Interacting Weyl semimetals on a lattice

We perform an exact renormalization group analysis of a fermionic system on a three-dimensional lattice, showing the persistence of the Weyl semimetallic phase up the quantum critical point discriminating between the semimetallic and insulating phases. The interaction produces finite modifications of the anisotropic Fermi velocity and of the overlap of the true (dressed) quasiparticle with the free electron wave function. The optical conductivity is the one of Weyl fermions with anisotropic Fermi velocities replacing the light velocity, provided that the frequencies are below a certain energy scale, which is vanishing at the quantum critical point; above such scale, a different behavior is found, dominated by the quadratic corrections to the dispersion relation.