  Non-Hermitian descriptions often model open or driven systems away from the
equilibrium. Nonetheless, in equilibrium electronic systems, a non-Hermitian
nature of an effective Hamiltonian manifests itself as unconventional
observables such as a bulk Fermi arc and skin effects. We theoretically reveal
that spin-dependent quasiparticle lifetimes, which signify the non-Hermiticity
of an effective model in the equilibrium, induce the anomalous Hall effect,
namely the Hall effect without an external magnetic field. We first examine the
effect of nonmagnetic and magnetic impurities and obtain a non-Hermitian
effective model. Then, we calculate the Kubo formula from the microscopic model
to ascertain a non-Hermitian interpretation of the longitudinal and Hall
conductivities. Our results elucidate the vital role of the non-Hermitian
equilibrium nature in the quantum transport phenomena.
