Skip to main content

The numerical renormalization group method for correlated electrons

  • Correlations and Disorder
  • Conference paper
  • First Online:
Book cover Advances in Solid State Physics 40

Part of the book series: Advances in Solid State Physics ((ASSP,volume 40))

Abstract

The Numerical Renormalization Group method (NRG) has been developed by Wilson in the 1970's to investigate the Kondo problem. The NRG allows the non-perturbative calculation of static and dynamic properties for a variety of impurity models. In addition, this method has been recently generalized to lattice models within the Dynamical Mean Field Theory. This paper gives a brief historical overview of the development of the NRG and discusses its application to the Hubbard model; in particular the results for the Mott metal-insulator transition at low temperatures.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975).

    Article  ADS  Google Scholar 

  2. K.G. Wilson, in Nobel lectures in physics 1981–1990 (World Scientific, Singapore 1993).

    Google Scholar 

  3. A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, Cambridge 1993).

    Book  Google Scholar 

  4. W.J. de Haas, J.H. de Boer, and G.J. van den Berg, Physica 1, 1115 (1934).

    Article  ADS  Google Scholar 

  5. J. Kondo, Prog. Theor. Phys. 32, 37 (1964).

    Article  ADS  Google Scholar 

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

    ADS  Google Scholar 

  7. P.W. Anderson, Phys. Rev. 124, 41 (1961).

    Article  ADS  MathSciNet  Google Scholar 

  8. H.R. Krishna-murthy, J.W. Wilkins, and K.G. Wilson, Phys. Rev. B 21, 1003 (1980); 21, 1044 (1980).

    Article  ADS  Google Scholar 

  9. Density-Matrix Renormalization, eds. I. Peschel et al. (Springer, Berlin 1999).

    MATH  Google Scholar 

  10. D.M. Cragg, P. Lloyd, and Ph. Nozières, J. Phys. C 13, 803 (1980); H.-B. Pang, D.L. Cox, Phys. Rev. B 44, 9454 (1991). R. Bulla, A.C. Hewson, and G.-M. Zhang, Phys. Rev. B 56, 11721 (1997).

    Article  ADS  Google Scholar 

  11. K. Chen, C. Jayaprakash, J. Phys.: Condens. Matter 7, L491 (1995); K. Ingersent, Phys. Rev. B 54, 11936 (1996); R. Bulla, Th. Pruschke, and A.C. Hewson, J. Phys.: Condens. Matter 9, 10463 (1997). R. Bulla, M.T. Glossop, D.E. Logan, and Th. Pruschke, preprint cond-mat/9909101 (1999).

    Article  ADS  Google Scholar 

  12. O. Sakai, Y. Shimizu, and T. Kasuya, J. Phys.: Cond. Matter 6, 2519 (1994).

    Article  Google Scholar 

  13. T.A. Costi, A.C. Hewson, and V. Zlatic, J. Phys.: Cond. Matter 6, 2519 (1994).

    Article  ADS  Google Scholar 

  14. W. Metzner and D. Vollhardt, Phys. Rev. Lett. 62, 324 (1989); for an introduction, see D. Vollhardt, Int. J. Mod. Phys. B 3, 2189 (1989).

    Article  ADS  Google Scholar 

  15. R. Bulla, A.C. Hewson, and Th. Pruschke, J. Phys.: Cond. Matter 10, 8365 (1998).

    Article  ADS  Google Scholar 

  16. O. Sakai and Y. Kuramoto, Sol. Sci. Comm. 89, 307 (1994).

    Article  ADS  Google Scholar 

  17. R. Bulla, Phys. Rev. Lett. 83, 136 (1999).

    Article  ADS  Google Scholar 

  18. N.F. Mott, Proc. Phys. Soc. London A 62, 416 (1949); Metal-Insulator Transitions, 2nd ed. (Taylor and Francis, London 1990).

