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功能重整化群（fRG）方案来计算多波段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带的有效相互作用中。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作为计算扩展Hubbard模型的相互作用参数的工具，用于描述费米能级附近的波段。我们认为，在新的fRG方案中，我们可以通过将不仅仅是一类特定的图相加来评估cRPA的有效性。在玩具模型中的首次应用（发表在《物理学》上）。Rev. B)揭示了确实存在一些参数制度，其中cRPA和较少特设的fRG方法在有效相互作用的频率结构以及裸排斥的平均抑制方面给出了不同的结果。目前的项目旨在改进fRG计划的实施，以便能够处理更现实的模型，并能够获得cRPA之外的有效相互作用的更详细的图像。使我们能够处理实际模型的关键分析是对相互作用的矢量和频率依赖性进行适当的分解，这种分解先前已用于研究单波段哈伯德和杂质模型。我们给出了可行性论证，说明利用这种分解方法，数值努力是可处理的。第一个应用将解决石墨烯的模型，我们认为更精确地确定有效的相互作用参数对于正确和令人满意地描述相关效应可能是重要的。这个项目是多粒子物理的系统发展和当前固体物理的关键材料之间的接口，我们要求一个博士职位的资助，为期36个月。

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.