Anomaly non-renormalization in interacting Weyl semimetals

Weyl semimetals are three-dimensional condensed matter systems characterized by a degenerate Fermi surface, consisting of a pair of `Weyl nodes'. Correspondingly, in the infrared limit, these systems behave effectively as Weyl fermions in 3+1 dimensions. As predicted by Nielsen and Ninomiya in 1983, when exposed to electromagnetic fields these materials are expected to simulate the axial anomaly of QED, by giving rise to a net quasi-particle flow between Weyl nodes.

We consider a class of interacting lattice models for Weyl semimetals and prove that the quadratic response of the quasi-particle flow is universal, and equal to the chiral triangle graph of QED. Universality is the counterpart of the Adler-Bardeen non-renormalization property of the axial anomaly for QED, in a condensed matter setting. Our proof relies on the rigorous Wick rotation for real-time transport coefficients, on constructive bounds for Euclidean ground state correlations, and on lattice Ward Identities.

Joint work with A. Giuliani and V. Mastropietro.