Integrable Quantum Spin Chains and Some Problems Related to Integrable Systems

  • A. Kundu
  • B. Basumallick
Conference paper
Part of the Research Reports in Physics book series (RESREPORTS)


The correspondence between integrable systems and conformally invariant models is explored through the example of nonlinear σ-models to find some intriguing relation between integrability, boundary condition and conformal symmetry of the model. In the second part, an integrable generalisation of the XYZ model with higher spins is presented and some novel symmetry of the related R-matrix is found out leading to many anisotropic integrable models.


Integrable System Spin Chain Conformal Symmetry Baxter Equation Canonical Dimension 
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.


  1. [1]
    D. Rolfsen, Knots and Links ( Publish or Perish, Berkeley, 1976 ).MATHGoogle Scholar
  2. [2]
    A. B. Zamolodchikov, JETP Lett. 46 (1987) 160.MathSciNetADSGoogle Scholar
  3. [3]
    S. Novikov, V. Manakov, L. Pitaevskii and V. Zakharov, Theory of Solitons ( Plenum, New York, 1984 ).MATHGoogle Scholar
  4. [4]
    L. D. Faddeev, Les Houches Lectures, ed. J. Zuber and S. Stora ( North-Holland, Amsterdam, 1984 ), p. 561.Google Scholar
  5. [5]
    S. Ghosh and A. Kundu, Phys. Rev. Lett. 63 (1989) 1207.ADSCrossRefGoogle Scholar
  6. [6]
    K. Pohlmayer, Comm. Math. Phys. 46 (1976) 207.MathSciNetADSCrossRefGoogle Scholar
  7. [7]
    L. D. Faddeev, proc. 7th Int. Conf. on the Problems of QFT, Alushta (Dubna, USSR, 1984), p. 34.Google Scholar
  8. [8]
    S. Ghosh, SINP Preprint No. SINP/TNP-89-25, 1989.Google Scholar
  9. [9]
    P. Kulish, N. Reshetikhin and E. K. Sklyanin, Lett. Math. Phys. 5 (1981) 393.MathSciNetADSMATHCrossRefGoogle Scholar
  10. [10]
    A. Kirillov and N. Reshetikhin, J. Phys. A20 (1987) 1565.MathSciNetADSGoogle Scholar
  11. [11]
    E. Date, M. Jimbo, M. Miwa and M. Okado, Lett. Math. Phys. 12 (1986) 209.MathSciNetADSCrossRefGoogle Scholar
  12. [12]
    V. A. Fateev, Sov. J. Nucl. Phys. 33(5) (1981) 761.Google Scholar
  13. [13]
    B. Basumallick, A. Kundu, SINP preprint No. SINP/TNP/90-2, 1990.Google Scholar
  14. [14]
    M. Wadati, T. Deguchi and Y. Akutsu, Phys. Reports 180 (1989) 247.MathSciNetADSCrossRefGoogle Scholar
  15. [15]
    K. Sogo, M. Uchinomi, Y. Akutsu and M. Wadati, Prog. Theor. Phys. 68 (1982) 508.ADSMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • A. Kundu
    • 1
  • B. Basumallick
    • 1
  1. 1.Theoretical Nuclear Physcis DivisionSaha Institute of Nuclear PhysicsCalcuttaIndia

Personalised recommendations