  The out-of-time-ordered correlator (OTOC) is central to the understanding of
information scrambling in quantum many-body systems. In this work, we show that
the OTOC in a quantum many-body system close to its critical point obeys
dynamical scaling laws which are specified by a few universal critical
exponents of the quantum critical point. Such scaling laws of the OTOC imply a
universal form for the butterfly velocity of a chaotic system in the quantum
critical region and allow one to locate the quantum critical point and extract
all universal critical exponents of the quantum phase transitions. We
numerically confirm the universality of the butterfly velocity in a chaotic
model, namely the transverse axial next-nearest-neighbor Ising model, and show
the feasibility of extracting the critical properties of quantum phase
transitions from OTOC using the Lipkin-Meshkov-Glick (LMG) model.
