Pinning of Fermionic Occupation Numbers

TL;DR

This paper analyzes the physical significance of generalized Pauli constraints on fermionic occupation numbers, revealing near-pinning phenomena in interacting fermion ground states and suggesting a broader role for these constraints beyond energy limits.

Contribution

It provides the first analytic study of the relevance of generalized Pauli constraints in physical systems, showing their influence on ground states and proposing a generalization of the Hartree-Fock approximation.

Findings

Occupation numbers are nearly pinned to the boundary of allowed regions.

Generalized Pauli constraints influence ground states without affecting energy.

Results indicate a richer physics behind occupation number constraints.

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.