Effective interactions in multi-band systems from constrained summations

TL;DR

This paper compares methods for deriving low-energy effective models in multi-band systems, highlighting the constrained RPA as a resummation technique and proposing an enhanced fRG scheme to go beyond it, demonstrated on a two-band model.

Contribution

It introduces an adapted fRG scheme that extends the cRPA approach for more accurate low-energy effective theories in multi-band systems.

Findings

cRPA is a specific resummation of higher-order interactions.

The proposed fRG scheme can incorporate effects beyond cRPA.

Differences between approximations are explored using a two-band model.

Abstract

In correlated electron materials, the application of many-body techniques for the study of interaction effects or unconventional superconductivity often requires the formulation of an effective low-energy model that contains only the relevant bands near the Fermi level. However the bands away from the Fermi level are known to renormalize the low-energy interactions substantially. Here we compare different schemes to derive low-energy effective theories for interacting electrons in solids. The frequently used constrained random phase approximation (cRPA) is identified as a particular resummation of higher-order interaction terms that includes important virtual corrections. We then propose an adapted functional renormalization group (fRG) scheme that includes the cPRA, but also allows one to go beyond the cRPA approximation. We study a simple two-band model in order to explore the differences between the approximations.