Mapping the Critical Point of the Two-Impurity Kondo Model to a Two-Channel Problem

The two-impurity Kondo model with particle-hole symmetry is known to have a critical point at comparable RKKY interaction and Kondo temperature. Using bosonization and controlled low energy projection, we identify the critical point and map it to a solvable resonant level model. The physics of the critical point is shown to be the same as the two-channel Kondo model. An effective Hamiltonian is derived from which the solutions for the critical point and surrounding Fermi-liquid phase follow immediately. The universality of the critical point is strongly supported by the overall excellent agreement with the numerical renormalization group and conformal field theory results.