Interactions in nodal-line semimetals with quadratic band touching*

We address the problem of Coloumb interactions in 3D nodal-line semimetals with quadratic band touching using perturbative Wilsonian renormalization group approach. At one loop order, we find that the non-interacting fixed point is unstable and flows to an interacting fixed point. We compute corrections to the dynamical exponent, the screening charge and find corrections to other experimentally measurable quantities such as the specific heat, compressibility, etc. We also consider the emergence of other competing instabilities in the charge sector from short-range interactions.