Two-Channel Kondo Model as a Fixed Point of Local Electron-Phonon Coupling System

It is shown on the basis of the multiplicative renormalization-group method of two-loop order that the low-energy effective Hamiltonian of a strongly coupled local electron-phonon system is mapped to the two-channel Kondo model. A phonon is treated as an Einstein oscillator with restricted Hilbert space such that up to one-phonon process is taken into account. By eliminating the high energy process of conduction electrons, it is shown that a certain class of couplings between ion vibrations and conduction electrons is selectively grown up. As a result the system is reduced to the two-channel Kondo model. The crossover temperature TK and the renormalized phonon frequency ∆ x are expressed in terms of the mass ratio m/M , m and M being the mass of electron and ion, and the electron-phonon coupling g/D, D being half the bandwidth of conduction electrons. The anomalous behaviors associated with this renormalization can be mesuarable if the condition TK > ∆ x is fulfilled. It is demonstrated that such condition is satisfied when g/D is sufficiently large but in a realistic range.