
    13. N. Gromov, F. Levkovich-Maslyuk, “New compact construction of eigenstates for supersymmetric spin chains”, J. High Energy Phys., 2018, no. 9, 085  crossref  isi  scopus
  • Symmetry, Integrability and Geometry: Methods and Applications
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