Emergence of many-body quantum chaos via spontaneous breaking of unitarity

Abstract

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 $K(\ensuremath{\eta},t)=\ensuremath{\langle}|\mathrm{Tr}exp(\ensuremath{-}\ensuremath{\eta}H+itH){|}^{2}\ensuremath{\rangle}$, is dominated by a diffuson-type mode in a field theory analysis. The key finding of this Letter is that the ``unitary'' $\ensuremath{\eta}=0$ case is different from the $\ensuremath{\eta}\ensuremath{\rightarrow}{0}^{\ifmmode\pm\else\textpm\fi{}}$ 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.