We compute the zero-point renormalization (ZPR) of the optical band gap of diamond from many-body perturbation theory using the perturbative G0W0 approximation as well as quasiparticle self-consistent GW. The electron-phonon coupling energies are found to be more than 40% higher than standard density functional theory when many-body effects are included with the frozen-phonon calculations. A similar increase is observed for the zero-point renormalization in GaAs when G0W0 corrections are applied. We show that these many-body corrections are necessary to accurately predict the temperature dependence of the band gap. The frozen-phonon method also allows us to validate the rigid-ion approximation which is always present in density functional perturbation theory.
Geadah-Antonius, G., Poncé, S., Boulanger, P., Côté, M., & Gonze, X. (2014). Many-Body Effects on the Zero-Point Renormalization of the Band Structure. Physical Review Letters, 112(21), 215501. https://doi.org/10.1103/PhysRevLett.112.215501 (Original work published 2014)