Skip to main content
SpringerLink
Log in

Non-equivalence between Heisenberg XXZ spin chain and Thirring model

  • theoretical physics
  • Published:
The European Physical Journal C - Particles and Fields Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. J. Goldstone, Nuovo Cimento 19, 154 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  2. J. Goldstone, A. Salam, S. Weinberg, Phys. Rev. 127, 965 (1962)

    MATH  ADS  MathSciNet  Google Scholar 

  3. S. Coleman, Comm. Math. Phys. 31, 259 (1973)

    MATH  ADS  MathSciNet  Google Scholar 

  4. Y. Nambu, G. Jona-Lasinio, Phys. Rev. 122, 345 (1961)

    Article  ADS  Google Scholar 

  5. M. Hiramoto, T. Fujita, No massless boson in chiral symmetry breaking in NJL and Thirring model, hep-th/0306083

  6. T. Fujita, M. Hiramoto, H. Takahashi, No Goldstone boson in NJL and Thirring model, hep-th/0306110

  7. T. Fujita, M. Hiramoto, H. Takahashi, Historic mistake in spontaneous symmetry breaking, hep-th/0410220

  8. M. Faber, A.N. Ivanov, Eur. Phys. J. C 20, 723 (2001)

    MATH  ADS  Google Scholar 

  9. A. Luther, Phys. Rev. B 14, 2153 (1976)

    ADS  Google Scholar 

  10. I. Affleck, Les Houches, Session XLIX, 1990, North-Holland

  11. H.A. Bethe, Z. Phys. 71, 205 (1931)

    MATH  ADS  Google Scholar 

  12. R. Orbach, Phys. Rev. 112, 309 (1958)

    ADS  Google Scholar 

  13. M. Hiramoto, T. Fujita, Phys. Rev. D 66, 045007 (2002)

    ADS  MathSciNet  Google Scholar 

  14. H. Bergknoff, H.B. Thacker, Phys. Rev. Lett. 42, 135 (1979)

    ADS  Google Scholar 

  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/0410221

  16. T. Tomachi, T. Fujita, Ann. Phys. 223, 197 (1993)

    ADS  MathSciNet  Google Scholar 

  17. T. Fujita, M. Hiramoto, T. Homma, New spectrum and condensate in two dimensional QCD, Prog. Theor. Phys. in press, hep-th/0306085

  18. T. Fujita, T. Kobayashi, H. Takahashi, Phys. Rev. D 68 , 068701 (2003)

    ADS  Google Scholar 

  19. T. Fujita, Y. Sekiguchi, K. Yamamoto, Ann. Phys. 255, 204 (1997)

    MATH  ADS  Google Scholar 

  20. T. Fujita, T. Kobayashi, H. Takahashi, J. Phys. A 36, 1553 (2003)

    MATH  ADS  MathSciNet  Google Scholar 

  21. W. Thirring, Ann. Phys. (N.Y) 3, 91 (1958)

    MATH  ADS  MathSciNet  Google Scholar 

  22. T. Fujita, A. Ogura, Prog. Theor. Phys. 89, 23 (1993)

    ADS  Google Scholar 

  23. K. Odaka, S. Tokitake, J. Phys. Soc. Jpn. 56, 3062 (1987)

    ADS  MathSciNet  Google Scholar 

  24. N. Andrei, J.H. Lowenstein, Phys. Rev. Lett. 43, 1698 (1979)

    ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Science and Technology, Nihon University, Tokyo, Japan

    T. Fujita, T. Kobayashi, M. Hiramoto & H. Takahashi

Authors
  1. T. Fujita
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Kobayashi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. M. Hiramoto
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. H. Takahashi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Fujita.

Additional information

Received: 28 October 2004, Published online: 21 January 2005

PACS:

10.Kk, 03.70. + k, 11.30.-j, 11.30.Rd

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fujita, T., Kobayashi, T., Hiramoto, M. et al. Non-equivalence between Heisenberg XXZ spin chain and Thirring model. Eur. Phys. J. C 39, 511–518 (2005). https://doi.org/10.1140/epjc/s2004-02093-x

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1140/epjc/s2004-02093-x

Keywords

Search

Navigation