On the limitations of cRPA downfolding

TL;DR

This paper critically examines the accuracy of the cRPA downfolding method in modeling low-energy electronic interactions, revealing significant discrepancies due to overlooked diagram cancellations, which impact ab-initio parameter estimation.

Contribution

The study demonstrates that cRPA predictions can be inaccurate due to diagram cancellations, challenging its reliability for low-energy effective interaction calculations.

Findings

cRPA often misestimates screening effects

Effective interactions can be barely screened or antiscreened

Diagram cancellations significantly affect screening predictions

Abstract

We check the accuracy of the constrained random phase approximation (cRPA) downfolding scheme by considering one-dimensional two- and three-orbital Hubbard models with a target band at the Fermi level and one or two screening bands away from the Fermi level. Using numerically exact quantum Monte Carlo simulations of the full and downfolded model we demonstrate that depending on filling the effective interaction in the low-energy theory is either barely screened, or antiscreened, in contrast to the cRPA prediction. This observation is explained by a functional renormalization group analysis which shows that the cRPA contribution to the screening is to a large extent cancelled by other diagrams in the direct particle-hole channel. We comment on the implications of this finding for the ab-initio estimation of interaction parameters in low-energy descriptions of solids.