Efficient many-body perturbation theory calculations in 2D materials*

Many-body perturbation theory methods, such as the GW approximation, are able to accurately predict quasiparticle (QP) properties of several classes of materials. However, evaluating the GW self-energy is often computationally challenging due to the frequency and momentum convolutions. These difficulties were recently addressed by the developments of the multipole approximation (MPA) [1,2] and the W-av [3,4] methods. MPA gives an effective representation of the frequency dependence of the screened Coulomb interaction for both semiconductors and metals. An appropriate sampling of the polarizability in the frequency complex plane and a multi-pole interpolation lead to an accuracy comparable with full-frequency methods at much lower computational cost. W-av drastically improves the convergence of the QP corrections of 2D semiconductors with respect to the Brillouin zone sampling, by combining a Monte Carlo integration with an interpolation scheme able to represent the screened potential between the calculated grid points. In this work, we present the theoretical schemes and show examples of the accuracy and computational gains when applied to prototype 2D systems.