  Weyl semimetals (WSMs) are characterized by topologically stable pairs of
nodal points in the band structure, that typically originate from splitting a
degenerate Dirac point by breaking symmetries such as time reversal or
inversion symmetry. Within the independent electron approximation, the
transition between an insulating state and a WSM requires the local creation or
annihilation of one or several pairs of Weyl nodes in reciprocal space. Here,
we show that strong electron-electron interactions may qualitatively change
this scenario. In particular, we reveal that the transition to a Weyl
semi-metallic phase can become discontinuous, and, quite remarkably, pairs of
Weyl nodes with a finite distance in momentum space suddenly appear or
disappear in the spectral function. We associate this behavior to the buildup
of strong many-body correlations in the topologically non-trivial regions,
manifesting in dynamical fluctuations in the orbital channel. We also highlight
the impact of electronic correlations on the Fermi arcs.
