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

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.

5 revtex pages: new figure, new eqs. 20-22, and the discussion of the experiment of Jiang et al added (v2). Cosmetic changes (v3). Accepted in PRB

References in corpus (4)

• Unconventional Integer Quantum Hall effect in graphene
• Dissipative Quantum Hall Effect in Graphene near the Dirac Point
• Theory of integer quantum Hall effect in graphene
• Spontaneous Symmetry Breaking and Quantum Hall Effect in Graphene

Cited by in corpus (15)

• AC conductivity of graphene: from tight-binding model to 2+1-dimensional quantum electrodynamics
• Theory of interacting electrons on the honeycomb lattice
• Supercritical Coulomb center and excitonic instability in graphene
• Dynamics in the quantum Hall effect and the phase diagram of graphene
• Chiral asymmetry of the Fermi surface in dense relativistic matter in a magnetic field
• Edge states, mass and spin gaps, and quantum Hall effect in graphene
• Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
• The plasma picture of the fractional quantum Hall effect with internal SU(K) symmetries
• Zero-energy states and fragmentation of spin in the easy-plane antiferromagnet on a honeycomb lattice
• Edge states on graphene ribbon in magnetic field: interplay between Dirac and ferromagnetic-like gaps
• Entanglement Skyrmions in multicomponent quantum Hall systems
• Quantum critical scaling in magnetic field near the Dirac point in graphene
• Toward theory of quantum Hall effect in graphene
• Massive Dirac fermions and the zero field quantum Hall effect
• $\bar{\psi }\psi$-condensate in constant magnetic fields