Beyond the GW Approximation: Recent Developments and Future Perspectives

The GW approximation is known to cure the band gap problem of density functional theory in the local density approximation (LDA). It yields accurate band gaps of weakly correlated semiconductors and insulators and is established as a standard tool for studying electronic excitations. The method M has been applied to correlated materials as well during the last few years. The results show some :5 improvements over the LDA results but there remain some discrepancies with experiments revealing M limitation of the conventional GW method. These discrepancies indicate the importance of self-consistency and local correlation effects beyond the GW approximation. These issues are discussed in detail and formal theoretical framework, practical computational methods and applications to real materials are given in the present article. Generalization of the GW approximation to spin dependent interactions is also described.