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Iris Theophilou1, Nektarios N Lathiotakis2, Miguel A L Marques3

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This study investigates pure-state N-representability conditions in reduced density-matrix functional theory. Enforcing these conditions can alter correlation energies and occupation numbers compared to using only ensemble N-representability conditions.

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Area of Science:

  • Quantum chemistry
  • Computational physics
  • Many-body theory

Background:

  • Reduced density-matrix functional theory (RMFD) commonly uses ensemble N-representability conditions.
  • Pure-state N-representability conditions (generalized Pauli constraints) are gaining attention.
  • A systematic method for deriving pure-state conditions for any system size and Hilbert space dimension has been developed.

Purpose of the Study:

  • To evaluate the impact of pure-state N-representability conditions on RMFD calculations.
  • To determine if standard RMFD minimization violates pure-state conditions for 3-electron systems.
  • To compare results obtained with and without enforcing pure-state conditions.

Main Methods:

  • Minimization of one-body reduced density matrix (1-RDM) functionals.
  • Application of ensemble N-representability conditions.
  • Enforcement of pure-state N-representability conditions (generalized Pauli constraints).
  • Analysis of prototype 3-electron systems.

Main Results:

  • Standard minimization under ensemble conditions can violate pure-state conditions for 3-electron systems.
  • Enforcing pure-state conditions alongside ensemble conditions leads to different correlation energies.
  • Optimal occupation numbers also differ when pure-state conditions are enforced.

Conclusions:

  • Pure-state N-representability conditions are crucial for accurate RMFD calculations.
  • Ignoring pure-state conditions can lead to unphysical results.
  • Future RMFD studies should incorporate pure-state conditions for improved reliability.