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

• Published in: The European physical journal. B, Condensed matter physics Condensed matter physics, 2012-09, Vol.85 (9), Article 326
• Main Authors: Berger, J. A., Reining, L., Sottile, F.
• Format: Article
• Language: English
• Subjects: Complex Systems; Condensed Matter; Condensed Matter Physics; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Electron states; Exact sciences and technology; Fluid- and Aerodynamics; Methods of electronic structure calculations; Other; Physics; Physics and Astronomy; Regular Article; Solid State Physics; Topical issue: Challenges and solutions in GW calculations for complex systems
• ISSN: 1434-6028; 1434-6036
• DOI: 10.1140/epjb/e2012-30237-5

In a recent publication [J.A. Berger, L. Reining, F. Sottile, Phys. Rev. B 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.