Role of the pair potential for the saturation of generalized Pauli constraints

The dependence of the (quasi-)saturation of the generalized Pauli constraints on the pair potential is studied for ground states of few-fermion systems. For this, we consider spinless fermions in one dimension which are harmonically confined and interact by pair potentials of the form $|x_i-x_j|^s$ with $-1 \leq s\leq 5$. We use the Density Matrix Renormalization Group approach and large orbital basis to achieve the convergence on more than ten digits of both the variational energy and the natural occupation numbers. Our results confirm that the conflict between energy minimization and fermionic exchange symmetry results in a universal and non-trivial quasi-saturation of the generalized Pauli constraints (\emph{quasipinning}), implying tremendous structural simplifications of the fermionic ground state for all $s$. Those numerically exact results are complemented by an analytical study based on a self-consistent perturbation theory which we develop for this purpose. The respective results for the weak coupling regime eventually elucidate the singular behaviour found for the specific values $s=2,4,\ldots$, resulting in an extremely strong quasipinning.