Refining ensemble $N$-representability of one-body density matrices from partial information

• URL: http://arxiv.org/abs/2506.09960v1
• Date: Wed, 11 Jun 2025 17:36:32 GMT
• Title: Refining ensemble $N$-representability of one-body density matrices from partial information
• Authors: Julia Liebert, Anna O. Schouten, Irma Avdic, Christian Schilling, David A. Mazziotti,
• Abstract summary: We introduce a hierarchy of ensemble one-body $N$-representability problems.<n>We show that this relaxed problem is related to a generalization of Horn's problem.<n>An additional convex relaxation yields a convex polytope that provides physically meaningful restrictions on lattice site occupations.
• Score: 1.0485739694839669
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The $N$-representability problem places fundamental constraints on reduced density matrices (RDMs) that originate from physical many-fermion quantum states. Motivated by recent developments in functional theories, we introduce a hierarchy of ensemble one-body $N$-representability problems that incorporate partial knowledge of the one-body reduced density matrices (1RDMs) within an ensemble of $N$-fermion states with fixed weights $w_i$. Specifically, we propose a systematic relaxation that reduces the refined problem -- where full 1RDMs are fixed for certain ensemble elements -- to a more tractable form involving only natural occupation number vectors. Remarkably, we show that this relaxed problem is related to a generalization of Horn's problem, enabling an explicit solution by combining its constraints with those of the weighted ensemble $N$-representability conditions. An additional convex relaxation yields a convex polytope that provides physically meaningful restrictions on lattice site occupations in ensemble density functional theory for excited states.

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