Non-Equilibrium Phenomena in Strongly Correlated Systems

Correlated systems are a wide class of materials in which the strong electron-electron repulsion is the origin of very fascinating and unusual properties, among which metal-to-insulator transitions and high temperature superconductivity are the most striking examples. In the recent years, the fast development of non-adiabatic probing techniques opened new interesting perspectives for the investigation of such materials in non-equilibrium conditions. In this thesis, we discuss the theoretical description of few relevant cases which represent different examples of non-equilibrium phenomena in correlated materials. In particular, we will focus on the dynamics following a sudden excitation and the coupling to an external driving field. As a first example we consider the dynamics across a phase transition, namely we explore the possibility of driving a phase transition as the result of a sudden excitation, as e.g. the coupling with a short light pulse. We consider systems showing different equilibrium phases and study the conditions under which the off-equilibrium dynamics may lead to non-trivial dynamical phase transitions. A different case is represented by the dynamics induced by a driving electric field. This problem is particularly relevant for the possible applications of correlated materials in electronic devices. Here we consider the paradigmatic case of a correlated material coupled to external sources which impose a finite bias across the system. We analyze the formation and the properties of the non-equilibrium stationary states in which a finite current flows through the system. This allows us to study the non-linear response properties of a correlated system. In this context, a particularly relevant aspect is the problem of the dielectric breakdown of a Mott insulator, namely the formation of conducting states in the Mott insulating phase. In this thesis we explore different mechanisms leading to such possibility. First we discuss a quantum tunneling mechanism of carriers driven across the insulating gap by the effect of strong electric-fields. Eventually, we discuss the possibility of a resistive transition from an insulating to a metallic state induced by the application of an external electric-field