Theoretical and Mathematical Physics

, Volume 56, Issue 2, pp 805–812 | Cite as

Excitation spectrum of the anisotropic generalization of an SU3 magnet

  • V. I. Vichirko
  • N. Yu. Reshetikhin


The method proposed for calculating the eigenvalues of the transfer matrix is based on some fundamental properties of the R matrix such as unitarity, cross symmetry, and special relations related to the structure of the degeneracy of the R matrix at certain points. One can therefore hope that it applies to a large class of models in which the complicated structure of the R matrix makes it impossible to construct n-particle eigenstates of the transfer matrix by the Bethe ansatz.

The specific example of the Izergin-Korepin model demonstrates that in the thermodynamic limit the cross symmetry and unitarity (64) and (65) are insufficient for the calculation of the eigenvalues of the transfer matrix by the “inverse transfer matrix” method. For unique determination of the positions of the singularities of the analytic continuation of Λ (λ) it is necessary to use the bootstrap relation (66). This also applies to some other models, in particular to systems with the R matrices found in [14, 15]. It has not been our intention to give a mathematically rigorous justification of the proposed method, which we defer to a separate publication.


Large Class Excitation Spectrum Analytic Continuation Transfer Matrix Special Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Literature Cited

  1. 1.
    L. A. Takhtadzhyan, and L. D. Faddeev. Usp. Mat. Nauk.34, 13 (1979).Google Scholar
  2. 2.
    P. P. Kulish and E. K. Sklyanin. Zap. Nauchn. Semin. LOMI.95, 129 (1980); P. P. Kulish and E. K. Sklyanin, Lect. Notes Phys.,151, 61 (1982).Google Scholar
  3. 3.
    E. K. Sklyanin, L. A. Takhtadzhyan, and L. D. Faddeev, Teor. Mat. Fiz.,40, 194 (1979).Google Scholar
  4. 4.
    A. G. Izergin and V. E. Korepin, Fiz. Elem. Chastits At. Yadra.13, 501 (1982).Google Scholar
  5. 5.
    P. P. Kulish and N. Yu. Reshetikhin, Zh. Eksp. Teor. Fiz.,80, 214 (1981).Google Scholar
  6. 6.
    A. G. Izergin and V. E. Korepin. “The inverse scattering method approach to the quantum Shabat-Mikhailov model,” Preprint E-3-80 [in English], Leningrad Branch, V. A. Steklov Mathematics Institute (1980); Commun. Math. Phys.,79, 303 (1981).Google Scholar
  7. 7.
    Yu. G. Stroganiv, Phys. Lett. A.,74, 116 (1979).Google Scholar
  8. 8.
    A. B. Zamolodchikov, Soviet Science Rev.,2, 1 (1980).Google Scholar
  9. 9.
    P. P. Kulish, N. Yu. Reshetikhin, and E. K. Sklyanin. Lett. Math. Phys.,5, 393 (1981).Google Scholar
  10. 10.
    B. Sutherland, Phys. Rev. B,12, 3795 (1975).Google Scholar
  11. 11.
    V. E. Korepin, Teor. Mat. Fiz.,41, 169 (1979).Google Scholar
  12. 12.
    L. D. Faddeev and L. A. Takhtadjan, Phys. Lett. A,85, 375 (1981).Google Scholar
  13. 13.
    B. McCoy and T. T. Wu, Phys. Lett. B,87, 50 (1979).Google Scholar
  14. 14.
    A. A. Belavin, Funktsional. Analiz i Ego Prilozhen.,14, 18 (1980).Google Scholar

Copyright information

© Plenum Publishing Corporation 1984

Authors and Affiliations

  • V. I. Vichirko
  • N. Yu. Reshetikhin

There are no affiliations available

Personalised recommendations