Electron-phonon coupling in insulators beyond the Migdal limit

Motivated by the success of the momentum average (MA) approximation for the single-polaron and bipolaron cases, in this thesis we pursue the first generalization of this technique to the case of weakly-doped insulators beyond the Migdal limit. In search of a suitable starting point, we investigate the ground states of a variety of model Hamiltonians, inspired by real materials such as the rare-earth nickelates, polyacetylene, barium bismuthates, and buckminsterfullerene.