GW calculations in an exactly solvable model system at different dilution regimes: The problem of the self-interaction in the correlation part

The many-body perturbation theory in the Hedin's GW approximation is nowadays a common tool to carry out calculations in solids and molecular systems. Nevertheless a lot of theoretical issues concerning the self-interaction problem remain unresolved in the basic theory of this approximation. In this paper we carry out calculations in some very simple exactly solvable model systems and demonstrate that at this level of approach there are self-interaction problems in the correlation part that seriously affect the final results. This is especially important in the low-density regime. We also have carried out the calculations using different input data coming from the local-density approximation (LDA), generalized gradient approximation (GGA), and exact solutions of the Schroedinger equation to check how much affected are the final G0W0 results by the election of the input data. We have found that the final results inherit the errors from the input data and that only good results can be achieved if the input data are very close to (or are) the exact ones.