Stochastic methods for many-body perturbation theory*

We present the stochastic approach to formulation of the many-body perturbation theory and to calculations of the quasiparticle energies in the G₀W₀ approximation . General principles of the stochastic methods in TDDFT, GW and BSE will be discussed. We demonstrate how our approach overcomes the deficiencies of the conventional schemes and that with increasing system size it becomes effectively less expensive leading to approximately linear scaling of the algorithm. This is a fundamental nature of our method, which does not rely on particular character of the electronic structure (e.g. sparsity of the density matrices). In addition we demonstrate that the scaling prefactor is small and the stochastic method is thus a method of choice for all systems from few tenths to thousands of electrons.