Merging of dynamical mean-field theory and functional renormalization group

动力学平均场理论与泛函重正化群的融合

• 批准号: 299305516
• 负责人: Professorin Dr. Sabine Andergassen
• 金额: --
• 依托单位: Institut für Festkörperphysik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2016
• 资助国家: 德国
• 起止时间: 2015-12-31 至 2021-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/299305516?language=en
• 关键词: Merging; dynamical; mean; field; theory

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.

微扰区以外关联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，从体系统到纳米尺度的相关电子性质的实验工程的令人印象深刻的快速进展还没有完全平衡的理论工具来描述它们的相应进展。本项目旨在填补这一空白的算法实现的一种新的方案最近提出的申请人在[物理学评论快报。112，196402（2014）]，由两个最成功的量子多体方法的组合组成：动力学平均场理论（DMFT）和泛函重整化群（fRG）。尽管它们取得了成功，但事实上，这两种方法都有很大的局限性：由于其平均场描述，DMFT忽略了所有非局部空间相关性，而它捕获了电子相关性的局部部分，例如，Mott金属-绝缘体转变。相比之下，非本地的相关性可以有效地解决的fRG，其应用程序，但是，通常限于微扰制度的弱电子相关性。我们的新方法，创造DMF 2 RG，旨在通过使用DMFT解决方案作为fRG治疗的起点来克服两者的限制。通过这种方式，在DMFT中从一开始就充分考虑了局部相关性和可能的强相关性，而非局部相关性将通过fRG过程系统地包括在内。通过利用现有的最先进的方法的互补优势，DMF 2 RG代表了相关电子理论及其应用的突破。拟议的项目包括一个有效的算法实现DMF 2 RG的想法，它的基准对其他方法和限制的情况下，最后，它的应用原型模型和现实的系统。特别是，我们的目标是提供一个新的见解竞争的物理机制在工作中的系统的高科学利益，如pseudogap阶段的轻掺杂莫特绝缘体，非常规超导体和系统的吸附原子的半导体表面。一个长期的观点是DMF 2 RG的多轨道实施，鉴于我们的新方法被整个固态物理界广泛应用。