  We employ diagrammatic Monte Carlo simulations to establish criteria for the
stability of line-node semimetals in the presence of Coulomb interactions. Our
results indicate a phase transition to a chiral insulating state that occurs at
a finite interaction threshold which we determine. We also compute the Landau
levels for out-of-plane and in-plane magnetic fields in the symmetric and
symmetry-broken phases. We find that the magnetic field couples to the chiral
order parameter, implying that this degree of freedom can be manipulated in
situ in experiments. Finally, we check the existence of edge states in the
symmetry-broken phase. On the system's boundary, we note that the metallic
"drum-head" states that exist in the symmetric phase are gapped out. However,
the symmetry-broken phase permits topological defects in the macroscopic order
parameter in the form of domain walls, which host metallic "interface states."
These consist of line-like gap-closings that occur on the two-dimensional
interfaces.
