Coherent transport of interacting electrons through a single scatterer

Using the self-consistent Hartree-Fock method, we calculate the persistent current of weakly-interacting spinless electrons in a one-dimensional ring containing a single delta-barrier. We find that the persistent current decays with the system length (L) asymptotically like $I \propto L^{-1-\alpha}$, where $\alpha > 0$ is the power depending only on the electron-electron interaction. We also simulate tunneling of the weakly-interacting one-dimensional electron gas through a single delta-barrier in a finite wire biased by contacts. We find that the Landauer conductance decays with the system length asymptotically like $L^{-2\alpha}$. The power laws $L^{-1-\alpha}$ and $L^{-2\alpha}$ have so far been observed only in correlated models. Their existence in the Hartree-Fock model is thus surprising.