Abstract
I will discuss the role of dynamical correlations in predicting electronic excitation spectra in
systems ranging from molecules to condensed systems with thousands of electrons. Using the
many-body perturbation theory based on Green's function formalism, we can study individual
quasiparticle states and even non-trivial quasiparticle-quasiparticle interactions. First, I will
exemplify these approaches on small test systems, for which we can find numerically exact
excitation spectra and study the role of various theoretical formulations. Second, I will show
practical applications to quantum materials, e.g., in studying the correlated phenomena for
localized moire states in twisted bilayer graphene. For the latter, we employ our real-space
and real-time stochastic methods and combine them with embedding and ab-initio

downfolding onto explicitly correlated Hamiltonians. This framework, leveraging efficient low-
scaling numerical techniques, is generally applicable to (quantum) material science and

chemistry problems and constitutes an ideal platform for simulating complex nanoscale
systems with thousands of electrons at a minimal computational cost.