The RKKY Interaction and the Nature of the Ground State of Double Dots in Parallel

TL;DR

This paper uses theoretical methods to demonstrate that double quantum dots in parallel form a Fermi liquid ground state, characterized by zero entropy and conductance consistent with the Friedel sum rule, challenging previous numerical results.

Contribution

It provides a theoretical analysis combining slave boson mean field theory and Bethe ansatz to establish the Fermi liquid nature of the ground state of double quantum dots in parallel.

Findings

Ground state is a Fermi liquid with zero entropy at zero temperature.

Zero temperature conductance follows Friedel sum rule.

Contradicts previous numerical renormalization group studies.

Abstract

We argue through a combination of slave boson mean field theory and the Bethe ansatz that the ground state of closely spaced double quantum dots in parallel coupled to a single effective channel are Fermi liquids. We do so by studying the dots' conductance, impurity entropy, and spin correlation. In particularly we find that the zero temperature conductance is characterized by the Friedel sum rule, a hallmark of Fermi liquid physics, and that the impurity entropy vanishes in the limit of zero temperature, indicating the ground state is a singlet. This conclusion is in opposition to a number of numerical renormalization group studies. We suggest a possible reason for the discrepancy.