  The development of numerical methods capable of simulating realistic
materials with strongly correlated electrons, with controllable errors, is a
central challenge in quantum many-body physics. Here we describe how a hybrid
between self-consistent second order perturbation theory and exact
diagonalization can be used as a multi-scale solver for such systems. Using a
quantum impurity model, generated from a cluster dynamical mean field
approximation to the 2D Hubbard model, as a benchmark, we show that our method
allows us to obtain accurate results at a fraction of the cost of typical Monte
Carlo calculations. We test the behavior of our method in multiple regimes of
interaction strengths and doping of the model. The algorithm avoids
difficulties such as double counting corrections, frequency dependent
interactions, or vertex functions. As it is solely formulated at the level of
the single-particle Green's function, it provides a promising route for the
simulation of realistic materials that are currently difficult to study with
other methods.
