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

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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