  We propose a new dynamical method to connect equilibrium quantum phase
transitions and quantum coherence using out-of-time-order correlations (OTOCs).
Adopting the iconic Lipkin-Meshkov-Glick and transverse-field Ising models as
illustrative examples, we show that an abrupt change in coherence and
entanglement of the ground state across a quantum phase transition is
observable in the spectrum of multiple quantum coherence (MQC) intensities,
which are a special type of OTOC. We also develop a robust protocol to obtain
the relevant OTOCs using quasi-adiabatic quenches through the ground state
phase diagram. Our scheme allows for the detection of OTOCs without
time-reversal of coherent dynamics, making it applicable and important for a
broad range of current experiments where time-reversal cannot be achieved by
inverting the sign of the underlying Hamiltonian.
