Local Self-Energy Approach for Electronic Structure Calculations

Using a novel self-consistent implementation of Hedin’s $GW$ perturbation theory, we calculate space- and energy-dependent self-energy for a number of materials. We find it to be local in real space and rapidly convergent on second- to third-nearest neighbors. Corrections beyond $GW$ are evaluated and shown to be completely localized within a single unit cell. This can be viewed as a fully self-consistent implementation of the dynamical mean field theory for electronic structure calculations of real solids using a perturbative impurity solver.