Hubbard model: Pinning of occupation numbers and role of symmetries

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.