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

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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.