Plaquette operators used in the rigorous study of ground states of the periodic Anderson model in $D=2\mathrm{}$ dimensions

The derivation procedure of exact ground states for the periodic Anderson model (PAM) in restricted regions of the parameter space and $D=2\mathrm{}$ dimensions using plaquette operators is presented in detail. Using this procedure, we are reporting exact ground states for PAM in two dimensions 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 localized phase is deduced whose physical properties are analyzed in detail. The obtained results provide exact theoretical data that 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 loss of the localization character is connected to the breakdown of the long-range density-density correlations rather than Kondo physics.