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Reduced density matrices/static correlation functions of Richardson-Gaudin states without rapidities
Alexandre Faribault1, Claude Dimo2, Jean-David Moisset3
1CNRS, LPCT, Université de Lorraine, F-54000 Nancy, France.
The Journal of Chemical Physics
|December 13, 2022
Summary
Seniority-zero geminal wavefunctions, specifically Richardson-Gaudin states, simplify calculating reduced density matrix (RDM) elements. New expressions directly use eigenvalue-based variables (EBV), bypassing complex rapidity calculations for improved computational efficiency.
Area of Science:
- Quantum chemistry
- Computational physics
Background:
- Seniority-zero geminal wavefunctions capture essential electron correlation, particularly for bond breaking.
- Richardson-Gaudin states offer a physically intuitive framework within this class of wavefunctions.
Purpose of the Study:
- To derive direct expressions for reduced density matrix (RDM) elements using eigenvalue-based variables (EBV).
- To eliminate the necessity of computing rapidities for RDM element calculation in Richardson-Gaudin states.
Main Methods:
- Derivation of RDM element expressions directly from EBV.
- Numerical stability analysis of matrix inversion for RDM calculation.
Main Results:
- New, computationally efficient expressions for RDM elements derived directly from EBV.
- Demonstrated that computing rapidities is often unnecessary, reducing computational cost.
- Identified matrix inversion for RDM elements as numerically stable, barring single-particle energy degeneracy.
Conclusions:
- The new method simplifies RDM calculations within the Richardson-Gaudin framework.
- This approach enhances the practical applicability of seniority-zero geminal wavefunctions in quantum chemistry.
- Further investigation is needed for cases with degenerate single-particle energies.
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