Is there a renormalization of the 1D conductance in Luttinger Liquid model?

TL;DR

This paper investigates whether the conductance of a 1D Luttinger Liquid is renormalized by interactions, concluding that under certain boundary conditions, the conductance remains universal and unrenormalized.

Contribution

The paper introduces a model with interaction switching off at boundaries, demonstrating no renormalization of conductance in this scenario.

Findings

Conductance remains universal with no renormalization.

Boundary conditions critically influence conductance properties.

Electrons behave freely in reservoirs despite interactions.

Abstract

Properties of 1D transport strongly depend on the proper choice of boundary conditions. It has been frequently stated that the Luttinger Liquid (LL) conductance is renormalized by the interaction as $g \frac{e^2} {h} $. To contest this result I develop a model of 1D LL wire with the interaction switching off at the infinities. Its solution shows that there is no renormalization of the universal conductance while the electrons have a free behavior in the source and drain reservoirs.