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 fermions with massless Dirac-like dispersion on two-dimensional lattices and perform numerically exact quantum Monte Carlo 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 [1,2]. We find thereby that the transition is continuous without an intermediate phase  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 Mott metal-insulator transition in the Dirac fermions: it is triggered only by the vanishing of the quasiparticle weight but not the Dirac Fermi velocity, which instead remains finite nearby the transition . This important feature cannot be captured by simple mean-field or Gutzwiller-type approximate pictures. Lastly, we briefly discuss quantum criticality of a metal-superconductivity transition of interacting Dirac fermions on the triangular lattice.
 S. Sorella, Y. Otsuka, and S. Yunoki, Sci. Rep. 2, 992 (2012).
 Y. Otsuka, S. Yunoki, and S. Sorella, Phys. Rev. X 6, 011029 (2016).