  The metal-insulator transition has been a subject of intense research since
Nevil Mott has first proposed that the metallic behavior of interacting
electrons could turn to the insulating one as electron correlations increase.
Here, we consider electrons with massless Dirac-like dispersion in two spatial
dimensions, described by the Hubbard models on two geometrically different
lattices, and perform numerically exact calculations on unprecedentedly large
systems that, combined with a careful finite size scaling analysis, allow us to
explore the quantum critical behavior in the vicinity of the interaction-driven
metal-insulator transition. We find thereby that the transition is continuous
and determine the quantum criticality for the corresponding universality class,
which is described in the continuous limit by the Gross-Neveu model, a model
extensively studied in quantum field theory. We furthermore discuss a
fluctuation-driven scenario for the metal-insulator transition in the
interacting Dirac electrons: the metal-insulator transition is triggered only
by the vanishing of the quasiparticle weight but not the Dirac Fermi velocity,
which instead remains finite near the transition. This important feature cannot
be captured by a simple mean-field or Gutzwiller-type approximate picture, but
is rather consistent with the low energy behavior of the Gross-Neveu model.
