Strongly Coupled Graphene on the Lattice

TL;DR

This paper reviews the application of Lattice Field Theory to graphene, emphasizing its relativistic electron properties, and discusses theoretical models and future research directions for strongly correlated states.

Contribution

It provides a comprehensive overview of lattice theories of graphene, including the Hubbard and Dirac models, and explores the potential of lattice calculations for response functions.

Findings

Graphene's electronic properties resemble relativistic Dirac fermions.

Lattice theories like Hubbard and Dirac models are key to understanding graphene.

Lattice Field Theory can be used to compute response functions such as conductivity.

Abstract

The two-dimensional carbon allotrope graphene has recently attracted a lot of attention from researchers in the disciplines of Lattice Field Theory, Lattice QCD and Monte Carlo calculations. This interest has been prompted by several remarkable properties of the conduction electrons in graphene. For instance, the conical band structure of graphene at low energies is strongly reminiscent of relativistic Dirac fermions. Also, due the low Fermi velocity of v_F = c/300, where c is the speed of light in vacuum, the physics of the conduction electrons in graphene is qualitatively similar to Quantum Electrodynamics in a strongly coupled regime. In turn, this opens up the prospect of the experimental realization of gapped, strongly correlated states in the electronic phase diagram of graphene. Here, we review the experimental and theoretical motivations for Lattice Field Theory studies of graphene, and describe the directions that such research is likely to progress in during the next few years. We also give a brief overview of the two main lattice theories of graphene, the hexagonal Hubbard theory and the low-energy Dirac theory. Finally, we describe the prospect of extracting response functions, such as the electric conductivity, using Lattice Field Theory calculations.