Theoretical Study of Strongly Correlated Electron Systems with Orbital Degeneracy

最近在钙钛矿型锰氧化物中发现了巨大的磁阻，随后在实验和相关材料的理论研究中发生了爆炸活动。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)基本的u…进一步了解了具有轨道简并性的强关联系统中出现铁磁性的条件、铁磁态的输运性质、反铁磁性与铁磁性之间的竞争以及量子涨落的影响。特别是阐明了a)当n(每格位的电子数密度)在1到2之间时，铁磁态在较宽的参数范围内是稳定的，因为所谓的双交换机制是非常有效的。b)当n=1伴随着轨道有序的铁磁性是稳定的，c)当n&lt；1)电子能带结构和/或晶格结构对铁磁性的稳定性有很大影响。2)从理论上推导了半金属中电阻率的T立方定律。3)从电子-声子相互作用的角度，从理论上推导了钙钛矿型锰氧化物中观察到的反常磁振子色散。4)LWE对双交换模型进行了大规模的量子蒙特卡罗模拟，并估算了铁磁相变的临界温度和临界铟。较少

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