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

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