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.
Preview
Unable to display preview. Download preview PDF.
Bibliography
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975).
K.G. Wilson, in Nobel lectures in physics 1981–1990 (World Scientific, Singapore 1993).
A.C. Hewson, The Kondo Problem to Heavy Fermions (Cambridge Univ. Press, Cambridge 1993).
W.J. de Haas, J.H. de Boer, and G.J. van den Berg, Physica 1, 1115 (1934).
J. Kondo, Prog. Theor. Phys. 32, 37 (1964).
P.W. Anderson, J. Phys. C 3, 2439 (1970).
P.W. Anderson, Phys. Rev. 124, 41 (1961).
H.R. Krishna-murthy, J.W. Wilkins, and K.G. Wilson, Phys. Rev. B 21, 1003 (1980); 21, 1044 (1980).
Density-Matrix Renormalization, eds. I. Peschel et al. (Springer, Berlin 1999).
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).
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).
O. Sakai, Y. Shimizu, and T. Kasuya, J. Phys.: Cond. Matter 6, 2519 (1994).
T.A. Costi, A.C. Hewson, and V. Zlatic, J. Phys.: Cond. Matter 6, 2519 (1994).
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).
R. Bulla, A.C. Hewson, and Th. Pruschke, J. Phys.: Cond. Matter 10, 8365 (1998).
O. Sakai and Y. Kuramoto, Sol. Sci. Comm. 89, 307 (1994).
R. Bulla, Phys. Rev. Lett. 83, 136 (1999).
N.F. Mott, Proc. Phys. Soc. London A 62, 416 (1949); Metal-Insulator Transitions, 2nd ed. (Taylor and Francis, London 1990).
F. Gebhard, The Mott Metal-Insulator Transition, Springer Tracts in Modern Physics Vol. 137 (Springer, Berlin 1997).
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).
J. Hubbard, Proc. R. Soc. London A 276, 238 (1963).
M.C. Gutzwiller, Phys. Rev. Lett. 10, 59 (1963).
J. Kanamori, Prog. Theor. Phys. 30, 275 (1963).
A. Georges, G. Kotliar, W. Krauth, and M.J. Rozenberg, Rev. Mod. Phys. 68, 13 (1996).
M. Jarrell, Phys. Rev. Lett. 69, 168 (1992); T. Pruschke, M. Jarrell, and J.K. Freericks, Adv. Phys. 44, 187 (1995).
D.E. Logan and Ph. Nozières, Phil. Trans. R. Soc. London A 356, 249 (1998).
S. Kehrein, Phys. Rev. Lett. 81, 3912 (1998).
R. Noack and F. Gebhard, Phys. Rev. Lett. 82, 1915 (1999).
J. Schlipf, M. Jarrell, P.G.J. van Dongen, S. Kehrein, N. Blümer, Th. Pruschke, and D. Vollhardt, Phys. Rev. Lett. 82, 4890 (1999).
M.J. Rozenberg, R. Chitra, and G. Kotliar, Phys. Rev. Lett. 83, 3498 (1999).
G. Moeller, Q. Si, G. Kotliar, M. Rozenberg, and D.S. Fisher, Phys. Rev. Lett. 74, 2082 (1995).
R. Bulla, T.A. Costi, and D. Vollhardt, in preparation.
U. Gerland, J. von Delft, T.A. Costi, and Y. Oreg, Phys. Rev. Lett. 84, 3710 (2000).
W. Hofstetter, R. Bulla, and D. Vollhardt, preprint cond-mat/9912396 (1999).
Th. Pruschke, R. Bulla, and M. Jarrell, preprint cond-mat/0001357 (2000).
R. Pietig, R. Bulla, and S. Blawid, Phys. Rev. Lett. 82, 4046 (1999).
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.
Author information
Authors and Affiliations
Editor information
Rights 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