Studying many-body versions of Landau-Zener-like problems of non-interacting electrons in the Slater formalism for several k center dot p models representing Weyl and Dirac semimetals, we systematically include non-adiabatic corrections to a quantum limit of chiral charge pumping in these models. In this paper, we show that relative homotopy invariant [Sun et al., Phys. Rev. Lett. 121, 106402 (2018)] and Euler class invariant [Bouhon et al., Nat. Phys. 16, 1137 (2020)] non-trivially manifest in the non-adiabatic corrections to the quantum limit of chiral charge pumping. These corrections could affect conductivity channels connected with the presence of chiral anomaly. Moreover, we show that, for non-symmorphic systems, this contribution is sensitive to the direction of the applied magnetic field (in respect to the so-called non-symmorphic nodal loop), suggesting that the conjectured direction-selective chiral anomaly in non-symmorphic systems [Bzdusek et al., Nature (London) 538, 75 (2016)] could lead to a strongly anisotropic longitudinal magnetoresistance. The presented approach can be easily applied to other k center dot p or tight-binding models.
