## Metal-insulator transitions

It is widely accepted that the intriguing behavior of many strongly correlated systems has origin in their proximity to a Mott insulating state. Thus, understanding the properties of the metal-insulator transitions (MIT)s is a key challenge to condensed matter physics (see fig. 1). In this context, we investigated the MIT in widely accepted models for both late transition-metal oxides (TMO) and heavy-fermions (HF) materials. These compounds are characterized by the coexistence of conduction band electrons with more localized d/ f -orbital electrons. At integer filling the competition between electronic interaction and Kondo-type screening can suppress the MIT. Taking into account the coupling to the non-interacting ligand orbitals, we demonstrated the existence of a Mott insulating state in such systems. This state is associated to the Mott localization of singlets states between itinerant and strongly correlated electrons, reminiscent of the Zhang-Rice singlets. This provide and ecient scheme to frame the physics of both TMO and some HF. |

*Starting from these results, we demonstrated the asymmetric nature of the doping driven MIT in presence of ligand-bands for a prototypical HF model.. We pointed out the stringent similarity with the observed behavior in Cuprates superconductors (see fig. 1). Indeed, the MIT induced by particle- doping shares the same universal first-order nature observed in the DMFT solution of the Hubbard model (see fig. 1 right). Conversely, the hole-doping driven MIT realizes a continuous quantum phase- transition (QPT) to a liquid of singlets states (see fig. 1 left). We associated the asymmetric behavior with respect to doping to the distinct electronic configurations of the system, which lead to dramatically different thermodynamic and transport properties.*

*Recently, we investigated the metal-insulator Mott transition in a generalized version of the periodic Anderson model, in which a band of itinerant non-interacting electrons is hybridrized with a narrow and strongly correlated band. Using the dynamical mean-field theory, we show that the precondition for the Mott transition is that the total filling of the two bands takes an odd integer value. Unlike the conventional portrait of the Mott transition, this condition corresponds to a non-integer filling of the correlated band. For an integer constant occupation of the correlated orbitals the system remains a correlated metal at arbitrary large interaction strength. We picture the transition at a non-integer filling of the correlated orbital as the Mott localization of the singlet states between itinerant and strongly interacting electrons, having occupation of one per lattice site. We show that the Mott transition is of the first order and we characterize the nature of the resulting insulating state with respect to relevant physical parameters, such as the charge-transfer energy.*

## Wigner-Mott transition and charge-ordering.

*Motivated by the recent experimental results for the 2D-electrons gas, we applied the concept of Mott transition to describe the Wigner crystallization transition in absence of disorder. Using a simplified model for down-folded electronic gas, we have studied the quantum melting of a charge-ordered “Mott- Wigner” insulator into a Fermi liquid metallic state, as a function of the electronic interaction. This transition can be directly related to the density driven Wigner crystal melting. The MIT was shown to occur in two stages: first the CDW-Insulator gap closes leading to the formation of a CDW-Metallic state; next the CDW order parameter vanishes (linearly), marking the transformation to Fermi liquid state.*