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arXiv · 2610.20737

A constructive solution to the $n$-representability problem

Nicholas C. Rubin·A. Eugene DePrince III
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Abstract

We present an instantiation of the constructive solution to the fermionic quantum marginal problem by building the complete family of two-body witnesses at each level of a weighted sum-of-squares hierarchy. Our construction combines positive-semidefinite Gram matrices with explicit linear nullspace constraints that exactly cancel all higher-body contributions following a similar idea to the existing solution but made explicit in open source software. We demonstrate the weighted sum-of-squares construction numerically by solving the associated semidefinite program and recovering the exact ground-state energy of a Richardson Hamiltonian in the three-fermion sector. We further prove that higher-degree particle-number multipliers are unnecessary when the full sum-of-squares generating algebra is used.

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Nicholas C. Rubin, A. Eugene DePrince III. 2026-10-21. A constructive solution to the $n$-representability problem. https://arxiv.org/abs/2610.20737

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