Wigner crystal vs. Friedel oscillations in the 1D Hubbard model
  We analyze the fermion density of the one-dimensional Hubbard model using bosonization and numerical DMRG calculations. For finite systems we find a relatively sharp crossover even for moderate short range interactions into a region with $4k_F$ density waves as a function of density. The results show that the unstable fixed point of a spin-incoherent state can dominate the physical behavior in a large region of parameter space in finite systems. The crossover may be observable in ultra cold fermionic gases in optical lattices and in finite quantum wires. 
Stefan A. Soeffing, Michael Bortz, Imke Schneider, Alexander Struck,   Michael Fleischhauer and Sebastian Eggert