Persistent Current and Drude Weight in Mesoscopic Rings

We study the persistent current and the Drude weight of a system of spinless fermions, with repulsive interactions and a hopping impurity, on a mesoscopic ring pierced by a magnetic flux, using a DMRG algorithm for complex fields. We find that the persistent current changes from an algebraic to an exponential decay with the system size, as the system crosses from the Luttinger Liquid (LL) to the Charge Density Wave (CDW) phase with increasing interaction $U$. We also find that in the interacting system the persistent current is invariant under the impurity transformation $\rho\rightarrow 1/\rho $, for large system sizes, where $\rho $ is the defect strength. In the LL phase the Drude weight decreases algebraically with the number of lattice sites $N$, due to the interplay of the electron interaction with the impurity, while in the CDW phase it decreases exponentially, defining a localization length which decreases with increasing interaction and impurity strength. Our results show that the impurity and the interactions always decrease the persistent current, and imply that the Drude weight vanishes in the limit $N\rightarrow\infty $, in both phases.