  Partially-projected Gutzwiller variational wavefunctions are used to describe
the ground state of disordered interacting systems of fermions. We compare
several different variational ground states with the exact ground state for
disordered one-dimensional chains, with the goal of determining a minimal set
of variational parameters required to accurately describe the
spatially-inhomogeneous charge densities and spin correlations. We find that,
for weak and intermediate disorder, it is sufficient to include spatial
variations of the charge densities in the product state alone, provided that
screening of the disorder potential is accounted for. For strong disorder, this
prescription is insufficient and it is necessary to include spatially
inhomogeneous variational parameters as well.
