Multicritical behavior of ${\mathbb{Z}}_2\times O\left(2\right)$ Gross-Neveu-Yukawa theory in graphene

Multicritical behavior of interacting fermions in graphene's honeycomb lattice is presented. In particular, we considered the spin triplet insulating orders, where the spin rotational symmetry of the order parameter is explicitly broken. By casting the problem in terms of Gross-Neveu-Yukawa theory, we show that such symmetry-breaking terms are irrelevant near the metal-insulator critical point. A finite Yukawa coupling among bosons and fermions improves the stability of such critical point against the symmetry-breaking perturbations. Physical sources of such symmetry-breaking terms are pointed out. Critical exponents are calculated near the transitions as well.

Figure 1

Flow diagram in the Yukawa coupling space. Fully stable fixed point is located at $g_{\parallel }^2=g_{\perp }^2=\frac{\epsilon }{2N+1}=\frac{\epsilon }{5}$ for $N=2$.