Theories of anomalous metallic state and Mott trasition

我们的项目对Mott-绝缘体-金属相变附近的d电子系统的理论研究已经取得了一些成果。我们项目的中心课题是金属-绝缘体转变或Mott转变，在那里我们发现了一个新的普适类，具有大的动力学指数。我们发现，强动量相关的重整化会导致奇异重整化。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。随着我们对低维的奇异动量依赖和由此产生的非相干电荷动力学的澄清，对Mott现象的量子相变的理论理解进入了一个新的阶段。我们研究的另一个重要课题是d电子系统中的络合物性质的研究。例如，在锰氧化物中，强相关效应、自旋/轨道简并、Jahn-Teller效应…之间的纠缠和相互作用更多的研究已经尽可能地以现实的方式进行。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/电荷有序和晶格扭曲的实验结果。对铜酸盐超导体的研究也取得了进展。各种方法，如t-J模型中的从属玻色子方法、1/N展开、自旋涨落理论和关联费米子的数值方法，已经被应用到具有许多新命题和概念的二维模型中来解释实验结果。尽管对超导电性的机制还没有达成共识，但在统一的框架下，已经提出了描述Mott绝缘体、欠掺杂和过掺杂金属的模型。在理解Mott绝缘体的量子磁性方面也取得了重要进展，特别是在单重态自旋间隙相和反铁磁相之间的竞争方面。梯形化合物也得到了广泛的研究。较少

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