Strong-coupling corrections to zero-point renormalization of quasiparticle band gaps

We investigate the question on the phonon renormalization of quasiparticle band gaps by extending the Allen-Heine theory to the case of strong electron-phonon coupling. In this regime, electron self-localization and polaron formation can provide a sizable contribution to the band gap and cannot be neglected. We perform calculations of quasiparticle band gaps in alkali halides and alkaline-earth oxides by including GW, Fan-Migdal, Debye-Waller, and polaron self-energies on the same footing. We find that the inclusion of polaronic effects improves the agreement between calculations and experiments for the zero-point renormalization of the band gap.