Two-impurity Kondo problem: Relevance to heavy fermions (invited) (abstract)

Abstract

We have applied the numerical renormalization group to the problem of two Kondo impurities in an electron gas.1 This approach allows an analysis of the physics at all temperature scales as a function of the initial (high-temperature) exchange coupling and of the initial RKKY interaction. A new symmetry of the Kondo and Anderson models, which we call the axial charge, provides further details of the important physical states involved in the evolution to the low-temperature (strong-coupling) fixed point. At high temperatures, we calculate the change of the coupling interactions as the temperature is lowered from the free-local-moment fixed point. We identify the relevant lower temperature fixed points, and provide scaling results for the flows in the crossover regions. We evaluate both the range of validity of thermodynamic scaling2 at high temperatures and the strong influence of the initial interimpurity interaction on the scaling of the effective RKKY interaction. At the strong-coupling fixed point we construct a Fermi-liquid model and calculate the low-temperature specific heat, susceptibility, and staggered susceptibility; and discuss the nonuniversality of the Sommerfeld ratio. In particular, antiferromagnetic correlations produce an increased tendency to Cooper-type pairing, and we discuss these interactions in light of the new axial charge symmetry. Extensions of these pair interactions to the Fermi liquid for a lattice provide a possible description of correlations in heavy fermions.