Microscopic derivation of effective lattice model Hamiltonians for long-range interacting atoms

该项目旨在提供一种基于功能重整化群(FRG)的方案，用于改进有效低能模型的构造，其精确确定对于定量理论至关重要。FRG以前是为了确定物质系统的真实有效相互作用而引入的，它解释了由于考虑到粒子从低能带到高能带的虚拟跃迁而导致的裸相互作用的重整化。对于具有短程相互作用的系统，这已被证明导致有效的多体相互作用，这可能对紧急集体行为和相关的低能相图产生重要影响。为了研究长程相互作用系统，我们将FRG推广到费米子系统的有效相互作用中。我们将对范例设置中远程相互作用和重整化效应之间的相互作用产生的相互作用结构进行系统分析，这也与研究单位的实验描述有关，其中有几个实验平台可供基准和直接应用。从长远来看，我们计划将FRG的实施与现有的计算里德堡势的软件包联系起来。

The proposed project aims to provide a functional renormalization group (fRG) based scheme for an improved construction of effective low-energy models whose precise determination is crucial for a quantitative theory. Previously introduced to determine realistic effective interactions for material systems, the fRG accounts for the renormalization of the bare interaction due to virtual transitions of particles from the low-energy bands in consideration to higher energy ones. For systems with short-range interactions, this has been shown to lead to effective multi-body interactions which can have an important impact on emergent collective behavior and the associated low-energy phase diagram. We here aim at the extension of the fRG for effective interactions formulated for fermionic systems in order to study long-range interacting systems. We will perform a systematic analysis of the interaction structures arising from the interplay between long-range interactions and renormalization effects in paradigmatic setups relevant also for the description of the experiments of the research unit, where several experimental platforms are available for benchmark and direct application. On a long-term perspective, we plan to link the fRG implementation to existing software packages for calculating Rydberg potentials.