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The chiral anomaly is one of the robust quantum effects in relativistic fieldtheories with a chiral symmetry where charges in chiral sectors appear to beseparately conserved. The chiral anomaly, which is often associated with arenormalization-invariant topological term, is a violation of this conservationlaw due to quantum effects. Such anomalies manifest in Weyl materials as anelectromagnetic field-induced transfer of charge between Fermi pockets.However, the emergent nature of the conservation of chiral charge leads tomanifestations of the chiral anomaly response that depend on the details of thesystem such as the strength of interactions. In this paper, we apply anapproach where the chiral symmetry in solid materials is replaced by thecombination of charge $U(1)$ gauge and spatial translation symmetry. The chiralanomaly in this case is replaced by a mixed anomaly between the two symmetriesand the chiral charge can be defined as being proportional to the totalmomentum. We show that the chiral anomaly associated with this chiral charge isunrenormalized by interactions in contrast to other chiral charges in $(1+1)D$whose renormalization is regularization dependent. In $(3+1)$D Weyl systems,this chiral anomaly is equivalent to the charge transferred between Fermisurfaces which can be measured through changes in Fermi-surface-enclosedvolume. We propose a pump-probe technique to measure this.

Interaction robustness of the chiral anomaly in Weyl semimetals and Luttinger liquids from a mixed anomaly approach