  We have studied a disordered $N_{\rm c} \times N_{\rm c}$ plaquette Hubbard
model on a two-dimensional square lattice at half-filling using a coherent
potential approximation (CPA) in combination with a single-site dynamical mean
field theory (DMFT) approach with a paramagnetic bath. Such a model
conveniently interpolates between the ionic Hubbard model at $N_{\rm
c}=\sqrt{2}$ and the Anderson model at $N_{\rm c} = \infty$ and enables the
analysis of the various limiting properties. We confirmed that within the CPA
approach a band insulator behavior appears for non-interacting strongly
disordered systems with a small plaquette size $N_{\rm c} = 4$, while the
paramagnetic Anderson insulator with nearly gapless density of states is
present for large plaquette sizes $N_{\rm c}=48$. When the interaction $U$ is
turned on in the strongly fluctuating random potential regions, the electrons
on the low energy states push each other into high energy states in DMFT in a
paramagnetic bath and correlated metallic states with a quasiparticle peak and
Hubbard bands emerge, though a larger critical interaction $U$ is needed to
obtain this state from the paramagnetic Anderson insulator ($N_{\rm c}=48$)
than from the band insulator ($N_{\rm c}=4$). Finally, we observe a Mott
insulator behavior in the strong interaction $U$ regions for both $N_{\rm c}=4$
and $N_{\rm c}=48$ independent of the disorder strength. We discuss the
application of this model to real materials.
