Validation of Power Series Expansion for Single Particle Green's Function in Model Hamiltonians and Simple Material Systems.

The GW method for single particle Green's function overlooks  self-consistency to achieve computational cost effectiveness. This manifests as incorrect estimation of the effect of collective modes (plasmons) on the quasiparticle and incorrect satelline band energies. The cumulant approximation which was developed to mitigate this is ad hoc, unsystematic and fails at intermediate to strong electron-collective mode coupling. We have developed a general scheme to re-establish self-consistency by post-processing GW calculations by using a power series. We show that we can not only derive the cumulant results but also get exact green’s function for simple multiband model hamiltonians at intermediate couplings. Finally, we use our scheme to produce corrected band-structures in simple crystal systems and compare them to GW and cumulants.