Complete renormalization group calculation up to two-loop order of an effective two-band model for iron-based superconductors

We perform a renormalization group (RG) study up to two-loop order of an effective low-energy two-band model to describe some of the recently discovered iron-based superconductors. Our starting point is the itinerant electronic model proposed by Chubukov \emph{et al.} [Phys. Rev. B $\mathbf{\text{78}}$, 134512 (2008)], which displays two small, almost nested Fermi pockets with one hole pocket centered at $(0,0)$ and one electron pocket centered at $$\mathbf{Q}$ = (\pi,\pi)$ in the folded Brillouin zone. We then proceed to implement a complete two-loop RG calculation for this model of four-point vertex corrections, quasiparticle weight and several order-parameter susceptibilities in order to evaluate the robustness of one-loop RG results available in the literature with respect to including self-energy effects and higher-order quantum fluctuations.