  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.
