Development of a unified theory for the dynamical mean-field and the spin fluctuations in strongly_correlated electron systems

在这个项目中，我为强相关电子系统开发了动态平均场（DMFT）和自洽重整自旋涨落（SCR）的统一理论。为此，我提出了一种新的修正微扰理论格式，用于解决我们统一理论中的有效杂质问题。然后，我得到了局部和整体的动态磁化率，我在其中引入了一个类似于可控硅的条件来控制磁矩的幅度。本理论在量子临界点（QCP）附近表现出与SCR相同的临界行为，但在SCR之外，可以纳入强相关效应和特定材料在有限能量和温度下的结构。我已经把这个理论应用到单波段哈伯德模型上，并证实它确实很有效。将修正的杂质微扰理论推广到轨道简并的情况。我还将自旋涨落的t…More二粒子自洽理论（TPSC）应用于杂质Anderson模型，发现它在强相关极限下不能得到正确的低能尺度。结果表明，这一点的改进导致了我们的统一理论。我还研究了近藤绝缘子，特别关注FeSi，它被认为是SCR描述的材料的典型例子。我从强相关性的角度对该材料进行了重新研究，阐明了光电导率的温度依赖性只能用多体效应来解释。最近，近藤绝缘体引起了研究人员的兴趣，因为它们是一种好的热电装置的候选材料。由于自旋涨落对热电性能的影响很大，我们将FeSi和YbB_12作为重要材料进行了研究。我发现，从波段计算得到的简化双波段模型中引入少量空穴的假设可以解释FeSi的热功率。相似的模型不能解释YbB12热能的温度依赖性。我发现强相关效应对于理解这些材料至关重要。少

In this project, I have developed a unified theory of the dynamical mean field (DMFT) and self-consistently renormalized spin-fluctuations (SCR) for the strongly correlated electron systems. To do this, I have formulated a new scheme of the modified perturbation theory which is used to solve the effective impurity problem in our unified theory. Then, I obtained the local and bulk dynamical susceptibility, to which I have introduced a condition similar to that in SCR to control the amplitude of the magnetic moment. The present theory exhibits the same critical behaviors in the vicinity of the quantum critical point (QCP) as SCR, but can incorporate, beyond SCR, the effects of strong correlation and the structures of specific materials at finite energy and temperature. I have applied the theory to the single-band Hubbard model and confirmed that it really works well. The modified perturbation theory for impurity is extended to the case of the orbital degeneracy. I have also applied the t … More wo-particle-self-consistent theory (TPSC) of spin fluctuations to the impurity Anderson model, and found that it does not yield the correct low energy scale in the strong correlation limit. It was shown that the improvement of this point leads to our unified theory.I have also studied the Kondo insulators, paying special attention to FeSi, which has been considered to be a typical example of the materials described by SCR. I have reinvestigated this material from the viewpoint of the strong correlation and clarified that the temperature dependence of the optical conductivity can be explained only by the many-body effect. Recently, the Kondo insulators are attracting researchers' interest because they are the candidates for a good thermoelectric device. Since the thermoelectric properties could be much affected by the spin fluctuations, we have studied FeSi and YbB_12 as important materials. I found that the thermopower of FeSi can be explained by the assumption that a small amount of holes are introduced to the simplified two-band model obtained from the band-calculation. The similar model cannot explain temperature dependence of the thermopower of YbB12. I found that the strong correlation effects are crucial to understand this material. Less