Localization in Fock Space: A Finite-Energy Scaling Hypothesis for Many-Particle Excitation Statistics

The concept of localization in Fock space is extended to the study of the many-particle excitation statistics of interacting electrons in a finite 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.