Quantum critical behavior in a graphenelike model

We present the results of numerical simulations of a $(2+1)$-dimensional fermion field theory based on a recent proposal for a model of graphene consisting of $N_f$ four-component Dirac fermions moving in the plane and interacting via an instantaneous Coulomb interaction. In the strong-coupling limit we identify a critical number of flavors $N_{fc}=4.8\left(2\right)$ separating an insulating from a conducting phase. This transition corresponds to the location of a quantum critical point, and we use a fit to the equation of state for the chiral order parameter to estimate the critical exponents. Next we simulate $N_f=2$ corresponding to real graphene and approximately locate a transition from strong- to weak-coupling behavior. Strong correlations are evident in the weak-coupling regime.

Figure 1

(Color online) $⟨\overline{\chi }\chi ⟩$ vs $1/g^2$ for $N_f=2$.

Figure 2

(Color online) $1/g_{\text{peak}}^2$ vs $N_f$.

Figure 3

(Color online) $⟨\overline{\chi }\chi ⟩$ vs $N_f$ at $m=0.01$ on various lattice volumes.

Figure 4

(Color online) Finite volume scaling fit to Eq. (17) to data with $m=0.01$ (circles), 0.02 (squares), 0.03 (diamonds), and 0.04 (triangles) in terms of $N_f^{\prime }$.

Figure 5

(Color online) $⟨\overline{\chi }\chi ⟩$ vs $1/g^2$ for $N_f=2$.

Figure 6

(Color online) $⟨\overline{\chi }\chi ⟩$ vs $m$ for $N_f=2$ in the weak-coupling regime.