H. Kusunose et K. Miyake, 2-CHANNEL KONDO MODEL AS A FIXED-POINT OF LOCAL ELECTRON-PHONON COUPLING SYSTEM, Journal of the Physical Society of Japan, 65(9), 1996, pp. 3032-3042
It is shown on the basis of the multiplicative renormalization-group m
ethod of two-loop order that the low-energy effective Hamiltonian of a
strongly coupled local electron-phonon system is mapped to the two-ch
annel Kondo model. A phonon is treated as an Einstein oscillator with
restricted Hilbert space such that up to one-phonon process:is taken i
nto account. By eliminating the high energy process of conduction elec
trons, it is shown that a certain class of couplings between ion vibra
tions and conduction electrons is selectively grown up. As a result th
e system is reduced to the two-channel Kondo model. The crossover temp
erature T-K and the renormalized phonon frequency Delta(x) are express
ed 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 bandw
idth 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 whe
n g/D is sufficiently large but in a realistic range.