Two-particle self-consistency in diagrammatic theories for strongly correlated electron systems

强相关电子系统图解理论中的双粒子自洽

• 批准号: 407372336
• 负责人: Dr. Georg Rohringer
• 金额: --
• 依托单位: Institut für Festkörperphysik
• 依托单位国家: 德国
• 项目类别: Independent Junior Research Groups
• 财政年份: 2018
• 资助国家: 德国
• 起止时间: 2017-12-31 至 2023-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/407372336?language=en
• 关键词: Two; particle; self; consistency; diagrammatic

Strongly correlated materials exhibit some of the most exciting phenomena in solid state physics, including high-temperature superconductivity, magnetism or giant magneto-resistance. In view of these fascinating physical properties, which are potentially also of high technological relevance, a comprehensive theoretical understanding of such systems is highly desirable. In this respect, substantial progress has been achieved in the last 20 years by dynamical mean field theory (DMFT) which captures a relevant part of the correlations, i.e. the local ones. However, most of the remarkable physics of correlated electrons on a lattice is also strongly influenced by non-local correlations effects. To include them in the theoretical description, a number of so-called “diagrammatic extensions” of DMFT has been developed in the last decade. These quantum field theoretical approaches perform a (Feynman) diagrammatic expansion around DMFT which includes non-local correlation effects on top of the local ones of DMFT. However, in spite of the intense forefront research on these techniques in the last years they still exhibit serious limitations. First of all, they are not fully two-particle self-consistent which means that they might yield different results for physical observables (such as the potential energy) when they are calculated in different ways (i.e. from one- or two-particle correlation functions). Moreover, in their current implementations they are applicable only to simple one-band model Hamiltonians but not for the description of realistic correlated materials. In this project, we will develop a new method on the basis of existing schemes, such as, e.g. the dynamical vertex approximation, which will overcome these limitations in an efficient way. This will be achieved by physically driven renormalization of the two-particle correlation functions (susceptibilities) which are obtained by the respective diagrammatic extensions of DMFT. This approach will be then extended from a single- to a multi-orbital treatment in order to make it applicable for the investigation of realistic correlated materials. The new algorithms developed within the project will be then exploited to obtain fundamentally new insights into the physics of strongly correlated electron systems. Specifically, we will investigate antiferromagnetism and its interplay with unconventional superconductivity in model as well as realistic systems such as cuprates, itinerant magnetism in iron and nickel, and the Hall conductivity in the Hubbard model in an external magnetic field. The latter will allow for exciting new insights into the effects of strong non-local correlations on topological states of matter. Eventually, our theoretical improvements will lead to an unambiguous and thermodynamically consistent description of many-electron properties, a highly relevant topic also for reliable lattice optimization calculations within the ab initio treatment of correlated materials.

强关联材料表现出固态物理中一些最令人兴奋的现象，包括高温超导性、磁性或巨磁阻。鉴于这些令人着迷的物理性质，它们也可能具有很高的技术相关性，因此非常需要对此类系统进行全面的理论了解。在这方面，在过去的20年里，动态平均场理论（DMFT）已经取得了实质性的进展，它捕获了相关的一部分，即本地的。然而，晶格上关联电子的大多数显著物理也受到非局域关联效应的强烈影响。为了将它们包括在理论描述中，在过去十年中已经开发了一些所谓的DMFT的“图解扩展”。这些量子场论方法围绕DMFT执行（费曼）图解扩展，其包括在DMFT的局部相关效应之上的非局部相关效应。然而，尽管这些技术在过去几年中进行了深入的前沿研究，但它们仍然表现出严重的局限性。首先，它们不是完全的两粒子自洽的，这意味着当它们以不同的方式（即从一个或两个粒子的相关函数）计算时，它们可能会产生不同的物理观测值（如势能）结果。此外，在他们目前的实现，他们只适用于简单的单带模型哈密顿，但不为现实的相关材料的描述。在这个项目中，我们将在现有方案的基础上开发一种新的方法，例如动态顶点近似，它将以有效的方式克服这些限制。这将通过物理驱动的重整化的两粒子相关函数（双折射率），这是由DMFT各自的图形扩展。然后，将这种方法从单轨道扩展到多轨道处理，以使其适用于现实相关材料的调查。在该项目中开发的新算法将被利用，以获得对强相关电子系统物理学的全新见解。具体来说，我们将研究反铁磁性及其与模型中的非常规超导性的相互作用，以及现实系统，如铜酸盐，铁和镍中的巡回磁性，以及外部磁场中Hubbard模型中的霍尔电导率。后者将允许令人兴奋的新见解的影响，强非局部相关性的拓扑状态的物质。最终，我们的理论改进将导致一个明确的和一致的多电子性质的描述，一个高度相关的主题，也为可靠的晶格优化计算相关材料的从头计算处理。