This chapter traces Anderson’s work from his invention of an impurity model to understand the fate of a magnetic atom immersed in a non-magnetic metal to his solution of the Kondo problem using an early version of the renormalization group invented by him and later generalized by Ken Wilson. Important events on this path are the experimental impetus provided by Bernd Matthias, the Coulomb repulsion model of insulating behavior due to Nevill Mott, and Jacques Friedel’s ideas about treating atoms embedded in metals. Speculation is offered about the award of the 1977 Nobel Prize to Anderson, Mott, and Van Vleck.
The Kondo problem of a magnetic impurity embedded in the Lieb lattice is studied by the numerical renormalization group. The magnetic impurity hybridizes with conduction electrons from both the flat- and the soft-gap bands. We find a competition between the soft gap and the molecular Kondo singlet formations. The molecular Kondo effect occurs only when the magnetic impurity strongly hybridizes with conduction electrons at edge center sites of the Lieb lattice, and at the temperature range between the artificial strong coupling and the local moment regimes.
Overscreened Kondo problem with large spin and large number of orbital channels: Two distinct semiclassical limits in quantum transport observables
