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

Coe, J. P.
Capelle, K.
D'Amico, I.
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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.
Comment: 4 pages, 2 figures. Accepted by PRA
Condensed Matter - Other Condensed Matter, Physics - Chemical Physics