Solution of then-channel Kondo problem (scaling and integrability)

Alexei M. Tsvelik, Paul B. Wiegmann

Lars Fritz, Andrew K. Mitchell, Eran Sela +1 more

Abijith Krishnan, Max A. Metlitski

The Kondo problem, which describes the interaction of a spin $s$ magnetic impurity with a free Fermi gas, is a classic example of strongly coupled physics. Historically, the problem has been solved by Wilson's numerical renormalization group and later by Bethe ansatz. In this paper, we present an alternate analytic solution of the Kondo problem that combines an expansion in $1/s$ with the renormalization group. We study both the case of an impurity interacting with a single channel $K=1$ of fermions in the $s \rightarrow \infty$ limit and the case with $K$ channels in the double-scaling limit $K \rightarrow \infty$, $s \to \infty$, $K/s$ fixed. Our approach allows us to describe analytically intermediate scales of the Kondo problem at large $s$ and compute thermodynamic observables such as the impurity entropy and susceptibility. We find these observables to agree with the Bethe ansatz results. We also compute the impurity spectral function, finite temperature resistivity and the Kondo screening cloud profile, properties that are not easily accessible from Bethe ansatz. Notably, in the regime $K > 2s$ we access the "non-Fermi-liquid" overscreened fixed point of the multichannel Kondo problem.

Philip Warren Anderson

H -U Desgranges

The thermodynamic Bethe ansatz equations of the n-channel Kondo problem have been solved numerically. Complete compensation of the impurity magnetic moment and Fermi liquid behaviour at low temperatures is obtained if the impurity spin S is equal to n/2. At high temperatures a qualitatively new behaviour is found for large n. For n>2S the crossover to the scaling regime described by critical exponents has been calculated numerically.

P. W. Anderson