We report on the dynamical formation of exceptional degeneracies in basic correlation functions of non-integrable one- and two-dimensional systems quenched to the vicinity of a critical point. Remarkably, fine-tuned semi-metallic points in the phase diagram of the considered systems are thereby promoted to topologically robust non-Hermitian (NH) nodal phases emerging in the coherent long-time evolution of a dynamically equilibrating system. In the framework of non-equilibrium Greens function methods within the conserving second Born approximation, we predict observable signatures of these novel NH nodal phases in simple spectral functions as well as in the time-evolution of momentum distribution functions.
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