Antiferromagnetic critical point on graphene's honeycomb lattice: A functional renormalization group approach

Understand

Electrons on the half-filled honeycomb lattice are expected to undergo a direct continuous transition from the semimetallic into the antiferromagnetic insulating phase with increase of on-site Hubbard repulsion.

• We attempt to further quantify the critical behavior at this quantum phase transition by means of functional renormalization group (RG), within an effective Gross-Neveu-Yukawa theory for an SO(3) order parameter ("chiral Heisenberg universality class").
• Our calculation yields an estimate of the critical exponents $\nu \simeq 1.31$, $\eta_\phi \simeq 1.01$, and $\eta_\Psi \simeq 0.08$, in reasonable agreement with the second-order expansion around the upper critical dimension.
• To test the validity of the present method we use the conventional Gross-Neveu-Yukawa theory with Z(2) order parameter ("chiral Ising universality class") as a benchmark system.