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Non-equivalence between Heisenberg XXZ spin chain and Thirring model

  • T. Fujita
  • T. Kobayashi
  • M. Hiramoto
  • H. Takahashi
theoretical physics

Abstract.

The Bethe ansatz equations for the spin 1/2 Heisenberg XXZ spin chain are numerically solved, and the energy eigenvalues are determined for the antiferromagnetic case. We examine the relation between the XXZ spin chain and the massless Thirring model, and show that the spectrum of the XXZ spin chain has a gapless excitation while the regularized Thirring model calculated with the Bogoliubov transformation method has a finite gap. This finite gap spectrum is also confirmed by the Bethe ansatz solution of the massless Thirring model.

Keywords

Field Theory Elementary Particle Quantum Field Theory Particle Acceleration Transformation Method 
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.

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References

  1. 1.
    J. Goldstone, Nuovo Cimento 19, 154 (1961)CrossRefMATHMathSciNetGoogle Scholar
  2. 2.
    J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)MATHADSMathSciNetGoogle Scholar
  3. 3.
    S. Coleman, Comm. Math. Phys. 31, 259 (1973)MATHADSMathSciNetGoogle Scholar
  4. 4.
    Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)CrossRefADSGoogle Scholar
  5. 5.
    M. Hiramoto, T. Fujita, No massless boson in chiral symmetry breaking in NJL and Thirring model, hep-th/0306083Google Scholar
  6. 6.
    T. Fujita, M. Hiramoto, H. Takahashi, No Goldstone boson in NJL and Thirring model, hep-th/0306110Google Scholar
  7. 7.
    T. Fujita, M. Hiramoto, H. Takahashi, Historic mistake in spontaneous symmetry breaking, hep-th/0410220Google Scholar
  8. 8.
    M. Faber, A.N. Ivanov, Eur. Phys. J. C 20, 723 (2001)MATHADSGoogle Scholar
  9. 9.
    A. Luther, Phys. Rev. B 14, 2153 (1976)ADSGoogle Scholar
  10. 10.
    I. Affleck, Les Houches, Session XLIX, 1990, North-HollandGoogle Scholar
  11. 11.
    H.A. Bethe, Z. Phys. 71, 205 (1931)MATHADSGoogle Scholar
  12. 12.
    R. Orbach, Phys. Rev. 112, 309 (1958)ADSGoogle Scholar
  13. 13.
    M. Hiramoto, T. Fujita, Phys. Rev. D 66, 045007 (2002)ADSMathSciNetGoogle Scholar
  14. 14.
    H. Bergknoff, H.B. Thacker, Phys. Rev. Lett. 42, 135 (1979)ADSGoogle Scholar
  15. 15.
    T. Fujita, M. Hiramoto, T. Homma, H. Takahashi New Vacuum of Bethe Ansatz Solutions in Thirring Model, J. Phys. Soc. Jpn., in press, hep-th/0410221Google Scholar
  16. 16.
    T. Tomachi, T. Fujita, Ann. Phys. 223, 197 (1993)ADSMathSciNetGoogle Scholar
  17. 17.
    T. Fujita, M. Hiramoto, T. Homma, New spectrum and condensate in two dimensional QCD, Prog. Theor. Phys. in press, hep-th/0306085Google Scholar
  18. 18.
    T. Fujita, T. Kobayashi, H. Takahashi, Phys. Rev. D 68 , 068701 (2003)ADSGoogle Scholar
  19. 19.
    T. Fujita, Y. Sekiguchi, K. Yamamoto, Ann. Phys. 255, 204 (1997)MATHADSGoogle Scholar
  20. 20.
    T. Fujita, T. Kobayashi, H. Takahashi, J. Phys. A 36, 1553 (2003)MATHADSMathSciNetGoogle Scholar
  21. 21.
    W. Thirring, Ann. Phys. (N.Y) 3, 91 (1958)MATHADSMathSciNetGoogle Scholar
  22. 22.
    T. Fujita, A. Ogura, Prog. Theor. Phys. 89, 23 (1993)ADSGoogle Scholar
  23. 23.
    K. Odaka, S. Tokitake, J. Phys. Soc. Jpn. 56, 3062 (1987)ADSMathSciNetGoogle Scholar
  24. 24.
    N. Andrei, J.H. Lowenstein, Phys. Rev. Lett. 43, 1698 (1979)ADSGoogle Scholar

Copyright information

© Springer-Verlag Berlin/Heidelberg 2005

Authors and Affiliations

  • T. Fujita
    • 1
  • T. Kobayashi
    • 1
  • M. Hiramoto
    • 1
  • H. Takahashi
    • 1
  1. 1.Department of Physics, Faculty of Science and TechnologyNihon UniversityTokyoJapan

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