Frequency dependence in GW made simple using a multi-pole approximation

TL;DR

This paper introduces a multi-pole approximation method for the GW screened interaction W, achieving high accuracy in frequency dependence modeling with reduced computational effort compared to full-frequency approaches.

Contribution

The paper develops and validates a multi-pole approach (MPA) that accurately models the frequency dependence of W with fewer poles, improving efficiency over traditional plasmon pole models.

Findings

MPA achieves full-frequency accuracy with fewer poles.

Sampling in the complex plane enhances approximation quality.

Validated on prototype systems with promising results.

Abstract

In the $GW$ approximation, the screened interaction $W$ is a non-local and dynamical potential that usually has a complex frequency dependence. A full description of such dependence is possible but often computationally demanding. For this reason, it is still common practice to approximate $W(\omega)$ using a plasmon pole (PP) model. Such approach, however, may deliver an accuracy limited by its simplistic description of the frequency dependence of the polarizability, i.e. of $W$. In this work we explore a multi-pole approach (MPA) and develop an effective representation of the frequency dependence of $W$. We show that an appropriate sampling of the polarizability in the frequency complex plane and a multi-pole interpolation can lead to a level of accuracy comparable with full-frequency methods at much lower computational cost. Moreover, both accuracy and cost are controllable by the number of poles used in MPA. Eventually we validate the MPA approach in selected prototype systems, showing that full-frequency quality results can be obtained with a limited number of poles.