A cardinal obstacle to understanding and predicting quantitatively the properties of solids and large molecules is that, for these systems, it is very challenging to describe beyond the mean-field level the quantum-mechanical interactions between electrons belonging to different atoms. Here we show that there exists an exact dual equivalence relationship between the seemingly-distinct physical problems of describing local and non-local interactions in many-electron systems. This is accomplished using a theoretical construction analogue to the quantum link approach in lattice gauge theories, featuring the non-local electron-electron interactions as if they were mediated by auxiliary high-energy fermionic particles interacting in a purely-local fashion. Besides providing an alternative theoretical direction of interpretation, this result may allow us to study both local and non-local interactions on the same footing, utilizing the powerful state-of-the-art theoretical and computational frameworks already available.
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