Numerical Renormalization Group Approach to the TwoImpurity Kondo Hamiltonian
Abstract
The physics of two magnetic impurities in a metal is studied with the numerical renormalization group used by Wilson for the Kondo problem. The lowtemperature behavior of the twoimpurity system is especially complex because of the interplay between the interimpurity (RKKY) interaction and the Kondo effect. The system is modeled by two spin onehalf magnetic moments in a structureless Fermi gas. A conserved quantity of the twoimpurity Hamiltonian arising from particlehole symmetry, axial charge, is identified. The reduction in computation time and storage that its use permits could also have been utilized in earlier studies of systems with particlehole symmetry: the oneimpurity Kondo and Anderson models. The following lowtemperature properties of the twoimpurity Kondo Hamiltonian are established. (1) The ground state is always a singlet for nonzero impurity separation. (2) For initial RKKY couplings not too antiferromagnetic, there is a correlated Kondo effect. The moments are completely quenched, but there are residual interimpurity spin correlations present, even when the Kondo temperature T_ {K} is much larger than the initial RKKY coupling I_{o}. (3) For larger antiferromagnetic initial RKKY couplings, no Kondo effect occurs. The impurities are strongly correlated, yet not locked in a singlet. (4) The transition between behavior (2) and (3) above occurs at a value of the antiferromagnetic RKKY coupling I_{o} ~ 2T_{K}, far larger than predicted by scaling theory for a Kondo effect to occur. The transition in (4) is characterized by a new unstable fixed point unlike any previously seen for the one or twoimpurity problems. It shows a diverging staggered susceptibility and specific heat constant, and a Sommerfeld ratio which approaches zero. The properties of the twoimpurity problem are thus highly nonuniversal. For ferromagnetic RKKY couplings the Sommerfeld ratio rises as much as 30% above the universal value, two, for independent impurities. For increasing antiferromagnetic couplings, the Sommerfeld ratio decreases sharply to near zero at the unstable fixed point before rising asymptotically for very large couplings to the free electron value one. The relevance of this work to concentrated impurity systemsespecially heavy fermionsis discussed.
 Publication:

Ph.D. Thesis
 Pub Date:
 June 1988
 Bibcode:
 1988PhDT........30J
 Keywords:

 RKKY;
 FERMIONS;
 Physics: Condensed Matter