  We investigate the interplay of many-body and band structure effects of
interacting Weyl semimetals (WSM). Attractive and repulsive Hubbard
interactions are studied within a model for a time-reversal-breaking WSM with
tetragonal symmetry, where we can approach the limit of weakly coupled planes
and coupled chains by varying the hopping amplitudes. Using a slab geometry, we
employ the variational cluster approach to describe the evolution of WSM Fermi
arc surface states as a function of interaction strength. We find spin and
charge density wave instabilities which can gap out Weyl nodes. We identify
scenarios where the bulk Weyl nodes are gapped while the Fermi arcs still
persist, hence realizing a quantum anomalous Hall state.
