Conformal-field-theory approach to the two-impurity Kondo problem: Comparison with numerical renormalization-group results

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 interimpurity 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 occurrence of the critical point. Much of the previous numerical work was done on models with the other type of P-H symmetry. We analyze 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 behavior, and a hidden SO(7) are analyzed.