Interaction quench in the Holstein model: Thermalization crossover from electron- to phonon-dominated relaxation

TL;DR

This study investigates how the relaxation dynamics of the Holstein model change with interaction strength, revealing a crossover from electron-dominated to phonon-dominated thermalization processes using nonequilibrium dynamical mean field theory.

Contribution

It demonstrates a qualitative change in thermalization behavior in the Holstein model depending on the electron-phonon interaction strength, highlighting the role of phonon dynamics.

Findings

Phonon oscillations damp faster than electron thermalization at weak coupling.

Electron relaxation becomes faster than phonon damping at strong coupling.

Self-energy behaviors explain the thermalization crossover.

Abstract

We study the relaxation of the Holstein model after a sudden switch-on of the interaction by means of the nonequilibrium dynamical mean field theory, with the self-consistent Migdal approximation as an impurity solver. We show that there exists a qualitative change in the thermalization dynamics as the interaction is varied in the weak-coupling regime. On the weaker interaction side of this crossover, the phonon oscillations are damped more rapidly than the electron thermalization timescale, as determined from the relaxation of the electron momentum distribution function. On the stronger interaction side, the relaxation of the electrons becomes faster than the phonon damping. In this regime, despite long-lived phonon oscillations, a thermalized momentum distribution is realized temporarily. The origin of the thermalization crossover found here is traced back to different behaviors of the electron and phonon self-energies as a function of the electron-phonon coupling. In addition, the importance of the phonon dynamics is demonstrated by comparing the self-consistent Migdal results with those obtained with a simpler Hatree-Fock impurity solver that neglects the phonon self-energy. The latter scheme does not properly describe the evolution and thermalization of isolated electron-phonon systems.