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

TL;DR

This paper demonstrates that a strongly coupled local electron-phonon system can be effectively described by the two-channel Kondo model using a two-loop renormalization-group approach, revealing conditions for observable anomalous behaviors.

Contribution

It shows how the low-energy effective Hamiltonian of a local electron-phonon system maps onto the two-channel Kondo model, including explicit expressions for crossover temperature and phonon frequency.

Findings

The system reduces to the two-channel Kondo model under certain conditions.

Crossover temperature and phonon frequency are expressed in terms of physical parameters.

Anomalous behaviors are observable when the electron-phonon coupling is sufficiently large.

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 $T_{\rm K}$ 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 $T_{\rm K}>\Delta^{x}$ is fulfilled. It is demonstrated that such condition is satisfied when $g/D$ is sufficiently large but in a realistic range.