Beyond Allen-Heine-Cardona: non-perturbative electron-phonon interactions in the linewidths and lineshifts of diamond
The temperature-dependent band gap of solids is usually computed from the perturbative Allen-Heine-Cardona (AHC) electron-phonon self-energy evaluated on-shell. Extending AHC to arbitrary frequency $\omega$ to determine the full spectral function via the Dyson equation is known to fail, misplacing satellites and yieldi...