Mott insulators in disguise

The Mott transition is the phenomenon of charge localization driven solely by electron-electron interaction. The other quantum numbers carried by the electrons, i.e. the spin and, eventually, the orbital, remain instead free to delocalise through the lattice. As such, the Mott phase is characterized by a disentanglement of the charge from the other quantum numbers, making its description unaccessible to independent particle schemes, where all the electron's quantum numbers are entangled in the single particle excitation. However, at low enough temperatures any realistic Mott insulator must get rid of the spin and, eventually, orbital entropies by some kind of ordering that occurs through a symmetry breaking mechanisms. This generically leads to a disguising of the Mott phase as a conventional band insulator, now well describable by independent particle theories. In this Thesis we analyze the occurrence of such disguised Mott insulators in the simplest generalizations of the half-filled single-band Hubbard model: lattice models still with occupation of one electron per site, but where the electron carries an additional two valued orbital quantum number, besides the spin one. We consider two distinct mechanisms that lift the orbital degeneracy, i.e. the case of two bands equal in shape but different in bandwidth, and the case of two bands equal in bandwidth but different in shape. The phase diagram of the former model includes a region of coexisting magnetic and orbital orders, as well as a topological Lifshitz transition from a two band metal to a single band one. The second model with two equal bandwidth but different shape bands is designed to mimic vanadium dioxide, and thus include a coupling to antiferro-distortive lattice modes. This model accurately describes several experimental results such as the transition temperature from the monoclinic insulator to the rutile metal as well as the size and the interband character of the gap of the insulating phase. Our results underline the leading role played by the local interaction in stabilising the distorted insulator