  As a measure of information scrambling and quantum chaos, out-of-time-ordered
correlator (OTOC) plays more and more important role in many different fields
of physics. In this work, we verify that the OTOC can also be used as a prober
of the excited-state quantum phase transition (ESQPT) in a quantum many body
system. By using the exact diagonalization method, we examine the dynamical
properties of OTOC in the Lipkin model, which undergoes an ESQPT. We
demonstrate that the OTOC exhibits a remarkable distinct evolution behaviors in
different phases of ESQPT. Therefore, the presence of an ESQPT in the quantum
many body system can be clearly signaled by the different dynamical behaviors
of the OTOC. In particular, we show that the steady state value of the OTOC
serves as the order parameter of the ESQPT. Our results highlight the
connections between the OTOC and ESQPT, which enable one to use OTOC for
experimental tests ESQPTs in quantum many body systems.
