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

TL;DR

This paper numerically investigates how impurities and electron interactions affect the conductance of quantum wires, revealing dependencies on wire length, temperature, and impurity strength, with results aligning with renormalization group analysis.

Contribution

It introduces a numerical approach combining Green's functions and Hartree-Fock approximation to study conductance in quantum wires with impurities and interactions, highlighting effects not captured by previous RG methods.

Findings

Conductance varies with wire length and temperature in agreement with RG analysis.

Repulsive and attractive impurities have different impacts on conductance due to bound states.

Large density deviations at short distances significantly influence conductance.

Abstract

We use the non-equilibrium Green's function formalism along with a self-consistent Hartree-Fock approximation to numerically study the effects of a single impurity and interactions between the electrons (with and without spin) on the conductance of a quantum wire. We study how the conductance varies with the wire length, the temperature, and the strength of the impurity and interactions. The dependence of the conductance on the wire length and temperature is found to be in rough agreement with the results obtained from a renormalization group analysis based on the Hartree-Fock approximation. For the spin-1/2 model with a repulsive on-site interaction or the spinless model with an attractive nearest neighbor interaction, we find that the conductance increases with increasing wire length or decreasing temperature. This can be qualitatively explained using the Born approximation in scattering theory. For a strong impurity, the conductance is significantly different for a repulsive and an attractive impurity; this is due to the existence of a bound state in the latter case. In general, the large density deviations at short distances have an appreciable effect on the conductance which is not captured by the renormalization group analysis.