Discrete quantum geometry and intrinsic spin Hall effect

We show that the quantum geometry of Fermi surface can be numerically described by a 3-dimensional discrete manifold. This approach not only avoids singularities in sea, but it also enables precise computation intrinsic Hall conductivity resolved spin, as well any other local properties surface. The method assures numerical accuracy when level is arbitrarily close to singularities, and remains robust Kramers degeneracy protected symmetry. demonstrated calculating anomalous spin conductivities 2-band lattice model Weyl semimetal full-band ab-initio zincblende GaAs.