Efficient calculation of the polarizability: a simplified effective-energy technique

In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B <Emphasis Type="Bold">82, 041103(R) (2010)] we introduced the effective-energy technique to calculate in an accurate and numerically efficient manner the GW self-energy as well as the polarizability, which is required to evaluate the screened Coulomb interaction W. In this work we show that the effective-energy technique can be used to further simplify the expression for the polarizability without a significant loss of accuracy. In contrast to standard sum-over-state methods where huge summations over empty states are required, our approach only requires summations over occupied states. The three simplest approximations we obtain for the polarizability are explicit functionals of an independent- or quasi-particle one-body reduced density matrix. We provide evidence of the numerical accuracy of this simplified effective-energy technique as well as an analysis of our method. Copyright EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2012