    Article  ADS  Google Scholar 

  19. F. Gebhard, The Mott Metal-Insulator Transition, Springer Tracts in Modern Physics Vol. 137 (Springer, Berlin 1997).

    Google Scholar 

  20. D.B. McWhan and J.P. Remeika, Phys. Rev. B 2, 3734 (1970); D.B. McWhan, A. Menth, J.P. Remeika, Q.F. Brinkman and T.M. Rice, Phys. Rev. B 7, 1920 (1973).

    Article  ADS  Google Scholar 

  21. J. Hubbard, Proc. R. Soc. London A 276, 238 (1963).

    Article  ADS  Google Scholar 

  22. M.C. Gutzwiller, Phys. Rev. Lett. 10, 59 (1963).

    Article  ADS  Google Scholar 

  23. J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  25. M. Jarrell, Phys. Rev. Lett. 69, 168 (1992); T. Pruschke, M. Jarrell, and J.K. Freericks, Adv. Phys. 44, 187 (1995).

    Article  ADS  Google Scholar 

  26. D.E. Logan and Ph. Nozières, Phil. Trans. R. Soc. London A 356, 249 (1998).

    Article  ADS  Google Scholar 

  27. S. Kehrein, Phys. Rev. Lett. 81, 3912 (1998).

    Article  ADS  Google Scholar 

  28. R. Noack and F. Gebhard, Phys. Rev. Lett. 82, 1915 (1999).

    Article  ADS  Google Scholar 

  29. J. Schlipf, M. Jarrell, P.G.J. van Dongen, S. Kehrein, N. Blümer, Th. Pruschke, and D. Vollhardt, Phys. Rev. Lett. 82, 4890 (1999).

    Article  ADS  Google Scholar 

  30. M.J. Rozenberg, R. Chitra, and G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999).

    Article  ADS  Google Scholar 

  31. G. Moeller, Q. Si, G. Kotliar, M. Rozenberg, and D.S. Fisher, Phys. Rev. Lett. 74, 2082 (1995).

    Article  ADS  Google Scholar 

  32. R. Bulla, T.A. Costi, and D. Vollhardt, in preparation.

    Google Scholar 

  33. U. Gerland, J. von Delft, T.A. Costi, and Y. Oreg, Phys. Rev. Lett. 84, 3710 (2000).

    Article  ADS  Google Scholar 

  34. W. Hofstetter, R. Bulla, and D. Vollhardt, preprint cond-mat/9912396 (1999).

    Google Scholar 

  35. Th. Pruschke, R. Bulla, and M. Jarrell, preprint cond-mat/0001357 (2000).

    Google Scholar 

  36. R. Pietig, R. Bulla, and S. Blawid, Phys. Rev. Lett. 82, 4046 (1999).

    Article  ADS  Google Scholar 

  37. V.I. Anisimov, A.I. Poteryaev, M.A. Korotin, A.O. Anokhin, and G. Kotliar, J. Phys.: Condens. Matter 9, 7359 (1997); A.I. Lichtenstein and M.I. Katsnelson, Phys. Rev. B 57, 6884 (1998); M.B. Zölfl, Th. Pruschke, J. Keller, A.I. Poteryaev, I.A. Nekrasov, and V.I. Anisimov, preprint cond-mat/9909359 (1999); M.I. Katsnelson and A.I. Lichtenstein, Phys. Rev. B 61, 8906 (2000); I.A. Nekrasov, K. Held, N. Blümer, V.I. Anisimov, and D. Vollhardt, in preparation.

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Bernhard Kramer

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Friedr. Vieweg & Sohn Verlagsgesellschaft mbH

About this paper

Cite this paper

Bulla, R. (2000). The numerical renormalization group method for correlated electrons. In: Kramer, B. (eds) Advances in Solid State Physics 40. Advances in Solid State Physics, vol 40. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0108352

Download citation

  • DOI: https://doi.org/10.1007/BFb0108352

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-41576-3

  • Online ISBN: 978-3-540-44560-9

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics