Quasipinning and its relevance for $N$-Fermion quantum states

Abstract

Fermionic natural occupation numbers (NON) do not only obey Pauli's famous exclusion principle but are even further restricted to a polytope by the generalized Pauli constraints, conditions which follow from the fermionic exchange statistics. Whenever given NON are pinned to the polytope's boundary the corresponding $N$-fermion quantum state $|{\Psi }_N⟩$ simplifies due to a selection rule. We show analytically and numerically for the most relevant settings that this rule is stable for NON close to the boundary, if the NON are non-degenerate. In case of degeneracy a modified selection rule is conjectured and its validity is supported. As a consequence the recently found effect of quasipinning is physically relevant in the sense that its occurrence allows to approximately reconstruct $|{\Psi }_N⟩$, its entanglement properties and correlations from 1-particle information. Our finding also provides the basis for a generalized Hartree-Fock method by a variational ansatz determined by the selection rule.

References in corpus (3)

• The Pauli principle revisited
• Pinning of Fermionic Occupation Numbers
• Generalized Pauli conditions on the spectra of one-electron reduced density matrices of atoms and molecules

Cited by in corpus (8)

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• Generalized Pauli constraints in reduced density matrix functional theory
• Quasipinning and selection rules for excitations in atoms and molecules
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• Natural Extension of Hartree-Fock through extremal $1$-fermion information: Overview and application to the lithium atom
• Asymptotic properties of entanglement polytopes for large number of qubits
• Detecting dimensional crossover and finite Hilbert space through entanglement entropies