  We investigate the Mott-Anderson physics in interacting disordered
one-dimensional chains through the average single-site entanglement quantified
by the linear entropy, which is obtained via density-functional theory
calculations. We show that the minimum disorder strength required to the
so-called full Anderson localization $-$ characterized by the real-space
localization of pairs $-$ is strongly dependent on the interaction regime. The
degree of localization is found to be intrinsically related to the interplay
between the correlations and the disorder potential. In magnetized systems, the
minimum entanglement characteristic of the full Anderson localization is split
into two, one for each of the spin species. We show that although all types of
localization eventually disappear with increasing temperature, the full
Anderson localization persists for higher temperatures than the Mott-like
localization.
