Stochastic many-body  perturbation theory for electronic excitations

I will present new developments in stochastic approaches to many-body perturbation theory, which accelerate calculations of quasiparticle energies and increase their accuracy. A new concept of sparse stochastic compression is used to speed up computations and leads to a decrease of statistical errors in large (finite and periodic) systems. It is thus feasible to treat systems with more than 10,000 electrons and simulate their photoemission spectra. Predictions of quasiparticle energies are improved by a simplified self-consistency approach, which can be implemented at zero additional cost irrespective of the system size. Finally, I will introduce stochastic vertex corrections which allow  application of beyond-GW approaches to large systems.