Theoretical Study of Strongly Correlated Electron Systems with Orbital Degeneracy

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Following the recent discovery of the colossal magneto-resistance in perovskite mangan oxides there occurred explosional activities in experimental as well as theoretical investigations of the related materials. In these materials the degeneracy of 3d atomic orbitals accompanied by Hund's coupling, anisotropic hopping matrix elements, and Jahn-Teller effect is playing a decisive role. This project aimed to clarify the effects of the orbtal degeneracy on the thermodynamic and transport properties of these materials and predict novel properties. We investigated following subjects :1) the ground state of the doubly-degenetrate Hubbard model in one dimension2) the groundstate of the double-exchange model in infinite dimensions3) electronic states and resistivity in the double exchange model in general dimensions4) anomalous magnon dispersion in perovskite mangan oxides5) ferromagnetic phase transitions in the double-exchange model.We obtained following results :1) We obtained fundamental u … More nderstanding on the conditions for the appearance of ferromagnetism in strongly correlated systems with orbital degeneracy, transport properties in ferromagnetic states, the competition between antiferromagnetism and ferromagnetism and the effects of quantum fluctuations.In particular we clarified that a) when n (electron number density per site) is between 1 and 2, ferromagnetic state is stable in a wide region of parameters since the so-called double-exchange mechanism is quite effective., b) when n=1 ferromagnetism accompanied by orbital order is stabilized and c) when n<1 the stability of ferromagnetism is strongly affected by the electronic band structure and/or the lattice structure.2) the T cube law of the resistivity in half metals was theoretically derived.3) the anomalous magnon dispersion observed in perovskite mangan oxides was theoretically derived in terms of electron-phonon interactions4) lwe have accomplished large scale quantum Monte Carlo simulations of the double exchange model and estimated the criticall temperature and critical indioes of the ferromagnetic phase transitions. Less