  The quasiparticle spectra of interacting Weyl and nodal-line semimetals on a
cubic lattice are studied using the cluster perturbation theory. By tracking
the spectral functions under interaction, we find that the Weyl points will
move to and meet at a specific point in one Weyl semimetal model, while in the
other Weyl semimetal model they are immobile. In the nodal-line semimetals, we
find that the nodal line shrinks to a point and then disappears under
interaction in one-nodal-line system. When we add another nodal line to this
system, we find that the two nodal lines both shrink to specific points, but
the disappearing processes of the two nodal lines are not synchronized. We
argue that the nontrivial evolution of Weyl points and nodal lines under
interaction is due to the presence of symmetry breaking order, e.g., a
ferromagnetic moment, in the framework of mean field theory, whereas the
stability of Weyl points under interaction is protected by symmetry. Among all
these models, the spectral gap is finally opened when the interaction is strong
enough.
