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 ς via a multipole approximation (MPA-ς). The MPA self-energy model is interpolated from a small set of numerical evaluations of ς in the complex frequency plane, similar to the MPA interpolation developed for the screened Coulomb interaction (MPA-W) [D. A. Leon, Phys. Rev. B 104, 115157 (2021)2469-995010.1103/PhysRevB.104.115157]. Crucially, MPA-ς enables a multipole representation for the interacting Green's function G (MPA-G) and, in turn, access to all the spectral properties, including quasiparticle energies (QP) and renormalization factors beyond the linearized QP equation. We validate the MPA-ς and MPA-G approaches for a diverse set of systems: bulk Si, Na, and Cu, monolayer MoS2, the NaCl ion pair, and the F2 molecule. We show that, just as for MPA-W, an appropriate choice of frequency sampling in MPA-ς is critical to guarantee computational efficiency and high accuracy. Moreover, the combined MPA-W and MPA-ς scheme considerably reduces the cost of full-frequency self-energy calculations, especially for spectral band structures over a wide energy range.