Efficient 𝐺⁢𝑊 calculations via interpolation of the screened interaction in momentum and frequency space. The case of graphene

The 𝐺⁢𝑊 self-energy may become computationally challenging to evaluate because of frequency and momentum convolutions. These difficulties were recently addressed by the development of the multipole approximation (MPA) and the W-av methods: MPA accurately approximates full-frequency response functions using a small number of poles, while W-av improves the convergence with respect to the 𝐤-point sampling in 2D materials. In this work, we (𝑖) present a theoretical scheme to combine them, and (𝑖⁢𝑖) apply the newly developed approach to the paradigmatic case of graphene. Our findings show an excellent agreement of the calculated QP band structure with angle resolved photoemission spectroscopy (ARPES) data. Furthermore, the computational efficiency of MPA and W-av allows us to explore the logarithmic renormalization of the Dirac cone. To this aim, we develop an analytical model, derived from a Dirac Hamiltonian, that we parametrize using ab initio data. The comparison of the models obtained with the plasmon pole approximation (PPA) and MPA results highlights an important role of the dynamical screening in the cone renormalization.