  In recent times it has been observed that signatures of equilibrium quantum
criticality surprisingly show up in many-body systems which are manifestly far
from equilibrium. We explore such scenarios in interacting spin systems subject
to a quench and develop a robust method to systematically probe ground state
critical physics through nonequilibrium post-quench dynamics. Analyzing
late-time behavior of finite string-like observables, we find emerging sharp
signatures of equilibrium criticality. Specifically, these observables
accurately detect equilibrium critical points and universal scaling exponents
after long times following a quench. This happens despite the fact that the
analyzed systems are strongly chaotic/ergodic and is interestingly due to a
strong memory of the initial conditions retained by these observables after
quench. We find that our results can also be used to explain critical
signatures in post-quench domain formation, seen in a recent experiment with
trapped ion quantum simulators.
