Stochastic Many-Body Perturbation theory beyond the GW approximation

I will present new stochastic approaches for the computation of electronic excitations within the many-body perturbation theory. The new methods go beyond the popular G₀W₀ approximation and include non-local vertex corrections in the screened Coulomb interaction (G₀W₀^tc) as well as in the self-energy (G₀W₀^tcΓ_X). I will discuss a stochastic implementation in real-time and space which scales linearly with the number of electrons. I will demonstrate that the vertex corrections predominantly affect unoccupied states and that they are crucial for predicting of the corresponding quasiparticle energies.