Abstract
The normal state of the Holstein model is studied at half-filling in infinite dimensions and in the adiabatic regime. The dynamical mean-field equations are solved using perturbation expansions around the extremal paths of the effective action for the atoms. We find that the Migdal-Eliashberg expansion breaks down in the metallic state if the electron-phonon coupling exceeds a value of about 1.3 in spite of the fact that the formal expansion parameter is the phonon frequency, the Fermi energy) is much smaller than 1. The breakdown is due to the appearance of more than one extremal path of the action. We present numerical results which illustrate in detail the evolution of the local Green’s function, the self-energy, and the effective atomic potential as a function of
- Received 6 July 1998
DOI:https://doi.org/10.1103/PhysRevB.58.14320
©1998 American Physical Society