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arXiv · 2312.07225

Solution of the v-representability problem on a one-dimensional torus

Sarina M. Sutter·Markus Penz·Michael Ruggenthaler·Robert van Leeuwen·Klaas J. H. Giesbertz
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Abstract

We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain in terms of Sobolev spaces and their duals. Any one-particle density that is square-integrable, has a square-integrable weak derivative, and is gapped away from zero can be realized from the solution of a many-particle Schr\"odinger equation, with or without interactions, by choosing a corresponding external potential. This potential can contain a distributional contribution but still gives rise to a self-adjoint Hamiltonian. Importantly, this allows for a well-defined Kohn-Sham procedure but, on the other hand, invalidates the usual proof of the Hohenberg-Kohn theorem.

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Sarina M. Sutter, Markus Penz, Michael Ruggenthaler, Robert van Leeuwen, Klaas J. H. Giesbertz. 2023-12-12. Solution of the v-representability problem on a one-dimensional torus. https://doi.org/10.1088/1751-8121%2Fad8a2a

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