  We calculate real-space static correlation functions related to basic
entities of the one-dimensional Hubbard model, which emerge from the exact
Bethe-ansatz solution. These entities involve complex rearrangements of the
original electrons. Basic ingredients are operators related to unoccupied,
singly occupied with spin up or spin down and doubly occupied sites. The
spatial decay of their correlation functions is determined using an approximate
mean-field-like approach based on the Zou-Anderson transformation and DMRG
results for the half-filled case. The nature and spatial extent of the
correlations between two sites on the Hubbard chain is studied using the
eigenstates and eigenvalues of the two-site reduced density matrix.
