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We investigate the interplay of many-body and band structure effects ofinteracting Weyl semimetals (WSM). Attractive and repulsive Hubbardinteractions are studied within a model for a time-reversal-breaking WSM withtetragonal symmetry, where we can approach the limit of weakly coupled planesand coupled chains by varying the hopping amplitudes. Using a slab geometry, weemploy the variational cluster approach to describe the evolution of WSM Fermiarc surface states as a function of interaction strength. We find spin andcharge density wave instabilities which can gap out Weyl nodes. We identifyscenarios where the bulk Weyl nodes are gapped while the Fermi arcs stillpersist, hence realizing a quantum anomalous Hall state.

Density wave instabilities and surface state evolution in interacting Weyl semimetals