Single-particle universality of the many-body spectral form factor

The dynamics of many-body systems is extraordinarily rich, including phenomena such as chaos and thermalization. A cornerstone of our understanding of the late-time dynamics of interacting quantum systems is random matrix theory (RMT), detected through measures of spectral statistics such as the Spectral Form Factor (SFF). In general, computing the SFF is a numerically difficult problem and it remains an outstanding challenge to design toy models which effectively probe different dynamical regimes. We introduce a model of free fermions in the presence of spatially correlated disorder which is designed to study random matrix statistics at the single-particle level and for which the SFF can be computed exactly. In contrast to standard RMT predictions, which predict linear growth of the SFF in time, our model grows through a series of exponential ramps. After analyzing the exactly solvable point, we will introduce interactions and discuss the crossover to a linear ramp, that is, the crossover from single-particle to many-body random matrix universality. The structure of the crossover is rich, including a numerical regime in which the SFF exhibits scale invariance consistent with predictions of an ergodicity-breaking transition.