Dynamical Localization-Delocalization Transition in the Infinite-Dimensional Hubbard-Holstein Model

We study electron localization due to the confinement by local phonons occurring at finite energies by using an expansion theory with respect to the effective hopping integral $A$ from the limit of zero bandwidth in infinite-dimensional electronic systems. The localization signaled by the divergence in the self-energy is found to exist for sufficiently small $A$, but it disappears for larger $A$, indicating a dynamical localization-delocalization transition.