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We use the non-equilibrium Green's function formalism along with aself-consistent Hartree-Fock approximation to numerically study the effects ofa single impurity and interactions between the electrons (with and withoutspin) on the conductance of a quantum wire. We study how the conductance varieswith the wire length, the temperature, and the strength of the impurity andinteractions. The dependence of the conductance on the wire length andtemperature is found to be in rough agreement with the results obtained from arenormalization group analysis based on the Hartree-Fock approximation. For thespin-1/2 model with a repulsive on-site interaction or the spinless model withan attractive nearest neighbor interaction, we find that the conductanceincreases with increasing wire length or decreasing temperature. This can bequalitatively explained using the Born approximation in scattering theory. Fora strong impurity, the conductance is significantly different for a repulsiveand an attractive impurity; this is due to the existence of a bound state inthe latter case. In general, the large density deviations at short distanceshave an appreciable effect on the conductance which is not captured by therenormalization group analysis.Comment: Revtex, 15 pages including 21 figures; all the numerical calculations  have been re-done with a Fermi wavenumber of pi/10; this is the version  published in Phys Rev

Conductance of quantum wires: A numerical study of effects of an impurity and interactions