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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 $1/N_{f}$. 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.