Weakly Interacting Disordered Electron Systems*

We report on the interplay of interactions and disorder within the typical medium dynamical cluster approximation using the Anderson-Hubbard model. By the systematical incorporation of non-local spatial correlations and the diagonal disorder on an equal footing, we study the initial effects of electron interactions ($U$) in one (1D), two (2D), and three (3D) dimensions. Treating the interacting non-local cluster self-energy ($\Sigma^{(SOPT)}_c[{\cal\tilde{G}}](i,j\neq i)$) up to $\mathcal{O}\left[U^2\right]$ order in the perturbation expansion, we obtain the ground-state phase diagram in 3D for the disorder induced paramagnetic metal to insulator transition in the presence of weak interactions. We find that the critical disorder strength ($W_c$), required to localize all states, increases with increasing $U$; implying that the metallic phase is stabilized by interactions. In 2D, our results agree with previous findings on the destruction of the insulating phase by $U$, while in 1D, we find strong competition between both phases.