Abstract
The metal-insulator transition has been a subject of intense research since Mott first proposed that the metallic behavior of interacting electrons could turn to an 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. Thereby, we find that the transition is continuous, and we 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. Furthermore, we 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, not by 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.
10 More- Received 24 March 2015
DOI:https://doi.org/10.1103/PhysRevX.6.011029
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Published by the American Physical Society
Physics Subject Headings (PhySH)
Popular Summary
How a metal changes its properties to become an insulator has been a fascinating topic since the advent of quantum mechanics. The so-called “band theory,” which neglects electron interactions, was initially rather successful at addressing this open question. However, researchers soon realized that this theory was incomplete because several materials become insulators even when the band theory predicted metallic behavior. The effect of electrons cannot be described by an average effective external potential; instead, each electron in the lattice strongly interacts with the nearby electrons because of the strong repulsive Coulomb interaction. Here, we present very accurate calculations of interacting electrons in which the electron correlations are effective only when two electrons occupy the same site.
We focus on two completely different lattice models that are variations on Hubbard models in two dimensions. The two lattices have between roughly 100 and 3000 sites, and one electron can occupy each site. We demonstrate a very interesting metal-insulator transition as the electron correlation increases, and our essentially exact calculations enable us to study the metal-insulator transition with unprecedented accuracy. The two models exhibit the same physics close to the transition, exactly as in a conventional phase transition close to the critical temperature.
Our study determines, for the first time, the universality class of the metal-insulator transition of interacting Dirac electrons. We expect that our findings will be relevant not only to condensed-matter materials but also to Dirac fermions in particle physics.