  Fermionic natural occupation numbers do not only obey Pauli's exclusion
principle, but are even further restricted by so-called generalized Pauli
constraints. Such restrictions are particularly relevant whenever they are
saturated by given natural occupation numbers $\vec{\lambda}=(\lambda_i)$. For
few-site Hubbard models we explore the occurrence of this pinning effect. By
varying the on-site interaction $U$ for the fermions we find sharp transitions
from pinning of $\vec{\lambda}$ to the boundary of the allowed region to
nonpinning. We analyze the origin of this phenomenon which turns out be either
a crossing of natural occupation numbers $\lambda_{i}(U), \lambda_{i+1}(U)$ or
a crossing of $N$-particle energies. Furthermore, we emphasize the relevance of
symmetries for the occurrence of pinning. Based on recent progress in the field
of ultracold atoms our findings suggest an experimental set-up for the
realization of the pinning effect.
