Effects of Electron Correlation, Orbital Degeneracy and Jahn-Teller Coupling in Perovskite Manganites

Roles of Coulomb interaction, orbital degeneracy and Jahn-Teller coupling in double-exchange models are examined for Mn perovskite oxides. We study the undoped Mott insulator as well as metal-insulator transitions by hole doping, and especially strong incoherence of ferromagnetic metal. We derive models where all the spins are fully polarized in two-dimensional planes as in the experimental indications, and investigate their ground-state properties by quantum Monte Carlo method. At half filling where the number of $e_{g}$ electron is one per site on average, the Coulomb interaction opens a Mott gap and induces a staggered orbital ordering. The opening of the Mott gap is, however, substantially slower than the mean-field results if the Jahn-Teller coupling is absent. The synergy between the strong correlation and the Jahn-Teller coupling largely enhances the Mott gap amplitude and reproduces realistic amplitudes and stabilization energy of the Jahn-Teller distortion. Upon doping, the orbital ordering stabilized by the Coulomb interaction is destroyed immediately. Toward the metal-insulator transition, the short-ranged orbital correlation is critically enhanced in metals, which should be related to strong incoherence of charge dynamics observed in experiments. Our model, moreover, exhibits a uniform ordering of $d_{x^{2}-y^{2}}$ orbital in a wide region of doping in agreement with experimental indications.