Skip to main content
SpringerLink
Log in

Self-Consistent Conserving Theory for Quantum Impurity Systems: Renormalization Group Analysis

  • Published:
Journal of Low Temperature Physics Aims and scope Submit manuscript

Abstract

We review the diagrammatic, conserving theory for quantum impurities with strong on-site repulsion. The method is based on auxiliary particle technique, where Wick's theorem is valid, which opens up the possibility for generalizations to more complicated situations. An analysis in terms of the perturbative renormalization group (RG) shows that on the level of the Conserving T-matrix Approximation the theory correctly describes the RG flow, including the non-scaling of potential scattering terms and the correct Kondo temperature.

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. For a comprehensive overview see A. C. Hewson, The Kondo Problem to Heavy Fermions (C.U.P., Cambridge, 1993).

    Google Scholar 

  2. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989).

    Google Scholar 

  3. A. Georges, G. Kotliar, W. Krauth, and M. J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).

    Google Scholar 

  4. L. I. Glazman, and M. E. Raikh, Pis'ma Zh. Eksp. Teor. Fiz. 47, 378 (1999) [JETP Lett. 47, 452 (1988)].

    Google Scholar 

  5. T. K. Ng, and P. A. Lee, Phys. Rev. Lett. 61, 1768 (1988).

    Google Scholar 

  6. For an overview and references see, e.g., Quantum dynamics of submicron structures, H. A. Cerdeira, B. Kramer, and G. Schön, eds., NATO ASI Series E 291 (Kluwer, 1995).

  7. J. Li, W.-D. Schneider, R. Berndt, and B. Delley, Phys. Rev. Lett. 80, 2893 (1998).

    Google Scholar 

  8. V. Madhavan, W. Chen, T. Jamneala, M. F. Crommie, and N. S. Wingreen, Science 280, 567 (1998).

    Google Scholar 

  9. O. Újsǵhy, J. Kroha, L. Szunyogh, and A. Zawadowski, Phys. Rev. Lett. 85, 2557 (2000).

    Google Scholar 

  10. M. Garnier, K. Breuer, D. Purdie, M. Hengsberger, Y. Baer, and B. Delley, Phys. Rev. Lett. 78, 4127 (1997).

    Google Scholar 

  11. F. Reinert, D. Ehm, S. Schmidt, G. Nicolay, S. Hüfner, J. Kroha, O. Trovarelli, and C. Geibel, Phys. Rev. Lett. 87, 106401 (2001).

    Google Scholar 

  12. S. E. Barnes, J. Phys. F 6, 1375 (1976); 7, 2637 (1977).

    Google Scholar 

  13. D. Goldhaber-Gordon et al., Nature 391, 156 (1998).

    Google Scholar 

  14. S. M. Cronenwett, T. H. Osterkamp, and L. P. Kouwenhoven, Science 281, 540 (1998).

    Google Scholar 

  15. J. Schmid, J. Weis, K. Eberl, and K. v. Klitzing, Physica B 258, 182 (1998).

    Google Scholar 

  16. J. Kroha, P. Hirschfeld, K. A. Muttalib, and P. Wölfle, Solid State Comm. 83(12), 1003 (1992).

    Google Scholar 

  17. J. Kroha, P. Wölfle, and T. A. Costi, Phys. Rev. Lett. 79, 261 (1997).

    Google Scholar 

  18. T. Schauerte, J. Kroha, and P. Wölfle, Phys. Rev. B 62, 4394 (2000).

    Google Scholar 

  19. K. Haule, S. Kirchner, J. Kroha, and P. Wölfle, Phys. Rev. B 64, 155111 (2001).

    Google Scholar 

  20. J. Kroha and P. Wölfle, Festkrperprobleme/Adv. Solid State Phys. 39, 271 (1999).

    Google Scholar 

  21. J. Kroha and P. Wölfle, in Proceedings of the International Conference on “Mathematical Methods in Physics”, Montreal 2000, D. Senechal, ed., in press (Springer, 2001); cond-mat/0105491.

  22. J. Kroha and P. Wölfle, Acta Phys. Pol. B 29, 3781 (1998); cond-mat/9811074.

    Google Scholar 

  23. A. Rosch, private communication.

  24. A. A. Abrikosov, Physics 2, 21 (1965).

    Google Scholar 

  25. P. Coleman, Phys. Rev. B 29, 3035 (1984).

    Google Scholar 

  26. G. Baym and L.P. Kadanoff, Phys. Rev. 124, 287 (1961); G. Baym, Phys. Rev. 127 1391 (1962).

    Google Scholar 

  27. P. Nozières and C. T. De Dominicis, Phys. Rev. 178, 1073; 1084; 1097 (1969).

    Google Scholar 

  28. P. W. Anderson, Phys. Rev. Lett. 18, 1049 (1967).

    Google Scholar 

  29. B. Menge and E. Müller-Hartmann, Z. Phys. B 73, 225 (1988).

    Google Scholar 

  30. K. D. Schotte and U. Schotte, Phys. Rev. 185, 509 (1969).

    Google Scholar 

  31. T. A. Costi, P. Schmitteckert, J. Kroha, and P. Wölfle, Phys. Rev. Lettakit. 73, 1275 (1994); Physica (Amsterdam) 235–240C, 2287 (1994).

    Google Scholar 

  32. S. Fujimoto, N. Kawakami and S. K. Yang, J. Phys. Korea 29, S136 (1996).

    Google Scholar 

  33. I. Affleck and A. W. W. Ludwig, Nucl. Phys. B 352, 849 (1991); 360, 641 (1991); Phys. Rev. B 48, 7297 (1993).

    Google Scholar 

  34. T.A. Costi, J. Kroha, and P. Wölfle, Phys. Rev. B 53, 1850 (1996).

    Google Scholar 

  35. H. Keiter and J. C. Kimball, J. Appl. Phys. 42, 1460 (1971); N. Grewe and H. Keiter, Phys. Rev. B 24, 4420 (1981). 4420 (1981).

    Google Scholar 

  36. Y. Kuramoto, Z. Phys. B 53, 37 (1983); H. Kojima, Y. Kuramoto and M. Tachiki, ibid. 54, 293 (1984); Y. Kuramoto and H. Kojima, ibid. 57, 95 (1984); Y. Kuramoto, ibid. 65, 29 (1986).

    Google Scholar 

  37. E. Müller-Hartmann, Z. Phys. B 57, 281 (1984).

    Google Scholar 

  38. N. Andrei, K. Furuya, J. H. Löwenstein, Rev. Mod. Phys. 55, 331 (1983).

    Google Scholar 

  39. G. Sellier, J. Kroha, and P. Wölfle, in preparation.

  40. P. W. Anderson and G. Yuval, Phys. Rev. Lett. 23, 89 (1969).

    Google Scholar 

  41. P. W. Anderson, J. Phys. C 3, 2439 (1970).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Theorie der Kondensierten Materie, Universität Karlsruhe, Postfach 6980, 76128, Karlsruhe, Germany

    Stefan Kirchner & Johann Kroha

Authors
  1. Stefan Kirchner
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Johann Kroha
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kirchner, S., Kroha, J. Self-Consistent Conserving Theory for Quantum Impurity Systems: Renormalization Group Analysis. Journal of Low Temperature Physics 126, 1233–1249 (2002). https://doi.org/10.1023/A:1013835817652

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1013835817652

Keywords

Search

Navigation