Disordered mesoscopic systems with interactions: induced two-body ensembles and the Hartree-Fock approach

TL;DR

This paper develops a framework to analyze interaction effects in disordered quantum dots using induced two-body ensembles and the Hartree-Fock approximation, revealing statistical properties of single-particle energies and conductance characteristics.

Contribution

It introduces a classification of induced two-body ensembles in quantum dots and applies Hartree-Fock to study their statistical properties, including energy levels and conductance features.

Findings

Statistical distributions of HF single-particle energies and wave functions.

Characterization of the HF gap and its fluctuations.

Distribution of conductance peak spacings and heights.

Abstract

We introduce a generic approach to study interaction effects in diffusive or chaotic quantum dots in the Coulomb blockade regime. The randomness of the single-particle wave functions induces randomness in the two-body interaction matrix elements. We classify the possible induced two-body ensembles, both in the presence and absence of spin degrees of freedom. The ensembles depend on the underlying space-time symmetries as well as on features of the two-body interaction. Confining ourselves to spinless electrons, we then use the Hartree-Fock (HF) approximation to calculate HF single-particle energies and HF wave functions for many realizations of the ensemble. We study the statistical properties of the resulting one-body HF ensemble for a fixed number of electrons. In particular, we determine the statistics of the interaction matrix elements in the HF basis, of the HF single-particle energies (including the HF gap between the last occupied and the first empty HF level), and of the HF single-particle wave functions. We also study the addition of electrons, and in particular the distribution of the distance between successive conductance peaks and of the conductance peak heights.