Interactions and phase transitions on graphene's honeycomb lattice

Abstract

The low-energy theory of interacting electrons on graphene's two-dimensional honeycomb lattice is derived and discussed. In particular, the Hubbard model in the large-N limit is shown to have a semi-metal - antiferromagnetic insulator quantum critical point in the universality class of the Gross-Neveu model. The same equivalence is conjectured to hold in the physical case N=2, and its consequences for various physical quantities are examined. The effects of the long-range Coulomb interaction and of the magnetic field are discussed.

four pages, one figure; few typos corrected, references added

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• Electric Field Effect in Atomically Thin Carbon Films
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• Chiral symmetry breaking in ${\mathrm{QED}}_3$ in presence of irrelevant interactions: a renormalization group study
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