Kondo Effect and the Physics of the Anderson Impurity Model

Abstract

AbstractIn this chapter we study the simplest example where correlation effects play a dominant role, namely, the physics of diluted magnetic impurities in metals. We first show what are the physical manifestations of those magnetic impurities and why they are so puzzling. Next, we introduce the simplest model able to capture the main physics, i.e., the Anderson impurity model, and study it, or its strongly coupling counterpart, the Kondo model, by complementary tools, Hartree-Fock approximation, perturbation theory in the Kondo exchange and Anderson’s poor man scaling. This analysis well describe the main steps of the observed physical evolution from the high-temperature local moment regime, down to the logarithmic crossover region around the Kondo temperature, and finally towards the low temperature screening of the impurity spin by the conduction electrons and the onset of the so-called Noziéres local Fermi liquid regime, which we microscopically derive properly adjusting to the Anderson impurity model the results derived in Chaps. 4 and 5.