Hartree-Fock Simulation of Persistent Current in Rings with Single Scatterer

Using the self-consistent Hartree-Fock approximation for spinless electrons at zero temperature, we calculate the persistent current of the interacting electron gas in a one-dimensional ring containing a single δ barrier. Our results agree with correlated models like the Luttinger liquid model and lattice model with nearest-neighbor interaction. The persistent current is a sine-like function of magnetic flux. It decays with the ring length (L) faster than L$\text{}^{-1}$ and eventually like L$\text{}^{-α-1}$, where α>0 is universal.