Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

TL;DR

This paper investigates how generalized Pauli constraints influence fermionic occupation numbers in higher dimensions with spin, revealing that quasipinning is more prominent in lower dimensions and with increased spin polarization.

Contribution

It systematically explores the impact of GPCs in higher dimensions and with spin, demonstrating the conditions under which quasipinning occurs and its dependence on dimensionality and spin polarization.

Findings

Quasipinning is stronger in lower spatial dimensions.

Increasing spin polarization enhances quasipinning.

Quasipinning weakens with stronger interactions.

Abstract

The role of the generalized Pauli constraints (GPCs) in higher spatial dimensions and by incorporating spin degrees of freedom is systematically explored for a system of interacting fermions confined by a harmonic trap. Physical relevance of the GPCs is confirmed by analytical means for the ground state in the regime of weak couplings by finding its vector of natural occupation numbers close to the boundary of the allowed region. Such quasipinning is found to become weaker in the intermediate and strong coupling regime. The study of crossovers between different spatial dimensions by detuning the harmonic trap frequencies suggests that quasipinning is essentially an effect for systems with reduced spatial dimensionality. In addition, we find that quasipinning becomes stronger by increasing the degree of spin-polarization. Consequently, the number of states available around the Fermi level plays a key role for the occurrence of quasipinning. This suggests that quasipinning emerges from the conflict between energy minimization and fermionic exchange symmetry.