Interactions and phase transitions on graphene's honeycomb lattice

TL;DR

This paper derives the low-energy theory of interacting electrons on graphene's honeycomb lattice, exploring quantum critical points, phase transitions, and the effects of Coulomb interactions and magnetic fields.

Contribution

It establishes a connection between the Hubbard model on graphene and the Gross-Neveu universality class, providing new insights into phase transitions in this system.

Findings

Identification of a semi-metal to antiferromagnetic insulator quantum critical point

Conjecture of the universality class for physical N=2 case

Discussion of Coulomb and magnetic field effects on phase behavior

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.