Pinning of Fermionic Occupation Numbers

Abstract

The Pauli exclusion principle is a constraint on the natural occupation numbers of fermionic states. It has been suspected since at least the 1970's, and only proved very recently, that there is a multitude of further constraints on these numbers, generalizing the Pauli principle. Here, we provide the first analytic analysis of the physical relevance of these constraints. We compute the natural occupation numbers for the ground states of a family of interacting fermions in a harmonic potential. Intriguingly, we find that the occupation numbers are almost, but not exactly, pinned to the boundary of the allowed region (quasi-pinned). The result suggests that the physics behind the phenomenon is richer than previously appreciated. In particular, it shows that for some models, the generalized Pauli constraints play a role for the ground state, even though they do not limit the ground-state energy. Our findings suggest a generalization of the Hartree-Fock approximation.

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• Entropic measures of Rydberg-like harmonic states
• Quasipinning and selection rules for excitations in atoms and molecules
• Relating correlation measures: the importance of the energy gap
• Analytic solutions of topologically disjoint systems
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• Quantum Marginal Problem and its Physical Relevance
• Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom
• Indistinguishability of causal relations from limited marginals
• Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers
• Duality of reduced density matrices and their eigenvalues