  The problem of spin-charge separation is analyzed numerically in the metallic
phase of the one-band Hubbard model in one dimension by studying the behavior
of the single-particle Green's function and of the spin and charge
susceptibilities. We first analyze the Quantum-Monte Carlo data for the
imaginary-time Green's function within the Maximum Entropy method in order to
obtain the spectral function at real frequencies. For some values of the
momentum sufficiently away from the Fermi surface two separate peaks are found,
which can be identified as charge and spin excitations.
  In order to improve our accuracy and to be able to extend our study to a
larger portion of the Brillouin zone, we also fit our data with the
imaginary-time Green's function obtained from the Luttinger-model solution with
two different velocities as fitting parameters. The excitation energies
associated with these velocities turn out to agree, in a broad range of
momenta, with the ones calculated from the charge and spin susceptibilities.
This allows us to identify these single-particle excitations as due to a
separation of spin and charge. Remarkably, the range of momenta where
spin-charge separation is seen extends well beyond the region of linear
dispersion about the Fermi surface. We finally discuss a possible extension of
our method to detect spin-charge separation numerically in two dimensions.
