Screened-interaction expansion for the Hubbard model and determination of the quantum Monte Carlo Fermi surface

We develop a systematic self-consistent perturbative expansion for the self-energy of Hubbard-like models. The interaction lines in the Feynman diagrams are dynamically screened by the charge fluctuations in the system. Although the formal expansion is exact-assuming that the model under the study is perturbativeonly if diagrams to all orders are included, it is shown that 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 intermediate-to-high temperatures, we use the exact charge-fluctuation susceptibility from quantum Monte Carlo ͑QMC͒ 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 filling, and it is found that our approximation for the imaginary part of the one-particle self-energy agrees well with the QMC results in the low-energy scales at this particular filling. But the usefulness of the approximation is hindered by the fact that it has the incorrect filling dependence when the filling deviates from this value. We also calculate the exact QMC Fermi surfaces for the two-dimensional ͑2D͒ Hubbard model for several fillings. Our results near half filling show extreme violation of the concepts of the band theory; in fact, instead of growing, the Fermi surface vanishes when doped toward the half-filled MottHubbard insulator. Sufficiently away from half filling, noninteractinglike Fermi surfaces are recovered. These results combined with the Luttinger theorem might show that diagrammatic expansions for the nearly-halffilled Hubbard model are unlikely to be possible; however, the nonperturbative part of the solution seems to be less important as the filling gradually moves away from one half. Results for the 2D one-band Hubbard model for several hole dopings are presented. Implications of this study for the high-temperature superconductors are also discussed

Screened-interaction expansion for the Hubbard model and determination of the quantum Monte Carlo Fermi surface

We develop a systematic self-consistent perturbative expansion for the self energy of Hubbard-like models. The interaction lines in the Feynman diagrams are dynamically screened by the charge fluctuations in the system. Although the formal expansion is exact-assuming that the model under the study is perturbative-only if diagrams to all orders are included, it is shown that for large-on-site-Coulomb-repulsion-U systems weak-coupling expansions to a few orders may already converge. We show that the screened interaction for the large-U system can be vanishingly small at a certain intermediate electron filling; and it is found that our approximation for the imaginary part of the one-particle self energy agrees well with the QMC results in the low energy scales at this particular filling. But, the usefulness of the approximation is hindered by the fact that it has the incorrect filling dependence when the filling deviates from this value. We also calculate the exact QMC Fermi surfaces for the two-dimensional (2-D) Hubbard model for several fillings. Our results near half filling show extreme violation of the concepts of the band theory; in fact, instead of growing, Fermi surface vanishes when doped toward the half-filled Mott-Hubbard insulator. Sufficiently away from half filling, noninteracting-like Fermi surfaces are recovered. These results combined with the Luttinger theorem might show that diagrammatic expansions for the nearly-half-filled Hubbard model are unlikely to be possible; however, the nonperturbative part of the solution seems to be less important as the filling gradually moves away from one half. Results for the 2-D one-band Hubbard model for several hole dopings are presented. Implications of this study for the high-temperature superconductors are also discussed.Comment: 11 pages, 12 eps figures embedded, REVTeX, submitted to Phys. Rev. B; (v2) minor revisions, scheduled for publication on November 1

Doping-dependent study of the periodic Anderson model in three dimensions

We study a simple model for $f$-electron systems, the three-dimensional periodic Anderson model, in which localized $f$ states hybridize with neighboring $d$ states. The $f$ states have a strong on-site repulsion which suppresses the double occupancy and can lead to the formation of a Mott-Hubbard insulator. When the hybridization between the $f$ and $d$ states increases, the effects of these strong electron correlations gradually diminish, giving rise to interesting phenomena on the way. We use the exact quantum Monte-Carlo, approximate diagrammatic fluctuation-exchange approximation, and mean-field Hartree-Fock methods to calculate the local moment, entropy, antiferromagnetic structure factor, singlet-correlator, and internal energy as a function of the $f-d$ hybridization for various dopings. Finally, we discuss the relevance of this work to the volume-collapse phenomenon experimentally observed in f-electron systems.Comment: 12 pages, 8 figure

Fluctuation Exchange Analysis of Superconductivity in the Standard Three-Band CuO2 Model

The fluctuation exchange, or FLEX, approximation for interacting electrons is applied to study instabilities in the standard three-band model for CuO2 layers in the high-temperature superconductors. Both intra-orbital and near-neigbor Coulomb interactions are retained. The filling dependence of the d(x2-y2) transition temperature is studied in both the "hole-doped" and "electron-doped" regimes using parameters derived from constrained-occupancy density-functional theory for La2CuO4. The agreement with experiment on the overdoped hole side of the phase diagram is remarkably good, i.e., transitions emerge in the 40 K range with no free parameters. In addition the importance of the "orbital antiferromagnetic," or flux phase, charge density channel is emphasized for an understanding of the underdoped regime.Comment: REVTex and PostScript, 31 pages, 26 figures; to appear in Phys. Rev. B (1998); only revised EPS figures 3, 4, 6a, 6b, 6c, 7 and 8 to correct disappearance of some labels due to technical problem