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Seniority-zero states are mean-field wavefunctions
Marco Martínez González1, Daniel F Calero-Osorio1, Michelle Richer1
1Department of Chemistry & Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada.
The Journal of Chemical Physics
|October 13, 2025
Summary
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.
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.
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