Interacting Weyl fermions: Phases, phase transitions, and global phase diagram

We study the effects of short-range interactions on a generalized three-dimensional Weyl semimetal, where the band touching points act as the (anti) monopoles of Abelian Berry curvature of strength n. We show that any local interaction has a negative scaling dimension -2/n. Consequently, all Weyl semimetals are stable against weak short-range interactions. For sufficiently strong interactions, we demonstrate that the Weyl semimetal either undergoes a first-order transition into a band insulator or a continuous transition into a symmetry breaking phase. A translational symmetry breaking axion insulator and a rotational symmetry breaking semimetal are two prominent candidates for the broken symmetry phase. At the one-loop order, the correlation length exponent for continuous transitions is upsilon = n/2, indicating their non-Gaussian nature for any n > 1. We also discuss the scaling of the thermodynamic and transport quantities in general Weyl semimetals as well as inside broken symmetry phases.