• Open Access

Universal Quantum Criticality in the Metal-Insulator Transition of Two-Dimensional Interacting Dirac Electrons

Yuichi Otsuka, Seiji Yunoki, and Sandro Sorella
Phys. Rev. X 6, 011029 – Published 17 March 2016

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.

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  • Received 24 March 2015

DOI:https://doi.org/10.1103/PhysRevX.6.011029

This article is available under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Yuichi Otsuka1,*, Seiji Yunoki1,2,3, and Sandro Sorella1,4,5

  • 1Computational Materials Science Research Team, RIKEN Advanced Institute for Computational Science (AICS), Kobe, Hyogo 650-0047, Japan
  • 2Computational Condensed Matter Physics Laboratory, RIKEN, Wako, Saitama 351-0198, Japan
  • 3Computational Quantum Matter Research Team, RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
  • 4SISSA—International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
  • 5Democritos Simulation Center CNR–IOM Instituto Officina dei Materiali, Via Bonomea 265, 34136 Trieste, Italy

  • *otsukay@riken.jp

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.

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Vol. 6, Iss. 1 — January - March 2016

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It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 3.0 License. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

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