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

TL;DR

This paper investigates the phenomenon of quasipinning in fermionic systems, demonstrating its stability and implications for simplifying quantum state descriptions and developing new computational methods.

Contribution

It analytically and numerically shows the stability of selection rules related to quasipinning and proposes a basis for a generalized Hartree-Fock method.

Findings

Quasipinning occurs near the boundary of the polytope of natural occupation numbers.

Selection rules simplify the structure of $N$-fermion quantum states.

Quasipinning enables approximate reconstruction of quantum states and their properties.

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 $|\Psi_N\rangle$ 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 $|\Psi_N\rangle$, 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.