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

2025/06/11 by Julia Liebert, Anna O. Schouten, Liebert, Julia +7 · 1 citation
Computer Science · Physics and Astronomy · #Chemical Physics (physics.chem-ph) #Cold Atom Physics and Bose-Einstein Condensates #FOS: Physical sciences #Quantum Information and Cryptography #Quantum Physics (quant-ph) #Quantum many-body systems

paper · doi:10.48550/arxiv.2506.09960

openalex publication_date 2025/06/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Solving one-body ensemble N-representability problems with spin
• Enhancing Reduced Density Matrix Functional Theory Calculations by Coupling Orbital and Occupation Optimizations
• Fewer measurements from shadow tomography with N-representability conditions
• Universal Generalization of Density Functional Theory for Static Correlation
• Variational Determination of the Two-Electron Reduced Density Matrix: A Tutorial Review
• Exact Conditions for Ensemble Density Functional Theory
• Data-driven Refinement of Electronic Energies from Two-Electron Reduced-Density-Matrix Theory
• Machine Learning Electronic Structure Methods Based On The One-Electron Reduced Density Matrix
• An effective solution to convex 1-body N-representability
• Probing topological spin liquids on a programmable quantum simulator
• Many-body physics with individually controlled Rydberg atoms
• The Pauli exclusion principle and beyond
• Quantum marginal problem and representations of the symmetric group
• The symplectic and algebraic geometry of Horn's problem
• Eigenvalues, invariant factors, highest weights, and Schubert calculus
• The honeycomb model of GL(n) tensor products I: proof of the saturation conjecture
• Doubly Stochastic Matrices and the Diagonal of a Rotation Matrix

Cited by

• Constrained Shadow Tomography for Molecular Simulation on Quantum Devices

Related

• An effective solution to convex 1-body N-representability
• Solving one-body ensemble N-representability problems with spin
• Approximate Solution of the Representability Problem
• Reduced density matrix of permutational invariant many-body systems
• Properties and N-representability conditions of the two-body density matrix