Reliable Ab initio Downfolding: From an Exact Formalism to Precise Benchmarks

Reliable model Hamiltonians are central to understanding correlated electron systems, yet their derivation from first principles often involves uncontrolled approximations. In this talk, I present a rigorous formulation of downfolding based on a path-integral representation of the many-body problem, which yields an exact effective action for a chosen set of low-energy degrees of freedom. This exact formalism provides a systematic foundation for constructing reliable effective models and identifies the conditions under which perturbative truncations remain justified. Within this framework, I analyze the constrained random phase approximation (cRPA), clarifying when and why it provides meaningful estimates for screened interactions in the low-energy target space. To assess its quantitative reliability, we perform a comprehensive benchmarking of the DFT+cRPA approach for a correlated molecular system, evaluating the effects of target-space basis choice, double-counting, and screening models. Together, these results connect formal control with practical accuracy in ab initio downfolding.