LAUSR

The anomalous Hall conductivity in holographic model of $\mathbb{Z}_2$ Dirac semimetals has been elaborated. The underlying model contains the kinetic mixing term of two $U(1)$-gauge fields, the ordinary Maxwell and the auxiliary one, as well as, the Chern-Simons gauge terms for the adequate combinations of the auxiliary and Maxwell fields. The holographic approach in the probe limit enables us to obtain the value of the anomalous Hall conductivity which depends on the background gauge fields and combinations of coupling constants binding kinetic mixing term and Chern-Simons ones. The holographic model in question describes the quantum phase transition for $\mathbb{Z}_2$ Dirac semimetals, from the topologically non-trivial to the trivial phase.