Abstract.
We show that the low energy behaviour of quite diverse impurity systems can be described by a single renormalized Anderson model, with three parameters, an effective level \(\tilde\epsilon_d\), an effective hybridization \(\tilde V\), and a quasiparticle interaction \(\tilde U\). The renormalized parameters are calculated as a function of the bare parameters for a number of impurity models, including those with coupling to phonons and a Falikov-Kimball interaction term. In the model with a coupling to phonons we determine where the interaction of the quasiparticles changes sign as a function of the electron-phonon coupling. In the model with a Falikov-Kimball interaction we show that to a good approximation the low energy behaviour corresponds to that of a bare Anderson model with a shifted impurity level.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
K.G. Wilson, Rev. Mod. Phys. 47, 773 (1975)
H.R. Krishnamurthy, J.W. Wilkins, K.G. Wilson, Phys. Rev. B 21, 1003 and 1044 (1980)
See for example, N.N. Bogoliubov, D.V. Shirkov, Introduction to the Theory of Quantized Fields (Wiley-Interscience, New York, 1980)
A.C. Hewson, Phys. Rev. Lett. 70, 4007 (1993)
A.C. Hewson, J. Phys.: Condens. Matter 13, 10011 (2001)
P.W. Anderson, Phys. Rev. 124, 41 (1961)
D.M. Newns, A.C. Hewson, J. Phys. F 10, 2429 (1980)
That these results are exact can be deduced from a Ward identity. For details see references [10,4]
J. Friedel, Can. J. Phys. 54, 1190 (1956); J.M. Langer, V. Ambegaokar, Phys. Rev. 164, 498 (1961); D.C. Langreth, Phys. Rev. 150, 516 (1966)
K. Yamada, Prog. Theor. Phys. 53, 1970 (1975); 54, 316 (1975)
P. Noziéres, J. Low Temp. Phys. 17, 31 (1974): Low Temperature Physics Conference Proceedings LT14
A. Oguri, Phys. Rev. B 64, 153305 (2001)
A.M. Tsvelick, P.B. Wiegmann, Adv. Phys. 32, (1983)
B. Horvatić, V. Zlatić, J. Phys. France 46, 1459 (1985)
A.C. Hewson, J. Phys.: Condens. Matter 5, 6277 (1993)
J. Rasul, A.C. Hewson, J. Phys. C 17, 3337 (1984)
G.M. Falco, R.A. Duine, H.T.C. Stoof, cond-mat/0304489 (2003)
O. Sakai, Y. Shimizu, T. Kasuya, Prog. Theor. Phys. Suppl. 108, 73 (1992)
O. Sakai, Y. Shimizu, T. Kasuya, J. Phys. Soc. Jpn 58, 3666 (1989)
T.A. Costi, A.C. Hewson, V. Zlatić, J. Phys.: Condens. Matter 6, 2519 (1994)
F.M.D. Haldane, Phys. Rev. Lett. 40, 416 (1978)
A.C. Hewson, The Kondo Problem to Heavy Fermions, Chap. 7 (Cambridge Univ. Press, Cambridge, 1993 and 1997)
This is a feature of the discrete model, more generally in a continuum case one might expect these terms to fall off as 1/N
T. Holstein, Ann. Phys. Lpz. 8, 325 (1959)
A.C. Hewson, D. Meyer, J. Phys. Condens. Matter 14, 427 (2002)
D. Meyer, A.C. Hewson, Acta Physica Polonica B 34, 769 (2003)
L.M. Falikov, J.C. Kimball, Phys. Rev. Lett. 22, 997 (1969)
J.K. Freericks, V. Zlatić, Rev. Mod. Phys. 75, 1333 (2003)
G.D. Mahan, Many Particle Physics (Plenum, New York, 1990)
Author information
Authors and Affiliations
Corresponding author
Additional information
Received: 2 July 2004, Published online: 12 August 2004
PACS:
75.20.Hr Local moment in compounds and alloys; Kondo effect, valence fluctuations, heavy fermions - 71.10.-w Theories and models of many-electron systems - 71.27. + a Strongly correlated electron systems; heavy fermions
Rights and permissions
About this article
Cite this article
Hewson, A.C., Oguri, A. & Meyer, D. Renormalized parameters for impurity models. Eur. Phys. J. B 40, 177–189 (2004). https://doi.org/10.1140/epjb/e2004-00256-0
Issue Date:
DOI: https://doi.org/10.1140/epjb/e2004-00256-0