It is suggested that many-body quantum chaos appears as 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 $K(beta,t)=langle|{rm Tr}, exp(-beta H + itH)|^2rangle$, is dominated by a diffusion-type mode in a field theory analysis. The key finding of this paper is that the unitary $beta=0$ case is different from the $beta to 0^+$ 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 non-interacting case, and gives rise to a non-trivial 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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