Efficient Treatment of Dynamical Renormalizations and Multiscale Approaches Through Stochastic Many-body Methods

Efficient numerical implementations enable applying the many-body perturbation theory to realistic systems. Stochastic approaches based on sampling single-particle states, propagators, and interactions are particularly successful in combination with one-shot perturbative corrections. These methods allow simulating nanoscale problems with thousands and tens of thousands of electrons. I will present our work on expanding this framework to (i) enable self-consistent treatments, and (ii) describe more complex quantum phenomena arising from strong interactions of excited states. The new implementation allows to quickly access both diagonal and off-diagonal elements of the self-energy, update the single-particle states, and identify energy regions characterized by strong couplings among quasiparticles. Further, I will present new randomized sampling methods to efficiently compute the dynamical renormalization via stochastic constrained RPA (and beyond RPA) methods within arbitrarily selected strongly interacting subspace. The approach is general and requires only minimal computational resources (in the order of 100s of CPU hours for systems with 10,000 electrons). I will outline the route towards multiscale simulations in which the weakly (and moderately) correlated electronic states are treated by stochastic perturbation theory combined with the embedding of strongly correlated states.