Stochastic Vertex Corrections: Linear Scaling Methods for Accurate Quasiparticle Energies.

New stochastic approaches for the computation of electronic excitations are developed within the many-body perturbation theory. Three approximations to the electronic self-energy are considered: G0W0, G0W0tc, and G0W0tcΓX. All three methods are formulated in the time domain, and the latter two incorporate nonlocal vertex corrections. In the case of G0W0tcΓX, the vertex corrections are included both in the screened Coulomb interaction and in the expression for the self-energy. The implementation of the three approximations is verified by comparison to deterministic results for a set of small molecules. The performance of the fully stochastic implementation is tested on acene molecules, C60 and PC60BM. The vertex correction appears crucial for the description of unoccupied states. Unlike conventional (deterministic) approaches, all three stochastic methods scale linearly with the number of electrons.