  We introduce an approach to treat localized correlated electronic states in
the otherwise weakly correlated host medium. Here, the environment is
dynamically downfolded on the correlated subspace. It is captured via
renormalization of one and two quasiparticle interaction terms which are
evaluated using many-body perturbation theory. We outline the strategy on how
to take the dynamical effects into account by going beyond the static limit
approximation. Further, we introduce an efficient stochastic implementation
that enables treating the host environment with a large number of electrons at
a minimal computational cost. For small explicitly correlated subspace, the
dynamical effects are critical. We demonstrate the methodology by reproducing
optical excitations in the negatively charged NV center defect in diamond, that
are in excellent agreement with experimental results.
