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...
