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GW approximation is one of the most popular parameter-free many-body methodsthat goes beyond the limitations of the standard density functional theory(DFT) to determine the excitation spectra for moderately correlated materialsand in particular the semiconductors. It is also the first step in developingthe diagrammatic Monte Carlo method into an electronic structure tool, whichwould offer a numerically exact solution to the solid-state problem. Currently,most electronic structure packages support GW calculations for theband-insulating materials, while the support for the metallic system remainslimited to only a few implementations. The metallic systems are challenging forGW, as it requires one to accurately resolve the Fermi surface singularities,which demands a dense momentum mesh. Here we implement GW algorithm within theall-electron Linear Augmented Plane Wave framework, where we pay specialattention to the metallic systems, the convergence with respect to momentummesh and proper treatment of the deep laying core states, as needed for thefuture variational diagrammatic Monte Carlo implementation. Our improvedalgorithm for resolving Fermi surface singularities allows us a stable andaccurate analytic continuation of imaginary axis data, which is carried out forGW excitation spectra throughout the Brillouin zone in both the metallic andinsulating materials, and is compared to numerically more stable contourdeformation integration technique. We compute band structures for elementalmetallic systems Li, Na, and Mg as well as for various narrow and wide bandgapinsulators such as Si, BN, SiC, MgO, LiF, ZnS, and CdS and compare our resultswith previous GW calculations and available experiments data. Our results arein good agreement with the available literature.

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