Accuracy of downfolding based on the constrained random phase approximation

TL;DR

This paper evaluates the accuracy of the constrained random phase approximation (cRPA) in deriving low-energy effective Hamiltonians for multi-orbital systems, highlighting issues with overscreening and proposing a Pauli principle-restoring variant.

Contribution

It systematically assesses cRPA's reliability in multi-orbital models and introduces a modified method to address overscreening caused by Pauli principle violations.

Findings

cRPA can lead to overscreening in certain regimes

Restoring the Pauli principle improves the accuracy of cRPA

Effective models better match multi-band systems with the modified cRPA

Abstract

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.