Improved mean-field scheme for the Hubbard model.

Ground state energies and on-site density-density correlations are calculated for the 1-D Hubbard model using a linear combination of the Hubbard projection operators. The mean-eld coeecients in the resulting linearized Equations of Motion (EOM) depend on both one-particle static expectation values as well as static two-particle correlations. To test the model, the one particle expectation values are determined self-consistently while using Lanczos determined values for the two particle correlation terms. Ground state energies and on-site density-density correlations are then compared as a function of U to the corresponding Lanczos values on a 12 site Hubbard chain for 1/2 and 5/12 llings. To further demonstrate the validity of the technique, the static correlation functions are also calculated using a similar EOM approach, which ignores the eeective vertex corrections for this problem, and compares those results as well for a 1/2 lled chain. These results show marked improvement over standard mean-eld techniques.