Spin and interaction effects on charge distribution and currents in one-dimensional conductors and rings within the Hartree-Fock approximation

Using the self-consistent Hartree-Fock approximation for electrons with spin at zero temperature, we study the effect of the electronic interactions on the charge distribution in a one-dimensional continuous ring containing a single $\delta$ scatterer. We reestablish that the interaction suppresses the decay of the Friedel oscillations. Based on this result, we show that in an infinite one-dimensional conductor containing a weak scatterer, the current is totally suppressed because of a gap opened at the Fermi energy. In a canonical ensemble of continuous rings containing many scatterers, the interactions enhance the average and the typical persistent current.