Universal quantum criticality in the metal-insulator transition of two-dimensional interacting Dirac electrons

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.