On the localization regime of certain random operators within Hartree-Fock theory

Abstract

Localization results for a class of random Schrödinger operators within the Hartree-Fock approximation are proved in two regimes: large disorder and weak disorder/extreme energies. A large disorder threshold ${\lambda }_{\mathrm{HF}}$ analogous to the threshold ${\lambda }_{\mathrm{And}}$ obtained by Schenker in \cite{Schenkl} is provided. We also show certain stability results for this large disorder threshold by giving examples of distributions for which ${\lambda }_{\mathrm{HF}}$ converges to ${\lambda }_{\mathrm{And}}$, or to a number arbitrarily close to it, as the interaction strength tends to zero.

arXiv comment20 pages