SO(3) symmetry between Neel and ferromagnetic order parameters for graphene in a magnetic field

TL;DR

This paper explores the near-symmetry between Neel and ferromagnetic order parameters in graphene under a magnetic field, revealing a quantum critical point and explaining the incompressible state at filling factor one.

Contribution

It uncovers an approximate SO(3) symmetry in the continuum limit of the Hubbard model for graphene and analyzes symmetry breaking effects leading to a quantum critical point.

Findings

Near-symmetry of order parameters in continuum limit

Quantum critical point where antiferromagnetic order vanishes

Incompressible state at filling factor one explained by finite N3

Abstract

I consider the Hubbard model of graphene in an external magnetic field and in the Hartree-Fock approximation. In the continuum limit, the ground state energy at half filling becomes nearly symmetric under rotations of the three-component vector (N1,N2,m), with the first two components representing the Neel order parameter orthogonal to and the third component the magnetization parallel with the external magnetic field. When the symmetry breaking effects arising from the lattice, Zeeman coupling, and higher Landau levels are included the system develops a quantum critical point at which the antiferromagnetic order disappears and the magnetization has a kink. The observed incompressible state at filling factor one is argued to arise due to a finite third component of the Neel order parameter at these electron densities. Recent experiments appear consistent with vanishing N1 and N2, and finite N3, at the filling factors zero and one, respectively.