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Numerical renormalization group

Numerical renormalization group (NRG) is a numerical non-perturbative approach to the renormalization group for many-particle problems, as devised by Kenneth Wilson. It is the most accurate method known to handle the quantum impurity problems, such as the Kondo problem and the Anderson impurity problem. Such models describe magnetic impurities in interaction with itinerant conduction band electrons in a metal. The impurity local moment (spin) couples antiferromagnetically to the conduction electrons, which leads to the screening of the spin at low temperatures (on the scale of the Kondo temperature, TK).

The method consists of the following main elements:

Further reading

K. G. Wilson, The renormalization Group: Critical Phenomena and the Kondo Problem, Rev. Mod. Phys. 47, 773-840 (1975).
H. R. Krishna-murthy, J. W. Wilkins and K. G. Wilson, Renormalization-group approach to the Anderson model of dilute magnetic alloys. I. Static properties for the symmetric case, Phys. Rev. B 21, 1003-1043 (1980).
Ralf Bulla, Theo Costi, Thomas Pruschke, The numerical renormalization group method for quantum impurity systems, arXiv:cond-mat/0701105 (2007).

Last modified: 1. 2. 2008