Ab-initio downfolding to interacting model Hamiltonians: comprehensive analysis and benchmarking*

Although regularly used to derive simplified model Hamiltonians and to describe correlated matter, ab-initio downfolding procedures have not been comprehensively analyzed.

We fill this gap with a systematic benchmark study in the vanadocene molecule, where we are able to first establish reference data for ground and charge-neutral excited state energies and charge densities using state-of-the-art first-principles methods (the equation-of-motion coupled-cluster method, fixed-node diffusion Monte Carlo, and auxiliary field quantum Monte Carlo). The downfolding procedure is assessed afterwards based on comparisons to these first-principles references. We analyze all downfolding aspects, including the Hamiltonian form, target basis, double-counting correction, and Coulomb interaction screening models. We find that the choice of target-space basis functions emerges as a key factor for the quality of the downfolded results, while orbital-dependent double-counting correction diminishes the quality. Background screening to the Coulomb interaction matrix elements primarily affects crystal-field excitations. Our benchmark uncovers the relative importance of each downfolding step and offers insights into the potential accuracy of minimal downfolded model Hamiltonians.