Many Body Perturbation Theory, Dynamical Mean Field Theory and All That

This chapter gives an introduction to the theoretical description of strongly correlated materials from first principles. Recent progress in the numerical solution of effective quantum impurity problems within continuous-time Quantum Monte Carlo schemes has opened the way to efficient dynamical mean field theory-based simulations of finite-temperature properties of correlated solids. Here, we review the combinations of dynamical mean-field theory (DMFT) with density functional theory (DFT) or first-order many-body perturbation theory (the so-called “GW approximation”) from a general functional formulation point of view, putting them into perspective with dual fermion and boson approaches. The goal of these theoretical constructions is to retain the many-body aspects of local atomic physics within the extended solid. We will describe the current state-of-the-art and future challenges.