The Fermi liquid nature of the ground state of double quantum dots in parallel from a 1/N expansion

TL;DR

This paper employs a 1/N expansion to demonstrate that the ground state of double quantum dots in parallel exhibits Fermi liquid behavior, aligning with previous theoretical approaches and enabling conductance calculations.

Contribution

It introduces a large-N diagrammatic approach to confirm Fermi liquid ground state properties of double quantum dots in parallel geometry.

Findings

Friedel sum rule holds at lowest order in 1/N expansion

Ground state is confirmed as a Fermi liquid

Conductance computed using dot occupancy and FSR

Abstract

A large-N diagrammatic approach is used to study coupled quantum dots in a parallel geometry. We show that the Friedel sum rule (FSR) holds at lowest order in a 1/N expansion for this system, thereby suggesting that the ground state is a Fermi liquid. Using the FSR together with the dot occupancy, we compute the dot system's conductance. Our finding that the 1/N expansion indicates the system is a Fermi liquid is in agreement with both prior results based on the Bethe ansatz and slave boson mean field theory.