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Seniority-zero states are mean-field wavefunctions.

Marco Martínez González1, Daniel F Calero-Osorio1, Michelle Richer1

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Summary
This summary is machine-generated.

This study introduces the (number-symmetry-broken) antisymmetric product of interacting geminals (APIG) as a novel representation for seniority-zero states. APIG wavefunctions offer an exponentially fast approximation to true wavefunctions, particularly for bosons.

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Area of Science:

  • Quantum chemistry
  • Many-body physics

Background:

  • Seniority-zero states are fundamental in understanding quantum systems.
  • Existing methods for describing these states can be computationally intensive.

Purpose of the Study:

  • To establish a new theoretical framework for representing seniority-zero states.
  • To explore the connection between these states and mean-field descriptions for bosons.

Main Methods:

  • Symbolic computation
  • Numerical experiments
  • Mathematical arguments

Main Results:

  • Every seniority-zero state can be expressed as a (number-symmetry-broken) antisymmetric product of interacting geminals (APIG).
  • For bosons, configuration interaction coefficients are exactly parameterized by matrix permanents.
  • APIG wavefunctions show exponential convergence to the true wavefunction with increasing geminal number.

Conclusions:

  • The APIG formalism provides an effective mean-field description for bosonic wavefunctions.
  • This approach offers a computationally tractable method for approximating complex quantum states.