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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.


S. E. Barnes, Physical Review B, 33, 3209-3246, 1986. "Copyright © 1986 by the American Physical Society.”

Link to the online abstract:

DOI: 10.1103/PhysRevB.33.3209