Quasiparticle Energies and Dyson orbitals from Stochastic MBPT in an Optimally Localized Basis*

The GW approximation for excited electronic states successfully predicts quasiparticle (QP) energies and states. This comes at large computational expense: in conventional implementations, we are limited to studying systems with 100s of electrons. Stochastic methods have recently succeeded in predicting QP energies for materials with unprecedented sizes (>10,000 electrons). Here, we extend the methodology to predict QP energies and Dyson orbitals in highly inhomogeneous systems. The key strategy is to downfold the many-body Hamiltonian, i.e.,  reduce a large system into an active subspace (defined by localized QP basis) and an effective environment. By using stochastically sampled vectors to represent the environment subspace, we are able to find QP energies in the active space from a much lower dimensional problem, provided that the dynamical response is entirely included in our solution. This treatment is completely basis-independent. We demonstrate the success of this method by solving for the orbital energies of a small molecule on a large gold substrate and a nanoparticle.