Title: Minimal models for many-body quantum chaos
Abstract:
I will present a class of solvable models for the study of quantum chaos in extended many-body systems. They are defined on a chain of spins where the time evolution is obtained by subsequently applying random gates to adjacent sites. Periodicity in time is enforced by applying exactly the same set of random gates after each period. In the limit of large spins, this class of models becomes exactly solvable by using many-body diagrammatic techniques. This gives access to exact predictions for the behavior of the entanglement growth and the out-of-time-order correlators in generic chaotic systems. Additionally, I will discuss the spectral correlation between eigenphases of the Floquet evolution operator. I will show with an exact calculation that the general conjecture about level repulsion and the emergence of random matrix (RM) behavior is confirmed in these models. Moreover, beyond RMT due to locality and spatial extension, there emerges a timescale (Thouless time) for the onset of quantum chaos.