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Weyl semimetals (WSMs) constitute a 3D phase with linearly-dispersing Weylexcitations at low energy, which lead to unusual electrodynamic responses andopen Fermi arcs on boundaries. We derive a simple criterion to identify andcharacterize WSMs in an interacting setting using the exact electronic Green'sfunction at zero frequency, which defines a topological Bloch Hamiltonian. Weapply this criterion by numerically analyzing, via cluster and other methods,interacting lattice models with and without time-reversal symmetry. We identifyvarious mechanisms for how interactions move and renormalize Weyl fermions. Ourmethods remain valid in the presence of long-ranged Coulomb repulsion. Finally,we introduce a WSM-like phase for which our criterion breaks down due tofractionalization: the charge-carrying Weyl quasiparticles are orthogonal tothe electron.

Interacting Weyl semimetals: characterization via the topological Hamiltonian and its breakdown