Relation between chiral anomaly and electric transport in $1D$ Dirac semimetal

Abstract

We investigate the interplay of chiral anomaly and dissipation in one - dimensional Dirac semimetal. For definiteness we consider the Su Schrieffer Heeger (SSH) model, which on the language of lattice field theory represents 1 D Wilson fermions. We employ the non-equilibrium Keldysh Green function formalism, and calculate the chiral imbalance and electric conductivity in the presence of energy dissipation, revealing how these observables are connected to the chiral anomaly. By systematically incorporating dissipation effects into the Keldysh framework, we demonstrate how the anomaly-induced contributions manifest in both axial charge density and electric current.