  Roles of orbital and lattice degrees of freedom in strongly correlated
systems are investigated to understand electronic properties of perovskite Mn
oxides such as La_{1-x}Sr_{x}MnO_{3}. An extended double-exchange model
containing Coulomb interaction, doubly degenerate orbitals and Jahn-Teller
coupling is derived under full polarization of spins with two-dimensional
anisotropy. Quantum fluctuation effects of Coulomb interaction and orbital
degrees of freedom are investigated by using the quantum Monte Carlo method. In
undoped states, it is crucial to consider both the Coulomb interaction and the
Jahn-Teller coupling in reproducing characteristic hierarchy of energy scales
among charge, orbital-lattice and spin degrees of freedom in experiments. Our
numerical results quantitatively reproduce the charge gap amplitude as well as
the stabilization energy and the amplitude of the cooperative Jahn-Teller
distortion in undoped compounds. Upon doping of carriers, in the absence of the
Jahn-Teller distortion, critical enhancement of both charge compressibility and
orbital correlation length is found with decreasing doping concentration. These
are discussed as origins of strong incoherence in charge dynamics. With the
Jahn-Teller coupling in the doped region, collapse of the Jahn-Teller
distortion and instability to phase separation are obtained and favorably
compared with experiments. These provide a possible way to understand the
complicated properties of lightly doped manganites.
