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The quasiparticle spectra of interacting Weyl and nodal-line semimetals on acubic lattice are studied using the cluster perturbation theory. By trackingthe spectral functions under interaction, we find that the Weyl points willmove to and meet at a specific point in one Weyl semimetal model, while in theother Weyl semimetal model they are immobile. In the nodal-line semimetals, wefind that the nodal line shrinks to a point and then disappears underinteraction in one-nodal-line system. When we add another nodal line to thissystem, we find that the two nodal lines both shrink to specific points, butthe disappearing processes of the two nodal lines are not synchronized. Weargue that the nontrivial evolution of Weyl points and nodal lines underinteraction is due to the presence of symmetry breaking order, e.g., aferromagnetic moment, in the framework of mean field theory, whereas thestability of Weyl points under interaction is protected by symmetry. Among allthese models, the spectral gap is finally opened when the interaction is strongenough.

Quasiparticle Properties under Interactions in Weyl and Nodal Line Semimetals