Accuracy of downfolding based on the constrained random phase approximation

We study the reliability of the constrained random phase approximation (cRPA) method for the calculation of low-energy effective Hamiltonians by considering multi-orbital lattice models with one strongly correlated "target" band and two weakly correlated "screening" bands. The full multi-orbital system and the effective model are solved within dynamical mean field theory (DMFT) in a consistent way. By comparing the quasi-particle weights for the correlated bands, we examine how accurately the effective model describes the low-energy properties of the multi-band system. We show that the violation of the Pauli principle in the cRPA method leads to overscreening effects when the inter-orbital interaction is small. This problem can be overcome by using a variant of the cRPA method which restores the Pauli principle.