Static screening and delocalization effects in the Hubbard-Anderson model

We study the suppression of electron localization due to the screening of disorder in a Hubbard-Anderson model. We focus on the change of the electron localization length at the Fermi level within a static picture, where interactions are absorbed into the redefinition of the random on-site energies. Two different approximations are presented, either one yielding a nonmonotonic dependence of the localization length on the interaction strength, with a pronounced maximum at an intermediate interaction strength. In spite of its simplicity, our approach is in good agreement with recent numerical results.

Figure 1

Site occupation in the atomic ground state with doubly occupied (black), singly occupied (gray), and empty states (white). (a) Weak interaction, (b) strong interaction for less than half filling (i.e., $\rho <1$), and (c) strong interaction for more than half filling $(\rho >1)$.

Figure 2

The renormalized on-site energy probability functions (solid line) for weak repulsion $U$: (a) atomic-limit approximation and (b) Hartree-Fock approximation. For comparison, also the original function is shown (dashed lines).

Figure 3

(Color online) Localization length $\xi$ at the Fermi level as a function of repulsion $U$ and lattice filling $\rho$ for $\Delta =15$: (a) atomic-limit approximation and (b) Hartree-Fock approximation.

Figure 4

(a) Localization length $\xi$ at the Fermi level, normalized by its noninteracting value, as a function of the on-site repulsion $U$ for $\Delta =15$ and $\rho =\frac{1}{2}$. (b) Variance of the renormalized on-site energy distribution, also normalized by its noninteracting value. The solid curves show the results for the atomic-limit approximation and the dashed curves are the Hartree-Fock results.

Figure 5

Inverse localization length ${\xi }^{-1}$ as a function of $\Delta$ for $\rho =\frac{1}{2}$ and (a) $U=7$ in the atomic-limit approximation and (b) $U=14$ in the Hartree-Fock approximation, respectively.