Pinning of fermionic occupation numbers: Higher spatial dimensions and spin

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.

arXiv commentpublished version

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• Towards a formal definition of static and dynamic electronic correlations
• Reconstructing quantum states from single-party information
• Generalized Pauli constraints in small atoms
• Influence of the Fermionic Exchange Symmetry beyond Pauli's Exclusion Principle
• Asymptotic properties of entanglement polytopes for large number of qubits
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• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• Quantum marginals from pure doubly excited states
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• Quantum Simulation of Molecules without Fermionic Encoding of the Wave Function
• A toolbox of spin-adapted generalized Pauli constraints