Universal Mechanism of Many-Body Quantum Chaos

The emergence of many-body quantum chaos and thermalization in interacting systems is a topic of great interest, yet its underlying principles remain elusive. This seminar will discuss the universal mechanisms that govern the transition to chaos in quantum many-body systems. First, we will introduce the basic notions of classical and quantum chaos in single-particle systems and explore different facets of quantum chaoticity, such as the distribution of energy levels and the quantum butterfly effect. The concept of many-body quantum chaos will be defined through an approach rooted in random matrix theory, which offers insight into the behavior of the spectral form factor (SFF). Our study highlights the significance of dephasing processes in the behavior of the spectral form factor (SFF) as a function of "time." Interactions introduce dephasing, disrupting interference and leading to a linear-in-time ramp in the SFF, reflecting Wigner-Dyson level repulsion. We will support these findings with a microscopic analysis of a large family of models, which demonstrates that dephasing and spontaneous breaking of unitarity are responsible for the emergence of chaos in many-body systems.