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SIGMA, 2015, Volume 11, 064, 18 pages (Mi sigma1045)  

This article is cited in 16 scientific papers (total in 16 papers)

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

Stanislav Pakuliakabc, Eric Ragoucyd, Nikita A. Slavnove

a Laboratory of Theoretical Physics, JINR, 141980 Dubna, Moscow reg., Russia
b Institute of Theoretical & Experimental Physics, 117259 Moscow, Russia
c Moscow Institute of Physics and Technology, 141700, Dolgoprudny, 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 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.

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

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-90405-ukr-a
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", RFBR-14-01-00860-a, RFBR-13-01-12405-ofi-m2.


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ArXiv: 1502.01966
MSC: 17B37; 81R50
Received: February 18, 2015; in final form July 22, 2015; Published online July 31, 2015

Citation: 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.

Citation in format AMSBIB
\by Stanislav~Pakuliak, Eric~Ragoucy, Nikita~A.~Slavnov
\paper ${\rm GL}(3)$-Based Quantum Integrable Composite Models. II.~Form Factors of Local Operators
\jour SIGMA
\yr 2015
\vol 11
\papernumber 064
\totalpages 18

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    1. 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
    2. N. A. Slavnov, E. Ragoucy, S. Pakuliak, “Form factors of local operators in a one-dimensional two-component Bose gas”, J. Phys. A, 48:43 (2015), 435001 , 21 pp., arXiv: 1503.00546  mathnet  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus
    3. H. M. Babujian, A. Foerster, M. Karowski, “Bethe ansatz and exact form factors of the $O(N)$ Gross–Neveu model”, Journal of High Energy Physics, 2016, no. 2, 042, 32 pp.  crossref  mathscinet  isi  scopus
    4. Arthur Hutsalyuk, Andrii Liashyk, Stanislav Z. Pakuliak, Eric Ragoucy, Nikita A. Slavnov, “Multiple actions of the monodromy matrix in $\mathfrak{gl}(2|1)$-invariant integrable models”, SIGMA, 12 (2016), 099, 22 pp.  mathnet  crossref  mathscinet  elib
    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. A. Hutsalyuk, A. Liashyk, S. Z. Pakuliak, E. Ragoucy, N. A. Slavnov, “Scalar products of Bethe vectors in models with $\mathfrak{g}\mathfrak{l}(2|1)$ symmetry 2. Determinant representation”, J. Phys. A-Math. Theor., 50:3 (2017), 034004  crossref  mathscinet  zmath  isi  elib  scopus
    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  mathscinet  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. J. A. James, R. M. Konik, Ph. Lecheminant, N. J. Robinson, A. M. Tsvelik, “Non-perturbative methodologies for low-dimensional strongly-correlated systems: from non-Abelian bosonization to truncated spectrum methods”, Rep. Prog. Phys., 81:4 (2018), 046002  crossref  mathscinet  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
    14. N. A. Slavnov, “Determinant representations for scalar products in the algebraic Bethe ansatz”, Theoret. and Math. Phys., 197:3 (2018), 1771–1778  mathnet  crossref  crossref  adsnasa  isi  elib
    15. Maillet J.M. Niccoli G., “Complete Spectrum of Quantum Integrable Lattice Models Associated to U-Q(Gl(N))Over-Bar)Over Cap> By Separation of Variables”, J. Phys. A-Math. Theor., 52:31 (2019), 315203  crossref  isi
    16. Maillet J.M. Niccoli G., “Complete Spectrum of Quantum Integrable Lattice Models Associated to Y (Gl(N)) By Separation of Variables”, SciPost Phys., 6:6 (2019), 071  crossref  isi
  • Symmetry, Integrability and Geometry: Methods and Applications
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