Theoretical Study of Strongly Correlated Electron Systems with Orbital Degeneracy

随着钙钛矿锰氧化物巨磁电阻效应的发现，相关材料的实验和理论研究都出现了爆炸性的发展。在这些材料中，伴随着Hund耦合、各向异性跳跃矩阵元和Jahn-Teller效应的3d原子轨道简并起着决定性的作用。该项目旨在阐明轨道简并度对这些材料的热力学和输运性质的影响，并预测新的性质。我们研究了以下问题：1）一维双简并Hubbard模型的基态; 2）无限维双交换模型的基态; 3）一般维双交换模型中的电子态和电阻率; 4）钙钛矿锰氧化物中的反常磁振子色散; 5）双交换模型中的铁磁相变。我们得到了以下结果：1）我们得到了双交换模型中的铁磁相变的基本规律; ...更多信息 理解了具有轨道简并的强关联系统中出现铁磁性的条件、铁磁态中的输运性质、反铁磁性与铁磁性之间的竞争以及量子涨落的影响，特别阐明了a）当n（每个位点的电子数密度）在1和2之间，由于所谓的双交换机制相当有效，铁磁状态在宽的参数范围内是稳定的，B）当n=1时，伴随轨道序的铁磁性是稳定的; c）当n<1时，铁磁性的稳定性受到电子能带结构和/或晶格结构的强烈影响; 2）从理论上推导了半金属电阻率的T立方定律; 3）从电子-声子相互作用的角度推导了钙钛矿锰氧化物中观察到的反常磁振子色散我们完成了双交换模型的大尺度量子MonteCarlo模拟，估计了铁磁相变的临界温度和临界指数。少

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