Quantum critical scaling of gapped phases in nodal-line semimetals

We study the effect of short-range interactions in three-dimensional nodal-line semimetals with linear band crossings. We analyze the Yukawa theories for gapped instabilities in the charge, spin, and superconducting channels using the Wilsonian renormalization group framework, employing a large number of fermion flavors ${N}_{f}$ for analytical control. We obtain stable nontrivial fixed points and provide a unified description of the critical exponents for the ordering transitions in terms of the number of order parameter components ${N}_{b}$ systematically to order $1/{N}_{f}$. We show that in all cases, the dynamical exponent $z=1$ in one loop, whereas $1/{N}_{f}$ corrections to various exponents follow from the anomalous dimension of the bosonic fields only.