  Dynamical phase transition (DPT) characterizes the abrupt change of dynamical
properties in nonequilibrium quantum many-body systems. It has been
demonstrated that extra quantum fluctuating modes besides the conventional
order parameter field can drastically change the properties of equilibrium
phase transitions. However, the counterpart phenomena in DPTs have rarely been
explored. Here, we study the DPT in the Dirac system after a sudden quench, and
find that the fermion fluctuations can round a putative first-order DPT into a
dynamical critical point, which is referred to as a fermion-induced dynamical
critical point (FIDCP). It is also a nonthermal critical point, in which the
universal short-time scaling behavior emerges despite the system goes through a
first-order transition after thermalization. In the novel scenario of FIDCP,
the quantum Yukawa coupling $g_q$ is indispensable for inducing the FIDCP
albeit irrelevant in the infrared scale. We call these variables {\it
indispensable irrelevant scaling variables}. Moreover, a dynamical tricritical
point which separates the first-order DPT and the FIDCP is discovered by tuning
this indispensable irrelevant scaling variable. We further mention possible
experimental realizations.
