Interplay between electron-phonon interaction and electron-electron repulsion in multiorbital Hubbard models

In the last decades, a lot of effort has been devoted to the study of strongly correlated systems with a multi-orbital electronic structure. The motivation of this surge has been largely due to iron-based superconductors, but this investigation has led to identify several distinctive features which are relevant to different classes of materials. The solution of simple multi-orbital models has revealed novel phenomena which are not accessible in single-band models such as orbital-selective Mott physics and Hund’s metals. In this thesis we make important steps towards a more complete and general description of two-orbital correlated systems, studying in detail, by means of Dynamical Mean-Field Theory, the role of electron-phonon coupling and its interplay with the electron-electron interactions, as well as the effect of interaction terms with a lower symmetry with respect to the popular Hubbard-Kanamori model. In all our analysis, we add step by step the different interaction terms analyzing their effects on the system and their mutual interplay. In particular we consider a model which is potentially relevant for different families of high-temperature superconductors (such as the fullerides and the iron-based superconductors), but also for manganites and chromates. The model features the interplay between a single Jahn-Teller phonon mode and the electron-electron interactions parametrized by the Hubbard U and the Hund’s coupling. We also analyze the dynamics of the phonons and the resulting retardation effects, studying their evolution between the two limiting situations given by the adiabatic limit and the antiadiabatic one. Finally in the last part of the thesis we consider a purely electronic model relaxing the relation between different electron-electron interaction terms. In this way we address the role of the inter-orbital interaction and the Hund’s coupling on the orbital-selective Mott transition.