  The derivation procedure of exact ground-states for the periodic Anderson
model (PAM) in restricted regions of the parameter space and D=2 dimensions
using plaquette operators is presented in detail. Using this procedure, we are
reporting for the first time exact ground-states for PAM in 2D and finite value
of the interaction, whose presence do not require the next to nearest neighbor
extension terms in the Hamiltonian. In order to do this, a completely new type
of plaquette operator is introduced for PAM, based on which a new localized
phase is deduced whose physical properties are analyzed in detail. The obtained
results provide exact theoretical data which can be used for the understanding
of system properties leading to metal-insulator transitions, strongly debated
in recent publications in the frame of PAM. In the described case, the lost of
the localization character is connected to the break-down of the long-range
density-density correlations rather than Kondo physics.
