All electron GW with linearized augmented plane waves for metals and semiconductors.

GW approximation is one of the most popular parameter-free many-body method that goes beyond the limitations of the standard density functional theory (DFT) to determine the excitation spectra for moderately correlated materials, and in particular the semiconductors. It is also the first step in developing the diagrammatic Monte Carlo method into electronic structure tool, which would offer numerically exact solution of the solid state problem. Currently most of the GW studies are confined to the band-insulating materials and the implementation for metallic system remained challenging as it requires one to accurately resolve the Fermi surface singularities to have stable analytical continuation of the self-energy. Here we implement GW algorithm within all electron Linear Augmented Plane Wave framework, where we pay special attention to the metallic systems, and proper treatment of deep laying core states, as needed for the future variational diagrammatic Monte Carlo implementation. Our improved algorithm for resolving Fermi surface singularities allows us a stable and accurate analytic continuation of imaginary axis data, which is carried out for GW excitation spectra throughout the Brillouin zone in both the metallic and insulating materials. We compute band structures for elemental metallic systems Li, Na, and Mg as well as for various narrow and wide bandgap insulators such as Si, BN, SiC, MgO, LiF, ZnS, and CdS and compare our results with previous GW calculations and available experiments data. Our results are in good agreement with available literature.