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 T-K and the renormalized phonon frequency Delta(x) are expressed in terms of the mass ratio m/M, m and M being the mass of elect ron 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 T-K > Delta(x) is fulfilled. It is demonstrated that such condition is satisfied when g/D is sufficiently large but in a realistic range.