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

Localization results for a class of random Schr\"odinger 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.