Interplay between global and local properties in many body systems: topological, superconducting and magnetic phases

In this presentation, I will discuss the interplay between global and local properties in many-body systems. This study explores three key areas: topological, superconducting, and magnetic systems, which hold significant promise for advancing quantum technologies. In order to harness their potential, it is necessary to understand and control the correspondent orderings. Here, we show how to control and manipulate topological phases by leveraging the coupling to a QED cavity. Furthermore, we address the strengthening of superconducting correlations by placing isoelectronic defects in the lattice structure. In addition, we study the impact of these defects on magnetic properties, revealing a mechanism that leads to significant changes in magnetization linked to charge fluctuations.