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Pinning of fermionic occupation numbers.

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Generalized Pauli constraints, which extend the Pauli exclusion principle, were recently proven. This study analyzes their physical relevance, finding occupation numbers are quasipinned to allowed regions, suggesting richer physics and a generalized Hartree-Fock approximation.

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Area of Science:

  • Quantum mechanics
  • Condensed matter physics
  • Atomic physics

Background:

  • The Pauli exclusion principle governs fermionic state occupation numbers.
  • Recent proofs confirm additional constraints generalizing the Pauli principle.
  • The physical relevance of these generalized constraints remains largely unexplored.

Purpose of the Study:

  • To provide the first analytic analysis of the physical relevance of generalized Pauli constraints.
  • To compute natural occupation numbers for interacting fermions in a harmonic potential.
  • To investigate the role of these constraints in ground states.

Main Methods:

  • Analytic analysis of generalized Pauli constraints.
  • Computation of natural occupation numbers for ground states.
  • Study of interacting fermions in a harmonic potential.

Main Results:

  • Fermionic occupation numbers are found to be quasipinned to the boundary of allowed regions.
  • The generalized Pauli constraints play a role in ground states for certain models.
  • These constraints do not limit the ground-state energy.

Conclusions:

  • The physics underlying generalized Pauli constraints is more complex than previously thought.
  • The quasipinned nature of occupation numbers highlights the significance of these constraints.
  • Findings suggest a potential generalization of the Hartree-Fock approximation for fermionic systems.