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The dependence of the (quasi-)saturation of the generalized Pauli constraintson the pair potential is studied for ground states of few-fermion systems. Forthis, we consider spinless fermions in one dimension which are harmonicallyconfined 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 andlarge orbital basis to achieve the convergence on more than ten digits of boththe variational energy and the natural occupation numbers. Our results confirmthat the conflict between energy minimization and fermionic exchange symmetryresults in a universal and non-trivial quasi-saturation of the generalizedPauli constraints (\emph{quasipinning}), implying tremendous structuralsimplifications of the fermionic ground state for all $s$. Those numericallyexact results are complemented by an analytical study based on aself-consistent perturbation theory which we develop for this purpose. Therespective results for the weak coupling regime eventually elucidate thesingular behaviour found for the specific values $s=2,4,\ldots$, resulting inan extremely strong quasipinning.

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