  Quantum phase transitions are central to our understanding of why matter at
very low temperatures can exhibit starkly different properties upon small
changes of microscopic parameters. Accurately locating those transitions is
challenging experimentally and theoretically. Here we show that the antithetic
strategy of forcing systems out of equilibrium via sudden quenches provides a
route to locate quantum phase transitions. Specifically, we show that such
transitions imprint distinctive features in the intermediate-time dynamics, and
results after equilibration, of local observables in quantum-chaotic spin
chains. Furthermore, we show that the effective temperature in the expected
thermal-like states after equilibration can exhibit minima in the vicinity of
the quantum critical points. We discuss how to test our results in experiments
with Rydberg atoms, and explore nonequilibrium signatures of quantum critical
points in models with topological transitions.
