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The GW self-energy may become computationally challenging to evaluate becauseof frequency and momentum convolutions. These difficulties were recentlyaddressed by the development of the multipole approximation (MPA) and the W-avmethods: MPA accurately approximates full-frequency response functions using asmall number of poles, while W-av improves the convergence with respect to thek-point sampling in 2D materials. In this work we (i) present a theoreticalscheme to combine them, and (ii) apply the newly developed approach to theparadigmatic case of graphene. Our findings show an excellent agreement of thecalculated QP band structure with angle resolved photoemission spectroscopy(ARPES) data. Furthermore, the computational efficiency of MPA and W-av allowsus to explore the logarithmic renormalization of the Dirac cone. To this aim,we develop an analytical model, derived from a Dirac Hamiltonian, that weparameterize using ab-initio data. The comparison of the models obtained withPPA and MPA results highlights an important role of the dynamical screening inthe cone renormalization.

Efficient GW calculations via the interpolation of the screened interaction in momentum and frequency space: The case of graphene