The Luttinger sum rule in the slave-particle theories

Original Paper


The usual mean field decoupling procedure applied to the slave-particle representations of the problems with strong local interaction produces a resonant band, but violates the Luttinger sum rule for the physical single-electron propagator. The number of occupied resonant states is small and equal to the deviation from the sum rule, shedding doubt on the overall results. It is therefore argued and illustrated on the example of the Emery model for the high-T c superconductors that, through the consistent application of the mean field procedure to the Hamiltonian and the propagators, the sum rule is restored and the resonant band conserved. In addition to the resonant band, the electron spectrum contains large number of occupied states close to the bare site-energy of the site with strong repulsion. These results are also related here to the other similar decoupling problems, which also lead to the breakdown of the Luttinger sum rule.


Electron Spectrum Local Interaction Resonant State Occupied State Field Procedure 
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  1. 1.
    P.C. Pattnaik, D.M. Newns, Phys. Rev. B 41, 880 (1990), and references thereinCrossRefGoogle Scholar
  2. 2.
    C.A.R. Sa de Melo, S. Doniach, Phys. Rev. B 41, 6633 (1990)CrossRefGoogle Scholar
  3. 3.
    A. Tsuruta, A. Kobayashi, K. Deguchi, Y. Ono, T. Matsuura, Y. Kuroda, J. Phys. Soc. Jpn 68, 1067 (1999)Google Scholar
  4. 4.
    J. Kroha, P.J. Hirschfeld, K. A. Muttalib, P. W\(\ddot{\rm{o}}\)lfle, Solid State Commun. 83, 1003 (1992)CrossRefGoogle Scholar
  5. 5.
    J. Kroha, P. W\(\ddot{\rm{o}}\)lfle, Proceedings at the XXXVIII Krakow School of Theoretical Physics, June 1-10 1998, Zakopane, Poland, Inst. Phys. Jagellonian Univ., Acta Physica Polonica B 29, 3781 (1988)Google Scholar
  6. 6.
    A. Georges, G. Kotliar, W. Krauth, M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996)CrossRefMathSciNetGoogle Scholar
  7. 7.
    G. Kotliar, S.Y. Savrasov, New Theoretical Approaches to Strongly Correlated Systems, Edited by A.M. Tsvelik, (Kluwer Academic Publishers, 2001), p. 259Google Scholar
  8. 8.
    M.B. Z\(\ddot{\rm{o}}\)lfl, Th. Maier, Th. Pruschke, J. Keller, Eur. Phys. J. B 13, 47 (2000) and references thereinGoogle Scholar
  9. 9.
    F.C. Zhang, T.M. Rice, Phys. Rev. B 37, 3759 (1987)CrossRefGoogle Scholar
  10. 10.
    G. Kotliar, A.E. Ruckenstein, Phys. Rev. Lett. 57, 1362 (1986)CrossRefMathSciNetGoogle Scholar
  11. 11.
    T. Saikawa, A. Ferraz, P.E. de Britto, H. Kaga, Phys. Rev. B 56, 4464 (1997)CrossRefGoogle Scholar
  12. 12.
    E. Tutiš, Ph.D. thesis, University of Zagreb, 1994Google Scholar
  13. 13.
    H. Nikši\’ c, E. Tutiš, S. Bariši\’ c, Physica C 241, 247 (1995)CrossRefGoogle Scholar
  14. 14.
    A. Ruckenstein, C.M. Varma, Physica C 185-189, 134 (1991)Google Scholar
  15. 15.
    C. Castellani, G. Kotliar, R. Raimondi, M. Grilli, Z. Wang, M. Rozenberg, Phys. Rev. Lett. 69, 2009 (1992)CrossRefGoogle Scholar
  16. 16.
    R. Raimondi, C. Castellani, Phys. Rev. B 48, 11453 (1993)CrossRefGoogle Scholar
  17. 17.
    S. Feng, J.B. Wu, Z.B. Su, L. Yu, Phys. Rev. B 47, 15192 (1993) and references thereinCrossRefGoogle Scholar
  18. 18.
    S.E. Barnes, J. Phys. F 6, 1375 (1976)CrossRefGoogle Scholar
  19. 19.
    P. Coleman, Phys. Rev. B 29, 3035 (1984)CrossRefGoogle Scholar
  20. 20.
    N. Read, D.M. Newns, J. Phys. C 16, 3273 (1983)CrossRefGoogle Scholar
  21. 21.
    A.J. Millis, P.A. Lee, Phys. Rev. B 35, 3394 (1987)CrossRefGoogle Scholar
  22. 22.
    C.A. Balseiro, M. Avignon, A.G. Rojo, B. Alascio, Phys. Rev. Lett. 62, 2624 (1989)CrossRefGoogle Scholar
  23. 23.
    B.G. Kotliar, P.A. Lee, N. Read, Physica C 153-155, 538 (1989)Google Scholar
  24. 24.
    Ju H. Kim, K. Levin, A. Auerbach, Phys. Rev. B 39, 11633 (1989)CrossRefGoogle Scholar
  25. 25.
    P.H. Dickinson, S. Doniach, Phys. Rev. B 47, 11447 (1993)CrossRefGoogle Scholar
  26. 26.
    M. Grilli, B.G. Kotliar, A.J. Millis, Phys. Rev. B 42, 329 (1990)CrossRefGoogle Scholar
  27. 27.
    H. Kaga, T. Saikawa, A. Ferraz, P. Brito, Phys. Rev. B 50, 13942 (1994)CrossRefGoogle Scholar
  28. 28.
    E. Cappelluti, Int. Journ. Mod. Phys. B 15, 479 (2001)CrossRefGoogle Scholar
  29. 29.
    V.J. Emery, Phys. Rev. Lett. 58, 2794 (1987)CrossRefGoogle Scholar
  30. 30.
    I. Mrkonji\’ c, S. Bariši\’ c, Eur. Phys. J. B 34, 69 (2003)Google Scholar
  31. 31.
    I. Mrkonji\’ c, Ph.D. thesis, University of Zagreb, 2003Google Scholar
  32. 32.
    D.I. Golosov, A.E. Ruckenstein, M.L. Horbach, J. Phys.: Cond. Matt. 10, L229 (1998)Google Scholar
  33. 33.
    A. Ino, C. Kim, M. Nakamura, T. Yoshida, T. Mizokawa, Z.-X. Shen, A. Fujimori, T. Kakeshita, H. Eisaki, S. Uchida, Phys. Rev. B 65, 94504 (2002)CrossRefGoogle Scholar

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© Springer-Verlag Berlin/Heidelberg 2003

Authors and Affiliations

  1. 1.Department of PhysicsUniversity of ZagrebZagrebCroatia

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