Quasiparticle spectra obtained through stochastic many-body methods

We present the linearly scaling stochastic approach to many-body perturbation theory and to calculations of quasiparticle energies in $G_0W_0$ approximation and beyond. Our approach overcomes the steep scaling of conventional deterministic schemes. Further, it allows a simple incorporation of higher order interactions (vertex corrections). Exemplifying on covalently bonded systems (nanocrystals and polymer chains), we show practical calculations of quasiparticle spectra, and self-energies for large systems with thousands of electrons. The linear scaling is fundamental nature of our approach, which does not rely on a particular character of the electronic structure (e.g., there is no need for sparsity of the density matrices). The scaling prefactor is small so the stochastic $G_0W_0$ method is thus a method of choice for all systems from few tens to thousands -- and in the near horizon hundreds of thousands -- of electrons.