  The ground state properties of Hubbard model with or without long-range
interactions in the regime with strongly repulsive on-site interaction are
investigated by means of the exact diagonalization method. We show that the
appearance of $N$-crests in the density profile of a trapped N-fermion system
is a natural result of "fermionization" between antiparallel-spin fermions in
the strongly repulsive limit and can not be taken as the only signature of
Wigner crystal phase, as the static structure factor does not show any
signature of crystallization. On the contrary, both the density distribution
and static structure factor of Hubbard model with strong long-range
interactions display clear signature of Wigner crystal. Our results indicate
the important role of long-range interaction in the formation of Wigner
crystal.
