Violation of particle number conservation in the GW approximation

TL;DR

This paper demonstrates that the GW approximation can violate particle number conservation when not calculated self-consistently, and shows that partial self-consistency can mitigate this issue.

Contribution

It provides an analytical example illustrating particle number violation in GW and proposes a simple correction to reduce this deviation.

Findings

Non-self-consistent GW violates particle number conservation.

Partial self-consistency reduces the violation.

Analytical model confirms the phenomenon.

Abstract

We present a nontrivial model system of interacting electrons that can be solved analytically in the GW approximation. We obtain the particle number from the GW Green's function strictly analytically, and prove that there is a genuine violation of particle number conservation if the self-energy is calculated non-self-consistently from a zeroth order Green's function, as done in virtually all practical implementations. We also show that a simple shift of the self-energy that partially restores self-consistency reduces the numerical deviation significantly.