  The chiral anomaly is a fundamental quantum mechanical phenomenon which is of
great importance to both particle physics and condensed matter physics alike.
In the context of QED it manifests as the breaking of chiral symmetry in the
presence of electromagnetic fields. It is also known that anomalous chiral
symmetry breaking can occur through interactions alone, as is the case for
interacting one dimensional systems. In this paper we investigate the interplay
between these two modes of anomalous chiral symmetry breaking in the context of
interacting Weyl semimetals. Using Fujikawa's path integral method we show that
the chiral charge continuity equation is modified by the presence of
interactions which can be viewed as including the effect of the electric and
magnetic fields generated by the interacting quantum matter. This can be
understood further using dimensional reduction and a Luttinger liquid
description of the lowest Landau level. These effects manifest themselves in
the non-linear response of the system. In particular we find an interaction
dependent density response due to a change in the magnetic field as well as a
contribution to the non-equilibrium and inhomogeneous anomalous Hall response
while preserving its equilibrium value.
