Tunneling of interacting fermions in 1D systems

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we study tunneling of the interacting electron gas through a single delta-barrier in a finite one-dimensional (1D) wire connected to contacts. Our results exhibit features known from correlated many-body models. In particular, the conductance decays with the wire length as $\propto L^{-2\alpha}$, where the power $\alpha$ is universal. We also show that a similar result for a wire conductance can be extracted from the persistent current (I) through the delta-barrier in a 1D ring, where it is known that I \propto L^{-1-\alpha}$.