Conformal Field Theory Approach to the 2-Impurity Kondo Problem: Comparison with Numerical Renormalization Group Results

Abstract

Numerical renormalization group and conformal field theory work indicate that the two impurity Kondo Hamiltonian has a non-Fermi liquid critical point separating the Kondo-screening phase from the inter-impurity singlet phase when particle-hole (P-H) symmetry is maintained. We clarify the circumstances under which this critical point occurs, pointing out that there are two types of P-H symmetry. Only one of them guarantees the occurance of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyse this critical point using the boundary conformal field theory technique. The finite-size spectrum is presented in detail and compared with about 50 energy levels obtained using the numerical renormalization group. Various Green's functions, general renormalization group behaviour, and a hidden $SO(7)$ are analysed.Comment: 38 pages, RevTex. 2 new sections clarify the circumstances under which a model will exhibit the non-trivial critical point (hence potentially resolving disagreements with other Authors) and explain the hidden SO(7) symmetry of the model, relating it to an alternative approach of Sire et al. and Ga