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We discuss exact plaquette-ordered ground states of the generalized Hubbardmodel based on the projection operator method for several corner sharinglattices: Kagome, checkerboard, and pyrochlore lattices. The obtained exactground states are interpreted as N\'eel ordered states on the plaquette-locatedelectrons. We demonstrate that these models also have exact edge states. Wealso calculate the entanglement entropy exactly in these systems.

Exact Plaquette-Ordered Ground States with Exact Edge States of the Generalized Hubbard Model in Corner Sharing Lattices