Multicomponent strongly correlated fermions in optical lattices

The present thesis is devoted to the study of physical phenomena emerging from strong correlations in strongly interacting quantum many-body systems with several components. Hubbard models are widely used as minimal models which take into account the interactions between particles and they have been studied in relation to phenomena such as Mott localization, unconventional superconductivity, quantum magnetism and many others. All of these striking phenomena share their origin from the strong correlations among fermions induced by their mutual interactions. Furthermore, condensed matter models are usually realized only in an approximate fashion in actual solid-state systems, making the situation all the more puzzling and hard to be treated analytically or numerically. Therefore, a great effort has been performed to simulate Hubbard models in a system of atoms cooled down to ultra low temperatures and trapped in optical lattices. The most peculiar feature of cold atoms experiments consists in the possibility of tuning relevant physical parameters of the systems, as the density or the interactions among atoms, using laser and/or magnetic fields. This paved the way to the observation of fundamental quantum states of matter as the weakly interacting Bose-Einstein condensate, the super fluid to Mott insulator transition, the super fluid BEC-BCS crossover, the Mott transition in systems of composite fermions and so on. Hence, it is considered of great interest establishing connections between the quantum simulations cold atomic toolbox and systems realized in solid-state physics...