# On the nature of the magnetic phase transition in a Weyl semimetal

## TL;DR

This paper studies the magnetic phase transition in Weyl semimetals caused by electron interactions, revealing an emergent Lorentz symmetry and analyzing the effects of disorder on the phase stability and phase diagram.

## Contribution

It provides a detailed renormalization-group analysis of the quantum phase transition and the stability of the fixed point under disorder in Weyl semimetals.

## Key findings

- Critical point is a Gaussian fixed point with a dangerously irrelevant operator.
- Emergent Lorentz symmetry at low energies due to velocity renormalization.
- Weak disorder generally stable, but certain disorders can induce a transition to a disorder-dominated phase.

## Abstract

We investigate the nature of the magnetic phase transition induced by the short-ranged electron-electron interactions in a Weyl semimetal by using the perturbative renormalization-group method. We find that the critical point associated with the quantum phase transition is characterized by a Gaussian fixed point perturbed by a dangerously irrelevant operator. Although the low-energy and long-distance physics is governed by a free theory, the velocities of the fermionic quasiparticles and the magnetic excitations suffer from nontrivial renormalization effects. In particular, their ratio approaches one, which indicates an emergent Lorentz symmetry at low energies. We further investigate the stability of the fixed point in the presence of weak disorder. We show that while the fixed point is generally stable against weak disorder, among those disorders that are consistent with the emergent chiral symmetry of the clean system, a moderately strong random chemical potential and/or random vector potential may induce a quantum phase transition towards a disorder-dominated phase. We propose a global phase diagram of the Weyl semimetal in the presence of both electron-electron interactions and disorder based on our results.