Derivation of Exact Results for the Single-Ion Kondo Problem with the Use of Diagrammatic Methods

It is shown that exact results for the single-impurity Kondo problem can be obtained by diagrammatic methods. The results for the susceptibility and specific heat agree with those obtained by Wilson’s numerical methods. In particular, the crossover W’=(π/e)1/2 and Wilson R=2 ratios are reproduced exactly. Conduction-electron scattering from the impurity reaches the unitarity limit corresponding to a phase shift δ=π/2. Both this and the compensation of the impurity spin are also exact results. The methods described are relatively easily extended to the Anderson model and the corresponding lattice problems