Exact Plaquette-Ordered Ground States in the Generalized Hubbard Model in Arbitrary Dimensions

We show the existance of the exact plaquette-ordered ground states of the Hubbard model including site-off-diagonal interactions in arbitrary dimensions, by decomposing the Hamiltonian as sum of products of projection operators for each spin sector. The obtatined exact ground states are interpreted as N\'eel ordered states on the dual lattices. We demonstrate this idea in the one-dimensional chain and higher-dimensional lattices such as the Kagom\'e lattice, and determine parameter regions of the exact ground states.