Is there spin-charge separation in the 2D Hubbard and t-J models at low electronic densities?

The spin and density correlation functions of the two-dimensional Hubbard model at low electronic density $<n>$ are calculated in the ground state by using the power method, and at finite temperatures by using the quantum Monte Carlo technique. Both approaches produce similar results, which are in close agreement with numerical and high temperature expansion results for the two-dimensional ${\rm t-J}$ model. Using perturbative approximations, we show that the examination of the density correlation function alone is not enough to support recent claims in the literature that suggested spin and charge separation in the low electronic density regime of the ${\rm t-J}$ model.