电子关联、阻挫及非常规超导已经成为强关联物理的中心问题。大量非常规超导现象出现在材料的磁性边缘，而重费米子系统则是研究量子临界涨落、磁性阻挫及配对涨落的理想系统。处理关联费米子的标准方法是动态平均场理论(DMFT)。该理论能够精确处理局域的动态关联效应，但是忽略了高斯近似之外的空间延展的关联效应，所以无法处理磁性关联与近藤屏蔽的动态相互作用，非常规配对涨落，或磁性阻挫等。为此，本项目拟建立一套动态平均场理论（DMFT）的延伸。该延伸结合了一套可以捕获近藤效应与RKKY相互作用动态竞争的拓展动态平均场理论，以及一个可以用于研究空间延展关联作用的微扰方法--对偶费米子法。若项目获得成功，这将有助于我们理解自旋阻挫在重费米子普适相图中，及其在近藤破坏量子临界点附近的超导产生中所起的作用。同时，该方法也应适用于d-电子材料。

The interplay of electron correlation and frustration and the emergence of unconventional superconductivity have become a central issue in the physics of strongly correlated electron systems and are highly relevant in materials science. Unconventional superconductivity has been found in a variety of materials at the brink of magnetism. Heavy fermion systems turned out to be ideal setting to explore the interplay of quantum critical fluctuations with spin frustration and pairing fluctuations. Rare earth compounds where frustration dominates physical properties include Pr2Ir2O7 and the Shastry-Sutherland lattice compound Yb2Pt2Pb. A concrete example where a metallic spin liquid seems to occur in close proximity to a Kondo-destroying quantum critical point is Ir-doped YbRh2Si2. The standard approach to correlated fermions is the dynamical mean field theory (DMFT) that treats local dynamical correlations accurately but ignores any spatially extended correlations beyond the Gaussian approximation. It is thus inapt to study the dynamic interplay of magnetic correlations with Kondo screening processes, unconventional pairing fluctuations, or spin frustration. Here, I propose to develop an extension of the DMFT that combines an extended DMFT version capable of capturing the dynamic competition between the Kondo effect and the RKKY interaction with a perturbative scheme, termed dual fermions, that would allow the study of spatially extended correlations like spin frustration and pairing fluctuations. In important technical aspect in any DMFT scheme is how to obtain the solution of the underlying self-consistent quantum impurity problem. In addition to the now standard solver, the continuous-time quantum Monte Carlo, we will investigate how the dual fermion scheme can be applied on real frequencies in order to bring in dynamical large-N and self-consistent diagrammatic methods and if the numerical renormalization group (NRG) can be used within the proposed multiscale method. If successful, we expect a number of insights regarding the role of spin frustration on the universal phase diagram of the heavy fermions and to the emergence of superconductivity near Kondo-destroying quantum criticality. An application to d-electron based materials should also be possible.