Effect of short-range electron correlations in dynamic transport in a Luttinger liquid

TL;DR

This paper investigates how short-range electron correlations, specifically the charge-density-wave component, influence the dynamic conductance of a clean Luttinger liquid, revealing their dominant role at low frequencies.

Contribution

It introduces a corrected CDW density operator that conserves particle number and demonstrates its significant impact on conductance in a Luttinger liquid.

Findings

CDW component dominates conductance at low frequencies

Corrected CDW operator conserves particle number

Short-range correlations significantly affect transport properties

Abstract

The density operator in the Luttinger model consists of two components, one of which describes long-wave fluctuations and the other is related to the rapid oscillations of the charge-density-wave (CDW) type, caused by short-range electron correlations. It is commonly believed that the conductance is determined by the long-wave component. The CDW component is considered only when an impurity is present. We investigate the contribution of this component to the dynamic density response of a Luttinger liquid free from impurities. We show that the conventional form of the CDW density operator does not conserve the number of particles in the system. We propose the corrected CDW density operator devoid of this shortcoming and calculate the dissipative conductance in the case when the one-dimensional conductor is locally disturbed by a conducting probe. The contribution of the CDW component to conductance is found to dominate over that of the long-wave component in the low-frequency regime.