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

Abstract

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 $T_{\mathrm{K}}$ and the renormalized phonon frequency ${\Delta }^x$ are expressed in terms of the mass ratio $m/M$, $m$ and $M$ being the mass of 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 $T_{\mathrm{K}}>{\Delta }^x$ is fulfilled. It is demonstrated that such condition is satisfied when $g/D$ is sufficiently large but in a realistic range.

25 pages ReVTeX, one PS file including 7 figures, submitted to J. Phys. Soc. Jpn

References in corpus (1)

• Numerical Renormalization-Group Study of Particle-Hole Symmetry Breaking in Two-Channel Kondo Problem : Effect of Repulsion between Conduction Electrons and Potential Scattering

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