Screened-interaction expansion for the Hubbard model and determination of the quantum Monte Carlo Fermi surface - art. no. 195105

We develop a systematic self-consistent perturbative expansion for the self -energy of Hubbard-like models. The interaction lines in the Feynman diagra ms are dynamically screened by the charge fluctuations in the system. Altho ugh the formal expansion is exact-assuming that the model under the study i s perturbative-only if diagrams to all orders are included, it is shown tha t for large-on-site-Coulomb-repulsion-U systems weak-coupling expansions to a few orders may already converge. In order to test the approximation at i ntermediate-to-high temperatures, we use the exact charge-fluctuation susce ptibility from quantum Monte Carlo (QMC) simulation studies as input, which determines the exact screened interaction, and compare our results for the self-energy to the QMC results. We also make comparisons with fluctuation- exchange approximation. We show that the screened interaction for the large -U system can be vanishingly small at a certain intermediate electron filli ng, and it is found that our approximation for the imaginary part of the on e-particle self-energy agrees well with the QMC results in the low-energy s cales at this particular filling. But the usefulness of the approximation i s hindered by the fact that it has the incorrect filling dependence when th e filling deviates from this value. We also calculate the exact QMC Fermi s urfaces for the two-dimensional (2D) Hubbard model for several fillings. Ou r results near half filling show extreme violation of the concepts of the b and theory; in fact, instead of growing, the Fermi surface vanishes when do ped toward the half-filled Mott-Hubbard insulator. Sufficiently away from h alf filling, noninteractinglike Fermi surfaces are recovered. These results combined with the Luttinger theorem might show that diagrammatic expansion s for the nearly-half-filled Hubbard model are unlikely to be possible; how ever, the nonperturbative part of the solution seems to be less important a s the filling gradually moves away from one half. Results for the 2D one-ba nd Hubbard model for several hole dopings are presented. Implications of th is study for the high-temperature superconductors are also discussed.