Pinning of Fermionic Occupation Numbers: General Concepts and One Dimension

Abstract

Analytical evidence for the physical relevance of generalized Pauli constraints (GPCs) has recently been provided in [PRL 110, 040404]: Natural occupation numbers $\vec{\lambda }\equiv ({\lambda }_i)$ of the ground state of a model system in the regime of weak couplings $\kappa$ of three spinless fermions in one spatial dimension were found extremely close, in a distance $D_{min}\sim {\kappa }^8$ to the boundary of the allowed region. We provide a self-contained and complete study of this quasipinning phenomenon. In particular, we develop tools for its systematic exploration and quantification. We confirm that quasipinning in one dimension occurs also for larger particle numbers and extends to intermediate coupling strengths, but vanishes for very strong couplings. We further explore the non-triviality of our findings by comparing quasipinning by GPCs to potential quasipinning by the less restrictive Pauli exclusion principle constraints. This allows us to eventually confirm the significance of GPCs beyond Pauli's exclusion principle.

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Cited by in corpus (15)

• 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
• Pinning of fermionic occupation numbers: Higher spatial dimensions and spin
• Asymptotic properties of entanglement polytopes for large number of qubits
• Locally Maximally Entangled States of Multipart Quantum Systems
• Role of the pair potential for the saturation of generalized Pauli constraints
• On the time evolution of fermionic occupation numbers
• Implications of pinned occupation numbers for natural orbital expansions. I: Generalizing the concept of active spaces
• Bias Cancellation in One-Determinant Fixed-Node Diffusion Monte Carlo: Insights from Fermionic Occupation Numbers
• Quantum marginals from pure doubly excited states
• Quantum correlations in one-dimensional Wigner molecules
• A toolbox of spin-adapted generalized Pauli constraints
• Generalized Pauli constraints in large systems: the Pauli principle dominates