Formulae for zero-temperature conductance through a region with interaction

TL;DR

This paper derives formulas linking zero-temperature conductance in interacting mesoscopic systems to ground-state energies and persistent currents, validated through comparisons with exact and other methods.

Contribution

It introduces a novel formalism expressing conductance via ground-state properties for interacting systems, assuming Fermi liquid behavior.

Findings

Formulas accurately predict conductance in quantum dot systems.

Excellent agreement with exact and alternative methods.

Method applicable to systems exhibiting Fermi liquid properties.

Abstract

The zero-temperature linear response conductance through an interacting mesoscopic region attached to noninteracting leads is investigated. We present a set of formulae expressing the conductance in terms of the ground-state energy or persistent currents in an auxiliary system, namely a ring threaded by a magnetic flux and containing the correlated electron region. We first derive the conductance formulae for the noninteracting case and then give arguments why the formalism is also correct in the interacting case if the ground state of a system exhibits Fermi liquid properties. We prove that in such systems, the ground-state energy is a universal function of the magnetic flux, where the conductance is the only parameter. The method is tested by comparing its predictions with exact results and results of other methods for problems such as the transport through single and double quantum dots containing interacting electrons. The comparisons show an excellent quantitative agreement.