  We study the effects of strong $1/r$ long-range Coulomb interactions in a
Weyl semimetal. We consider a three-dimensional (3D) Dirac fermion system on a
lattice with a time-reversal symmetry breaking term, and take into account
$1/r$ long-range Coulomb interactions between the bulk electrons. This model is
regarded as the case where magnetic impurities are doped into the bulk of a 3D
topological insulator. With the use of the strong coupling expansion of the
lattice gauge theory and the mean-field approximation, we analyze the system
from the strong coupling limit. It is shown that parity symmetry of the system
is spontaneously broken in the strong coupling limit, and a different type of
the Weyl semimetal, in which time-reversal and parity symmetries are broken,
appears in the strong coupling limit. A possible global phase diagram of a
correlated Weyl semimetal is presented.
