  We develop a systematic typical medium dynamical cluster approximation that
provides a proper description of the Anderson localization transition in three
dimensions (3D). Our method successfully captures the localization phenomenon
both in the low and large disorder regimes, and allows us to study the
localization in different momenta cells, which renders the discovery that the
Anderson localization transition occurs in a cell-selective fashion. As a
function of cluster size, our method systematically recovers the re-entrance
behavior of the mobility edge and obtains the correct critical disorder
strength for Anderson localization in 3D.
