Localization in Fock space: A finite size scaling hypothesis for many particle excitation statistics

TL;DR

This paper extends the concept of localization in Fock space to many-particle excitation statistics in a quantum dot, proposing a finite size scaling hypothesis that aligns with numerical data and highlights the importance of Fock space localization.

Contribution

It introduces a finite size scaling hypothesis for Fock space localization using excitation energy, tested on quantum dot spectral data, linking localization to many-particle excitations.

Findings

Scaling hypothesis fits numerical data well

Fock space localization is relevant for many-particle excitations

Spectral properties support the localization scenario

Abstract

The concept of localization in Fock space is extended to the study of the many particle excitation statistics of interacting electrons in a two dimensional quantum dot. In addition, a finite size scaling hypothesis for Fock space localization, in which the excitation energy replaces the system size, is developed and tested by analyzing the spectral properties of the quantum dot. This scaling hypothesis, modeled after the usual Anderson transition scaling, fits the numerical data obtained for the interacting states in the dot. It therefore attests to the relevance of the Fock space localization scenario to the description of many particle excitation properties.