  The Bethe-Ansatz local density approximation (LDA) to lattice density
functional theory (LDFT) for the one-dimensional repulsive Hubbard model is
extended to current-LDFT (CLDFT). The transport properties of mesoscopic
Hubbard rings threaded by a magnetic flux are then systematically investigated
by this scheme. In particular we present calculations of ground state energies,
persistent currents and Drude weights for both a repulsive homogeneous and a
single impurity Hubbard model. Our results for the ground state energies in the
metallic phase compares favorably well with those obtained with numerically
accurate many-body techniques. Also the dependence of the persistent currents
on the Coulomb and the impurity interaction strength, and on the ring size are
all well captured by LDA-CLDFT. Our study demonstrates that CLDFT is a powerful
tool for studying one-dimensional correlated electron systems with high
accuracy and low computational costs.
