Merging of dynamical mean-field theory and functional renormalization group

超越微扰状态的相关电子系统的理论描述是凝聚态物理前沿研究的主要挑战之一。事实上，从体系到纳米级的相关电子性质的实验工程取得的令人印象深刻的快速进展，尚未与描述它们的理论工具的相应进展完全平衡。该项目旨在填补这一空白与算法实现的新方案最近提出的申请人[物理]。[j]，由两种最成功的量子多体方法组成：动态平均场理论（DMFT）和泛函重整化群（fRG）。尽管它们取得了成功，但事实上，这两种方法都有明显的局限性：由于其平均场描述，DMFT忽略了所有非局部空间相关性，而它捕获了驱动的电子相关性的局部部分，例如Mott金属-绝缘体跃迁。相比之下，非局域相关可以有效地解决由fRG，其应用，然而，通常限于弱电子相关的摄动制度。我们的新方法，称为DMF2RG，旨在通过使用DMFT溶液作为fRG治疗的起点，克服两者的限制。通过这种方式，DMFT从一开始就充分考虑了局部（可能是强）相关性，而非局部相关性将通过fRG程序系统地包括在内。通过利用现有最先进方法的互补优势，DMF2RG代表了相关电子理论及其应用的突破。提议的项目包括DMF2RG思想的有效算法实现，对其他方法和限制案例进行基准测试，最后将其应用于原型模型和现实系统。特别是，我们的目标是为高科学兴趣系统中工作的相互竞争的物理机制提供新的见解，例如轻掺杂莫特绝缘体的赝隙相，非常规超导体和半导体表面上的附原子系统。考虑到我们的新方法在整个固态物理学界的广泛应用，从长远来看，DMF2RG的多轨道实现是一个长远的前景。

The theoretical description of correlated electron systems beyond the perturbative regime represents one of the main challenges for the forefront research in condensed matter physics. In fact, the impressively fast progress in the experimental engineering of correlated electron properties from bulk systems down to the nanoscale is not fully balanced yet by corresponding advances in the theoretical tools to describe them. This project aims at filling this gap with the algorithmic implementation of a novel scheme recently proposed by the applicants in [Phys. Rev. Lett. 112, 196402 (2014)], consisting in the combination of two of the most successful quantum many-body methods: the dynamical mean field theory (DMFT) and the functional renormalization group (fRG). In spite of their success, in fact, both methods have significant limitations: due to its mean-field description, DMFT neglects all non-local spatial correlations, while it captures the local part of the electronic correlations which drive, e.g., the Mott metal-insulator transitions. In contrast, the non-local correlations can be efficiently tackled by the fRG, whose application is, however, typically limited to the pertubative regime of weak electronic correlations. Our novel approach, coined DMF2RG, aims at overcoming the restrictions of both, by using the DMFT solution as starting point of the fRG treatment. This way, local - and possibly strong - correlations are fully taken into account from the very beginning within DMFT, while non-local correlations will be systematically included through the fRG procedure. By exploiting the complementary strengths of the existing state-of-the-art approaches, the DMF2RG represents a breakthrough for the theory of correlated electrons and its applications. The proposed project includes an efficient algorithmic implementation of the DMF2RG idea, its benchmarking against other methods and limiting cases and, finally, its application to prototype models and realistic systems. In particular, we aim at providing a new insight on the competing physical mechanisms at work in systems of high scientific interests, such as the pseudogap phases of lightly doped Mott insulators, unconventional superconductors and systems of adatoms on semiconducting surfaces. A long-term perspective is the multi-orbital implementation of the DMF2RG in view of a broad application of our new method by the whole solid state physics community.