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The use of effective local Coulomb interactions that are dynamical, that is,frequency-dependent, is an efficient tool to describe the effect of long-rangeCoulomb interactions and screening thereof in solids. The dynamical characterof the interaction introduces the coupling to screening degrees of freedom suchas plasmons or particle-hole excitations into the many-body description. Wesummarize recent progress using these concepts, putting emphasis on dynamicalmean field theory (DMFT) calculations with dynamical interactions ("doublydynamical mean field theory"). We discuss the relation to the combined GW+DMFTmethod and its simplified version "Screened Exchange DMFT", as well as thecumulant schemes of many-body perturbation theory. On the example of the simpletransition metal SrVO3, we illustrate the mechanism of the appearance ofplasmonic satellite structures in the spectral properties, and discussimplications for the low-energy electronic structure.

Electronic Polarons, Cumulants and Doubly Dynamical Mean Field Theory: Theoretical Spectroscopy for Correlated and Less Correlated Materials