  The accuracy of the constrained random phase approximation(cRPA) method is
examined in multi-orbital Hubbard models containing all possible on-site
density-density interactions. Using DMFT, we show that the effective model
constructed using cRPA fails to reproduce the spectral properties of the
original full model in a wide parameter range. By comparing quantities such as
the density of states and quasiparticle residues of the full and the effective
models, we show that cRPA systematically overestimates the screening of Hubbard
U for DMFT impurity solvers. We instead propose a new method to investigate the
screening mechanism in the system using the local polarization, which is highly
successful in reproducing spectra and also shows that the true screening is far
less than that predicted by RPA. Furthermore, we compare the fully screened
interaction $W$ given by RPA and our new method and show that the RPA $W$ is
also overscreened and misses the signatures of local screening, which are
clearly present in our new method.
