Origami rules for the construction of localized eigenstates of the Hubbard model in decorated lattices

We present a method of construction of exact localized many-body eigenstates of the Hubbard model in decorated lattices, both for $U=0$ and $U\rightarrow\infty$. These states are localized in what concerns both hole and particle movement. The starting point of the method is the construction of a plaquette or a set of plaquettes with a higher symmetry than that of the whole lattice. Using a simple set of rules, the tight-binding localized state in such a plaquette can be divided, folded and unfolded to new plaquette geometries. This set of rules is also valid for the construction of a localized state for one hole in the $U\rightarrow\infty$ limit of the same plaquette, assuming a spin configuration which is a uniform linear combination of all possible permutations of the set of spins in the plaquette.