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 non-trivial 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 $1\mathrm{/}{N}_f$. We show that in all cases, the dynamical exponent z = 1 in one loop, whereas $1\mathrm{/}{N}_f$ corrections to various exponents follow from the anomalous dimension of the bosonic fields only.