The Addition Spectrum and Koopmans' Theorem for Disordered Quantum Dots

TL;DR

This paper studies the addition spectrum of disordered quantum dots with interacting fermions, revealing that fluctuations do not scale with mean level spacing and that Koopmans' approximation can introduce significant errors.

Contribution

It demonstrates the limitations of Koopmans' approximation and the non-scaling of peak spacing fluctuations in disordered quantum dots with interactions.

Findings

Peak spacing fluctuations do not scale with mean single particle level spacing for r_s >~1.

Koopmans' approximation can cause errors comparable to or larger than the mean level spacing.

Fluctuation behavior is consistent across Coulomb and nearest neighbor interactions.

Abstract

We investigate the addition spectrum of disordered quantum dots containing spinless interacting fermions using the self-consistent Hartree-Fock approximation. We concentrate on the regime r_s >~1, with finite dimensionless conductance g. We find that in this approximation the peak spacing fluctuations do not scale with the mean single particle level spacing for either Coulomb or nearest neighbour interactions when r_s >~1. We also show that Koopmans' approximation to the addition spectrum can lead to errors that are of order the mean level spacing or larger, both in the mean addition spectrum peak spacings, and in the peak spacing fluctuations.