title: 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 1970s, 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 (quasipinned). 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.
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
authors.forename: Christian
authors.initials: C
authors.lastname: Schilling
authors.affiliation: Institute for Physics, University of Freiburg, Rheinstrasse 10, D-79104 Freiburg, Germany.
authors.forename: David
authors.initials: D
authors.lastname: Gross
authors.affiliation: Institute for Theoretical Physics, ETH Zurich, Wolfgang-Pauli-Strasse 27, CH-8093 Zurich, Switzerland.
authors.forename: Matthias
authors.initials: M
authors.lastname: Christandl