Many-body physics of cavity embedded quantum matter

Controlling the properties of quantum matter is a central goal of condensed matter physics. In recent years, cavity embedding—that is, shaping the electromagnetic environment surrounding a material by placing it inside a cavity—has emerged as a new potential tuning knob. While such concepts were first successfully explored with ultracold atomic clouds, more recent experiments have demonstrated their feasibility in solid-state systems. Despite the differences between these platforms, they share a key feature: the coexistence of degrees of freedom with distinct levels of locality. On one hand, electrons or atoms exhibit local dynamics (hopping, interactions), while on the other, cavity modes are typically delocalized across the entire system. The study of this unconventional quantum many-body framework—investigated through aspects such as phase transitions, topology, and dynamical properties—constitutes the main focus of this thesis.