Exact spin states and analytic formulas for nonequilibrium spin transport in a three-site one-dimensional system with interacting electrons

We choose a typical three-site one-dimensional (1D) quantum chain system to deduce exact spin states and nonequilibrium spin transport properties analytically. The initial spin-up and spin-down electron charges on each site of the chain are calculated from the exactly derived spin ground state with the assumption of half-filling. Based on the Keldysh formalism, we describe the basic theoretical methods and derive some analytic formulas (differential spin conductance, spin transport current, electron charge distribution, etc.) for nonequilibrium spin transport of the 1D chain systems within the Hartree–Fock approximation when Coulomb electron interaction is present. The scattering processes including Coulomb repulsion between the spin-up and spin-down electrons, and spin–spin interactions due to spin degrees freedom are taken into account. We also report the numerical results of the nonequilibrium spin transport of the three-site 1D chain system in some special cases using the initial spin-up/down electron charges.