Numerical methods for efficient GW calculations and the applications in low-dimensional systems

Abstract

Abstract The GW approximation (GWA) of quasiparticle self-energy is a well-established method for quantitative description of single-particle excitations and has been successfully applied to a wide range of systems. However, the relatively huge computational cost and non-trivial convergence behavior hinder the applications of the GWA in large and complex material systems. Due to the recent interest in low-dimensional materials, such as two-dimensional (2D) nanosheets and nanoclusters, researchers have focused on designing novel numerical methods for efficient and accurate prediction of quasiparticle excitations in low-dimensional materials. This topical review recaps the basic concepts of the GWA and presents several conventional code implementations. We review some of the most recent advances in innovative GWA methods and reformulations, focusing on applications to 2D and localized systems.