  Disorder or sufficiently strong interactions can render a metallic state
unstable causing it to turn into an insulating one. Despite the fact that the
interplay of these two routes to a vanishing conductivity has been a central
research topic, a unifying picture has not emerged so far. Here, we establish
that the two-dimensional Falicov-Kimball model, one of the simplest lattice
models of strong electron correlation does allow for the study of this
interplay. In particular, we show that this model at particle-hole symmetry
possesses three distinct thermodynamic insulating phases and exhibits Anderson
localization. The previously reported metallic phase is identified as a
finite-size feature due to the presence of weak localization. We characterize
these phases by their electronic density of states, staggered occupation,
conductivity, and the generalized inverse participation ratio. The implications
of our findings for other strongly correlated systems are discussed.
