Journal Article

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

Liebert, Julia, Schouten, Anna O, Avdic, Irma, Mazziotti, David A, Schilling, Christian

2025

Overview

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 RDMs (1RDMs) within an ensemble of N-fermion states with fixed weights wi. 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.

• Publisher: IOP Publishing
• Subject: Approximation / Constraints / Density functional theory / ensemble / ensemble N-representability / excited states / excited-state ensembles / Fermions / Hilbert space / Physics / reduced density functional theory / reduced density matrices / representability