Numerical Studies of Strongly Correlated Electrons in Transition Metal Oxides

The purpose of this dissertation is to study different properties of the transition metal oxides, especially the high-Tc superconductors. Applying Monte Carlo methods to a Spin- Fermion model, the behavior of the band structure, Fermi surface, pairing correlations, and optical conductivity are studied. The numerical simulations are done at different temperatures, and densities relevant for the cuprates Previous Monte Carlo simulations of this model have shown the existence of charge stripes separated by anti ferromagnetic domains upon doping. These results are consistent with neutron scattering experiments. At half ling the ground state of the Spin-Fermion model is an insulator. The doped holes contribute to the formation of midgap bands by modifying the valence and the conduction band. The ground state appears to change from an insulator to a conductor. In the metallic regime the lower midgap and conduction bands overlap each other giving rise to a pseudogap in the density of states at the chemical potential. This agrees with the results from ARPES experiments. Both midgap and valence bands determine the Fermi surface. The D-wave pairing correlations, for all values of parameters, are stronger than S-wave. The D-wave pairing correlations are the strongest in the direction perpendicular to the dynamic stripes which appear in the ground state at some dopings. An optimal doping, where correlations are maximized, is observed close to 25% with an estimated critical temperature Tc = 100 200K in qualitative agreement with high-Tc cuprates phenomenology. The optical conductivity and Drude weight are studied as a function of electronic density and temperature. As temperature is reduced, spectral weight is transferred from high to low frequencies in agreement with the behavior observed experimentally. Varying the hole density, the Drude weight has a maximum at the optimal doping for the model are stronger. The inverse of the Drude weight, which is roughly proportional to resistivity, decreases linearly with temperature at the optimal doping, and it is abruptly reduced when robust pairing correlations develop upon further reducing the temperature. The general form of the optical conductivity is in good agreement with the experimental results for the cuprates.