Theories of anomalous metallic state and Mott trasition

本项目在mott -绝缘体-金属跃迁附近的d电子系统的理论研究已经取得了一些成果。我们项目的中心主题是金属绝缘体跃迁或莫特跃迁，在那里我们发现了一个具有大动态指数的新普适类。我们发现强动量相关重整化诱导奇异重整化。用自旋/轨道涨落和动量简并之间的协同效应成功地描述了跃迁的反常特征。随着我们对低维和由此产生的非相干电荷动力学的奇异动量依赖的澄清，对莫特现象的量子相变的理论认识进入了一个新的阶段。我们研究的另一个重要课题是研究d电子系统的复杂性质。例如，在锰氧化物中，强相关效应之间的纠缠和相互作用、自旋/轨道简并、Jahn-Teller效应等都得到了尽可能真实的研究。通过第一性原理方法和模型计算，成功地比较了金属和绝缘体中自旋/轨道/电荷有序和晶格畸变的实验结果。对铜超导体的研究也取得了进展。各种方法，如t-J模型中的从玻色子方法、1/N展开、自旋涨落理论和相关费米子的数值方法已被应用于二维模型，并提出了许多新的建议和概念来解释实验结果。虽然对超导机制尚未达成共识，但已经在统一的框架上提出了描述莫特绝缘体、欠掺杂和过掺杂金属的模型。在理解莫特绝缘体中的量子磁性方面也取得了重要进展，特别是在单线态自旋间隙相和反铁磁相之间的竞争方面。阶梯形化合物也得到了深入的研究。少

Theoretical studies of our project on d-electron systems near Mott-insulator-metal transitions have reached a number of achievements. The central subject of our project is metal-insulator transitions or Mott transitions, where we have found a new universality class with a large dynam-ical exponent. We have found that strong momentum dependent renormalization induces singular renormalization. The anomalous feature of the transition is successfully described by synergy effects between spin/orbital fluctuations and momentum degeneracy. With our clarification of singular momentum dependence due to low dimensionality and resultant incoherent charge dynamics, theoretical understanding of the quantum phase transition for the Mott phenomena has entered a new stage. Another important subject in our research was studies on complex properties in d-electron systems. For instance, in Mn oxides, entanglement and interplay among strong cor-relation effects, spin/orbital degeneracy, Jahn-Teller effect … More have been studied in a realistic way as much as possible. Through first principles methods and model calculations, experimental results on spin/orbital/charge orderings and lattice distortions in metals and insulators have successfully been compared. Studies on cuprate superconductors have also made progress. Various approaches such as slave boson methods in the t-J models, 1/N expansion, spin fluctuation theory and numerical methods for correlated fermions have been applied to two-dimensional models with many new pro-posals and concepts to interpret experimental results. Although the consensus on the mechanism of superconductivity has not been reached yet, models to describe the Mott insulator, underdoped and overdoped metals have been proposed on a unified framework. Important progress in under-standing on quantum magnetism in the Mott insulator has also been achieved, especially on the competition between the singlet spin-gapful and the antiferromagnetic phases. Ladder compounds have also been studied intensively. Less