Mapping of the two-channel Kondo problem to a resonant-level model

Abstract

Abelian bosonization is used to map the two-channel Kondo problem into a resonant-level Hamiltonian, which is equivalent to noninteracting fermions for a particular value of the longitudinal exchange coupling. This solvable point is analogous to the Toulouse limit of the ordinary Kondo problem. The impurity Green’s function, susceptibility, and thermodynamic properties, together with certain conduction-electron correlation functions, are evaluated at the solvable point. In particular, it is shown that the pairing resonance of the two-channel Kondo problem may be characterized as an enhancement of superconducting pairing of the conduction electrons at the impurity site, correlated with the impurity pseudospin (or equivalently odd-time pairing of the conduction electrons).