Realistic effective interactions from the functional renormalization group

固体中电子关联效应的一种广泛使用的方法是基于低能量有效模型(LEEM)的推导，该模型关注费米能级附近的能带。LEEM的参数由包含所有材料特定信息的高能问题决定。在这里，我们旨在通过使用基于泛函重整化群(FRG)的方案来改进LEEM的构造。积分出高能问题导致有效相互作用的重整化，这与具有预测能力的从头计算描述相关。特别是，FRG方法通过在平等的基础上恢复所有通道的贡献来考虑Wannier投影中裸露的库仑相互作用的屏蔽和其他重整化。关于所选频道中的受限恢复的这种扩展允许人们获得不同放映频道、它们的相互作用和它们的频率结构的更完整的画面。有效相互作用参数的相应变化会对低能物理产生重要影响。我们计划应用和测试FRG对纳米系统和作为异质结构的非均质系统的有效相互作用。在这些部分之后，后续的目标是将FRG有效的交互方案与从头开始的软件包(如WIEN2K或VASP)联系起来。与子项目P02、P03和P07的密切联系使我们能够与ViCoM中使用的其他理论工具进行比较，并评估低能量前端(P03和P15)的FRG建造LEEM的影响。

A widely-used approach to electronic correlation effects in solids is based on the derivation of low-energy effective models (LEEM) that focus on the bands near the Fermi level. The parameters of the LEEM are determined by the high-energy problem that contains all the materials specific information. We here aim at an improved construction of the LEEM by using a functional renormalization group (fRG) based scheme. Integrating out the high-energy problem leads to renormalizations of the effective interactions that are relevant for an ab-initio description with predictive power. In particular, the fRG approach takes into account the screening and other renormalizations of the bare Coulomb interactions in the Wannier projection by resumming the contributions of all channels on equal footing. This extension with respect to constrained resummations in a selected channel allows one to obtain a more complete picture of the different screening channels, their interplay and their frequency structure. The corresponding changes on the effective interaction parameters can have an important impact on the low-energy physics. We plan to apply and test the fRG for the effective interactions to nanosystems and inhomogeneous systems as heterostructures. After these parts, a subsequent goal is to link fRG effective interaction schemes to ab-initio software packages (like WIEN2K or VASP). The close contact to subprojects P02, P03 and P07 allows to compare to other theoretical tools used in ViCoM and to assess the effects of the fRG construction of the LEEM on the low-energy frontend (P03 and P15).