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The ground state properties of Hubbard model with or without long-rangeinteractions in the regime with strongly repulsive on-site interaction areinvestigated by means of the exact diagonalization method. We show that theappearance of $N$-crests in the density profile of a trapped N-fermion systemis a natural result of "fermionization" between antiparallel-spin fermions inthe strongly repulsive limit and can not be taken as the only signature ofWigner crystal phase, as the static structure factor does not show anysignature of crystallization. On the contrary, both the density distributionand static structure factor of Hubbard model with strong long-rangeinteractions display clear signature of Wigner crystal. Our results indicatethe important role of long-range interaction in the formation of Wignercrystal.

Wigner crystal versus Fermionization for one-dimensional Hubbard models with and without long-range interactions