The out-of-equilibrium dynamics of the Sachdev-Ye-Kitaev model (SYK), comprising $N$ Majoranas with random all-to-all four-body interactions, minimally coupled to a Markovian bath modeled by the Lindblad formalism, displays intriguing nontrivial features. In particular, the decay rate toward the steady state is a nonmonotonic function of the bath coupling $\mu$, and the return probability undergoes a first-order dynamical phase transition that eventually becomes a crossover for sufficiently large $\mu$. We provide evidence that these features are closely associated with exceptional point–induced restructuring of the low-energy spectrum of the SYK Liouvillian, in particular those eigenvalues closest to the zero mode corresponding with the steady state. An analytic calculation at small $N$, supported by numerical results for larger $N$, reveals that the value of $\mu \sim 0.1$ at which the exceptional point corresponding to the longest living modes occurs is close to a local maximum of the decay rate. This value marks the start of a region of anomalous equilibration where the relaxation rate diminishes as the coupling to the bath becomes stronger. Moreover, the mentioned change from transition to crossover in the return probability occurs at a larger $\mu \sim 0.3$, corresponding to an increasing density of exceptional point–induced real eigenvalues in the low-energy sector of the Liouvillian spectrum. We expect these features to be generic in the approach to equilibrium in quantum strongly interacting many-body Liouvillians.

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• Exceptional points
• Lindblad equation
• Sachdev-Ye-Kitaev model