Correlations in the ground state of the one-dimensional Hubbard model

With eigenfunctional theory and a rigorous expression of exchange-correlation energy of a general interacting electron system, we study the ground state properties of the one-dimensional Hubbard model, and calculate the ground-state energy as well as the charge gap at half-filling for arbitrary coupling strength u=U/(4t) and electron density nc. We find that the simple linear approximation of the phase field works well in weak coupling case, but it becomes inappropriate as the on-site Coulomb interaction becomes strong where the fluctuations of the bosonic auxiliary field are strong. Then we propose a new scheme by adding Gutzwiller projection which suppresses the density fluctuations and the new results are quite close to the exact ones up to considerably strong coupling strength u=3.0 and for arbitrary electron density nc. Our calculation scheme is proved to be effective for strongly correlated electron systems in one dimension, and its extension to higher dimensions is straightforward.