Reverse engineering in many-body quantum physics: What many-body system corresponds to an effective single-particle equation?

TL;DR

This paper introduces a reverse engineering approach to identify the many-body systems corresponding to effective single-particle equations, enhancing understanding of density functional theory approximations.

Contribution

It proposes a method to map single-particle equations back to their originating many-body systems, clarifying the physical meaning of such approximations.

Findings

Reveals the many-body systems represented by Kohn-Sham equations.

Provides insights into the non-locality of the density-potential mapping.

Highlights the self-interaction error in approximate density functionals.

Abstract

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the non-locality of the density-potential mapping of DFT, and on the self-interaction error inherent in approximate density functionals.