  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 Green's 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.
