Spectral properties from an efficient analytical representation of the GW self-energy within a multipole approximation

We propose an efficient analytical representation of the frequency-dependent GW self-energy via a multipole approximation (MPA-Σ). Similar to the earlier developed multipole approach for the screening interaction W (MPA-W ) [Phys. Rev. B 104, 115157 (2021)], the multipole-Pade model for the self-energy is interpolated from a small set of values evaluated numerically in the complex frequency plane. As for MPA-W , we show that optimal frequency samplings increase computational efficiency and result in a very accurate description of the self-energy. Crucially, MPA-Σ allows us to build a multipole representation for the interacting Green's function G (MPA-G), providing straightforward evaluation of all the spectral properties. Combining the MPA-W and MPA-Σ schemes considerably reduces the cost of full-frequency self-energy calculations, especially when targeting spectral band structures in a wide energy range. We validate the MPA-Σ approach in bulk Si, Na and Cu, monolayer MoS2, and the NaCl and F2 molecules, as prototypical semiconducting and metallic materials of different dimensionality. Moreover, toy MPA-Σ models with one and two poles and their corresponding MPA-G solutions, are used to examine the quasiparticle picture in different situations, exposing the limitations of the renormalization factor, as defined from the local derivative of the self-energy, to describe the spectral weight of the quasiparticle pole.