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

• URL: http://arxiv.org/abs/2312.07225v2
• Date: Tue, 05 Nov 2024 15:25:04 GMT
• Title: Solution of the v-representability problem on a one-dimensional torus
• Authors: Sarina M. Sutter, Markus Penz, Michael Ruggenthaler, Robert van Leeuwen, Klaas J. H. Giesbertz,
• Abstract summary: We provide a solution to the v-representability problem for a non-relativistic quantum many-particle system on a ring domain. 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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• 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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