# Quasiparticle Properties under Interactions in Weyl and Nodal Line Semimetals

## TL;DR

This study investigates how interactions affect the quasiparticle spectra in Weyl and nodal-line semimetals, revealing movement, merging, and disappearance of Weyl points and nodal lines, with symmetry breaking playing a key role.

## Contribution

It provides a detailed analysis of the evolution of Weyl points and nodal lines under interactions using cluster perturbation theory, highlighting symmetry effects and spectral gap opening.

## Key findings

- Weyl points can move and meet or remain immobile under interaction.
- Nodal lines can shrink and disappear, with processes depending on system details.
- Spectral gaps open at strong interactions.

## Abstract

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.