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

GW approximation is one of the most popular parameter-free many-body methods that go 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 an electronic structure tool, which would offer a numerically exact solution to the solid-state problem. While most electronic structure packages offer support for GW calculations for band-insulating materials, the level of support for metallic systems is somewhat limited. This limitation can be partly attributed to the relatively minor differences often observed between GW and DFT results in treating metallic systems, which is not expected to persist to higher orders in pertutbation theory. Describing metals within the GW framework presents a challenge, as it requires accurate resolution of Fermi surface singularities, which, in turn, calls for a dense momentum mesh. Here we implement the GW algorithm within the all-electron Linear Augmented Plane Wave framework, where we pay special attention to the metallic systems, the convergence with respect to momentum mesh, and proper treatment of the 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 and is compared to numerically more stable contour deformation integration technique. 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 the available literature. Thus our software allows users to compute full bandstructures for metals and insulators using all-electron potential without downfolding to Wannier orbital basis.