Functional renormalization group approach to low-energy effective interactions in multi-band many-fermion systems

我们建议扩展和应用最近开发的泛函重整化群（fRG）计划来计算多带多费米子系统中的低能有效相互作用，其中高能量带的影响被吸收到一个或几个低能量带的有效相互作用。该fRG方案包括并扩展了约束RPA（cRPA）方法，该方法已在许多不同的材料系统中卓有成效地使用，作为一种工具来计算扩展的Hubbard模型的相互作用参数，用于描述费米能级附近的能带。我们认为，使用新的fRG方案，我们可以通过总结不仅仅是一类特定的图表来评估cRPA的有效性。玩具模型中的第一个应用（发表在Phys. Rev. B）显示，确实存在cRPA和较少ad-hoc fRG方法给出不同结果的参数机制，无论是关于有效相互作用的频率结构还是关于裸排斥的平均抑制。目前的项目旨在改进fRG方案的实施，以便可以处理更现实的模型，并可以获得cRPA之外的有效相互作用的更详细的图片。关键的分析，应该让我们来对待现实的模型是一个合适的分解的波矢量和频率依赖的相互作用，以前已被用于研究的单波段哈伯德和杂质模型。我们给出了可行性参数，数值的努力是易于使用这种分解。第一个应用程序将解决模型的石墨烯，我们认为，一个更精细的确定有效的相互作用参数可能是重要的相关效应的正确和令人满意的描述。对于这个项目在多粒子物理学的方法发展和当前固体物理学的关键材料之间的接口，我们要求一个博士学位的资金。36个月的职位。

We propose to extend and apply a recently developed functional renormalization group (fRG) scheme to compute low-energy effective interactions in multiband many-fermion systems, where the effects of higher-energy bands are absorbed into the effective interactions in one or few low-energy band. This fRG scheme includes and extends the constrained-RPA (cRPA) approach that has been used fruitfully in many different material systems as a tool to compute the interaction parameters of extended Hubbard models for the description of the bands near the Fermi level. We argue that with the new fRG scheme, we can assess the validity of the cRPA by summing more than just a particular class of diagrams. A first application in a toy model (published in Phys. Rev. B) revealed that there are indeed parameter regimes where cRPA and the less ad-hoc fRG approach give different results, both with respect to the frequency structure of the effective interaction as well as regarding the average suppression of the bare repulsion. The current project now aims atimproving the implementation of the fRG scheme such that more realistic models can be tackled and that a more detailed picture of the effective interactions beyond cRPA can be obtained. The key ansatz that should allow us to treat realistic models is a suitable decomposition of the wavevector- and frequency dependence of the interactions that has previously been used for the study of one-band Hubbard and impurity models. We give feasibility arguments that the numerical effort is tractable using this decomposition. First applications will address models for graphene, for which we argue that a more refined determination of effective interaction parameters may be important for a correct and satisfactory description of correlation effects. For this project at the interface between methodical development in many-particle physics and key materials in current solid physics we request the funding of one Ph.D. positions for 36 months.