Variational theory of the two-impurity Kondo problem

A pair of magnetically coupled Anderson impurities is studied by a variational method which is an extension of that used for mixed-valence Tm ions. The staggered susceptibility ${\mathrm{\chi }}_{\mathit{s}}$ is enhanced when the magnitude of the antiferromagnetic coupling J between two impurities competes with the Kondo energy scale of a single impurity, although it does not show divergence. ${\mathrm{\chi }}_{\mathit{s}}$ is, however, enhanced further by introducing the orbital degeneracy, and finally diverges at a critical value of J in the Coqblin-Schrieffer limit.