Universal Dephasing Mechanism of Many-Body Quantum Chaos

The quantum chaos conjecture states that the spectral statistics of quantum chaotic systems is universally described by the random matrix theory (RMT). It has been widely used as a diagnostics of quantum chaos, but the theoretical understanding of the underlying mechanism is far from complete. In this work, we show that the dephasing is essential for the emergence of RMT statistics. From RMT prediction, it is expected that if a generic type of interactions is introduced between the particles embedded in a chaotic medium, the exponential-in-time ramp in the spectral form factor is suppressed to a linear one, signaling a transition from single-particle to many-body chaos. We believe that this suppression is caused by the interaction-induced destruction of the quantum phase coherence between periodic paths which are related by independent time translation of each particle’s trajectory. Through a microscopic calculation of a SYK₂+SYK₂² model, we find that, in the chaotic regime, the suppression of the exponential ramp originates from a mass acquired by the diffuson-like collective modes - a manifestation of the dephasing effect due to interactions. In the integrable regime, these collective modes remain massless in the presence of interactions, suggesting the failure of dephasing.