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Spinon and eta-spinon correlation functions

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.