The European Physical Journal B

, Volume 84, Issue 2, pp 273–281 | Cite as

Numerical calculation of the fidelity for the Kondo and the Friedel-Anderson impurities

Regular Article Mesoscopic and Nanoscale Systems

Abstract

The fidelities of the Kondo and the Friedel-Anderson (FA) impurities are calculated numerically. The ground states of both systems are calculated with the FAIR (Friedel artificially inserted resonance) theory. The ground state in the interacting systems is compared with a nullstate in which the interaction is zero. The different multi-electron states are expressed in terms of Wilson states. The use of N Wilson states simulates the use of a large effective number Neff of states. A plot of ln(F) versus N ∝ ln(Neff) reveals whether one has an Anderson orthogonality catastrophe at zero energy. The results are at first glance surprising. The ln(F) – ln(Neff) plot for the Kondo impurity diverges for large Neff. On the other hand, the corresponding plot for the symmetric FA impurity saturates for large Neff when the level spacing at the Fermi level is of the order of the singlet-triplet excitation energy. The behavior of the fidelity allows one to determine the phase shift of the electron states in this regime.

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References

  1. 1.
    P. Zanardi, N. Paunkovic, Phys. Rev. E 74, 031123 (2006)CrossRefADSMathSciNetGoogle Scholar
  2. 2.
    M. Cozzini, P. Giorda, P. Zanardi, Phys. Rev. B 75, 014439 (2007)CrossRefADSGoogle Scholar
  3. 3.
    P. Buonsante, A. Vezzani, Phys. Rev. Lett. 98, 110601 (2007)CrossRefADSGoogle Scholar
  4. 4.
    L. Campos Venuti, P. Zanardi, Phys. Rev. Lett. 99, 095701 (2007)CrossRefADSGoogle Scholar
  5. 5.
    J. Sirker, Phys. Rev. Lett. 105, 117203 (2010)CrossRefADSGoogle Scholar
  6. 6.
    P.W. Anderson, Phys. Rev. Lett. 18, 1049 (1967)CrossRefADSGoogle Scholar
  7. 7.
    K.D. Schotte, Z. Phys. 235, 155 (1970)CrossRefADSGoogle Scholar
  8. 8.
    P.W. Anderson, G. Yuval, J. Phys. C: Solid State Phys. 4, 607 (1971)CrossRefADSGoogle Scholar
  9. 9.
    K.D. Schotte, U. Schotte, Phys. Rev. B 4, 2228 (1971)CrossRefADSGoogle Scholar
  10. 10.
    D.R. Hamann, Phys. Rev. Lett. 26, 1030 (1971)CrossRefADSMathSciNetGoogle Scholar
  11. 11.
    K. Yamada, K. Yosida, Prog. Theor. Phys. 59, 1061 (1979)CrossRefADSMathSciNetGoogle Scholar
  12. 12.
    K. Yamada, K. Yosida, Prog. Theor. Phys. 62, 363 (1979)CrossRefMATHADSMathSciNetGoogle Scholar
  13. 13.
    W. Götze, P. Schlottmann, J. Low Temp. Phys. 16, 87 (1974)CrossRefADSGoogle Scholar
  14. 14.
    J. Kondo, Prog. Theor. Phys. 32, 37 (1964)CrossRefADSGoogle Scholar
  15. 15.
    J. Friedel, Adv. Phys. 3, 446 (1954)CrossRefADSGoogle Scholar
  16. 16.
    J. Friedel, Can. J. Phys. 34, 1190 (1956)CrossRefADSGoogle Scholar
  17. 17.
    J. Friedel, Nuovo Cimento Suppl. 7, 287 (1958)CrossRefGoogle Scholar
  18. 18.
    J. Friedel, J. Phys. Radium 19, 573 (1958)CrossRefGoogle Scholar
  19. 19.
    P.W. Anderson, Phys. Rev. 124, 41 (1961)CrossRefADSMathSciNetGoogle Scholar
  20. 20.
    J.R. Schrieffer, P.A. Wolff, Phys. Rev. 149, 491 (1967)CrossRefADSGoogle Scholar
  21. 21.
    G. Bergmann, Z. Phys. B 102, 381 (1997)CrossRefADSGoogle Scholar
  22. 22.
    G. Bergmann, Eur. Phys. J. B 2, 233 (1998)CrossRefADSGoogle Scholar
  23. 23.
    G. Bergmann, Phys. Rev. B 74, 144420 (2006)CrossRefADSGoogle Scholar
  24. 24.
    G. Bergmann, Phys. Rev. B 73, 092418 (2006)CrossRefADSGoogle Scholar
  25. 25.
    G. Bergmann, L. Zhang, Phys. Rev. B 76, 064401 (2007)CrossRefADSGoogle Scholar
  26. 26.
    G. Bergmann, Phys. Rev. B 77, 104401 (2008)CrossRefADSGoogle Scholar
  27. 27.
    G. Bergmann, Phys. Rev. B 78, 195124 (2008)CrossRefADSGoogle Scholar
  28. 28.
    G. Bergmann, Eur. Phys. J. B 75, 497 (2010)CrossRefADSGoogle Scholar
  29. 29.
    G. Bergmann, Y. Tao, Eur. Phys. J. B 73, 95 (2010)CrossRefADSGoogle Scholar
  30. 30.
    K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975)CrossRefADSGoogle Scholar
  31. 31.
    R. Bulla, T.A. Costi, T. Pruschke, Rev. Mod. Phys. 80, 395 (2008)CrossRefADSGoogle Scholar
  32. 32.
    A. Weichselbaum, W. Münder, J.V. Delft, Phys. Rev. B 84, 075137 (2011)CrossRefADSGoogle Scholar

Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Department of Physics & AstronomyUniversity of Southern CaliforniaLos AngelesUSA

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