The self-screening correction to RPA and GW – A model and ab initio study

Sammanfattning: The self-screening error in the GW approximation is studied by applying correction schemes beyond the random-phase approximation in model and ab inito calculations. Two model systems in the form of Hubbard dimers, with one and two orbitals per site respectively, are considered. Both the self-screening (GW-ss) and self-polarization (GW-sp) correction schemes are compared to ordinary GW calculations as well as to the exact results. It is found that GW-ss provides a signicant improvement for small values of the interaction strength U0, almost correctly describing the linear density response function and improving the spectral function over that obtained within GW. GW-sp instead correctly describes the HOMOLUMO gap for the one-orbital model in the limit of large U0, and provides a better agreement also for the spectral function in that regime, while still being approximately as accurate as GW-ss in describing the response and spectral function for lower interaction strengths. It is further found that GW-sp suers from causality issues. The ab initio calculations were performed using a version of the SPEX code modied to include the self-screening correction. The correction is applied to four semiconductors: GaAs, ZnSe, Ge, and ZnO. It is found that the self-screening correction signicantly improved the band gap for GaAs and ZnSe compared to ordinary GW calculations, while it marginally overestimates the width for Ge, and improves the ZnO one slightly. Further it is found to provide a small improvement also of the energy-placement of the semicore 3d states. A comparison is also ade regarding the dierences of the two correction schemes. It is concluded that the GW-ss scheme seems to provide the best correction for delocalized systems. GW-sp instead gives the better description for large interaction strengths, and hence more localized systems, although simultaneously being able to give a good agreement for small U0 in the model calculations.