Title: On the nature of the magnetic phase transition in a Weyl semimetal,
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.