Relativistic Mott criticality in graphene

We formulate the effective Gross-Neveu-Yukawa theory of the semimetal-insulator transitions on the honeycomb lattice and compute its quantum critical behavior near three (spatial) dimensions. We find that at the critical point Dirac fermions do not survive as coherent excitations and that the $\sim 1/r$ tail of the weak Coulomb interaction is an irrelevant coupling. The emergent Lorentz invariance near criticality implies a universal ratio of the low-temperature specific heats of the metallic and the rotational-symmetry-broken insulating phase.

Figure 1

Schematic flow in the critical plane for Mott transitions in graphene. For any positive bosonic quartic coupling $\lambda$ the transition is continuous and governed by the fermionic critical point $F$. $g$ is the Yukawa coupling between the OP and Dirac fermions. The other marked fixed points are the Gaussian $\left(G\right)$ and the Wilson-Fisher (WF). The (unmarked) bicritical fixed point is unphysical, as argued below.