It is suggested that many-body quantum chaos appears as the spontaneous symmetry breaking of unitarity in interacting quantum many-body systems. It has been shown that many-body level statistics, probed by the spectral form factor (SFF) defined as $K(\eta ,t)=\langle |\mathrm{Tr}exp(-\eta H+itH){|}^2\rangle$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the “unitary” $\eta =0$ case is different from the $\eta \to 0^{\pm }$ limit, with the latter leading to a finite mass of these modes due to interactions. This mass suppresses a rapid exponential ramp in the SFF, which is responsible for the fast emergence of Poisson statistics in the noninteracting case, and gives rise to a nontrivial random matrix structure of many-body levels. The interaction-induced mass in the SFF shares similarities with the dephasing rate in the theory of weak localization and the Lyapunov exponent of the out-of-time-ordered correlators.

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• Quantum chaos
• Nonlinear sigma model
• Path-integral methods
• Random matrix theory