Physics of Particles and Nuclei Letters

, Volume 14, Issue 4, pp 624–630 | Cite as

On the structure of Bethe vectors

Physics of Solid State and Condensed Matter


The structure of Bethe vectors for generalised models associated with the rational and trigonometric R-matrix is investigated. The Bethe vectors in terms of two-component and multi-component models are described. Consequently, their structure in terms of local variables and operators is provided. This, as a consequence, proves the equivalence of coordinate and algebraic Bethe ansatzes for the Heisenberg spin chains. Hermitian conjugation of the elements of the monodromy matrix for the spin chains is studied.


quantum integrable systems Bethe ansatz spin chains 


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  1. 1.
    H. Bethe, “Zur theorie der metalle,” Zeitschr. Phys. 71, 205–226 (1931).ADSCrossRefMATHGoogle Scholar
  2. 2.
    Č. Burdík, J. Fuksa, and A. Isaev, “Bethe vectors for xxx-spin chain,” J. Phys.: Conf. Ser. 563, 012011 (2014).Google Scholar
  3. 3.
    Č. Burdík, J. Fuksa, A. P. Isaev, S. O. Krivonos, and O. Navrátil, “Remarks towards the spectrum of the Heisenberg spin chain type models,” Phys. Part. Nucl. 46, 277–309 (2015); arXiv:1412.3999v2 [math-ph].CrossRefGoogle Scholar
  4. 4.
    F. Essler, H. Frahm, F. Gohmann, A. Klumper, and V. E. Korepin, The One-Dimensional Hubbard Model (Cambridge Univ. Press, Cambridge, 2005).CrossRefMATHGoogle Scholar
  5. 5.
    L. D. Faddeev, “How algebraic Bethe Ansatz works for integrable model,” arXiv:hep-th/9605187v1.Google Scholar
  6. 6.
    L. D. Faddeev, E. K. Sklyanin, and L. A. Takhtajan, “The quantum inverse problem method. 1,” Theor. Math. Phys. 40, 688 (1980).MATHGoogle Scholar
  7. 7.
    A. Izergin and V. Korepin, “The pauli principle for one-dimensional bosons and the algebraic Bethe Ansatz,” J. Sov. Math. 34, 1933–1937 (1986).CrossRefGoogle Scholar
  8. 8.
    A. G. Izergin and V. E. Korepin, “The quantum inverse scattering method approach to correlation functions,” Comm. Math. Phys. 94, 67–92 (1984).ADSMathSciNetCrossRefMATHGoogle Scholar
  9. 9.
    A. G. Izergin, V. E. Korepin, and N. Y. Reshetikhin, “Correlation functions in a one-dimensional Bose gas,” J. Phys. A: Math. Gen. 20, 4799–4822 (1987).ADSMathSciNetCrossRefGoogle Scholar
  10. 10.
    V. E. Korepin, N. M. Bogoliubov, and A. G. Izergin, Quantum Inverse Scattering Method and Correlation Functions (Cambridge Univ. Press, Cambridge, 1993).CrossRefMATHGoogle Scholar
  11. 11.
    E. K. Sklyanin, “Method of the inverse scattering problem and the nonlinear quantum Schrödinger equation,” Sov. Phys. Dokl. 24, 107 (1979).ADSGoogle Scholar
  12. 12.
    E. K. Sklyanin and L. D. Faddeev, “Quantum mechanical approach to completely integrable field theory models,” Sov. Phys. Dokl. 23, 978 (1978).Google Scholar
  13. 13.
    N. A. Slavnov, “The algebraic Bethe Ansatz and quantum integrable systems,” Russ. Math. Surv. 62, 727 (2007).MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    L. A. Takhtajan and L. D. Faddeev, “The quantum method of the inverse problem and the Heisenberg XYZ model,” Russ. Math. Surv. 34, 11 (1979).Google Scholar

Copyright information

© Pleiades Publishing, Ltd. 2017

Authors and Affiliations

  1. 1.Bogoliubov Laboratory of Theoretical PhysicsJoint Institute for Nuclear ResearchDubnaRussia
  2. 2.Faculty of Nuclear Sciences and Physical EngineeringCzech Technical UniversityPragueCzech Republic

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