Geminal Replacement Models Based on AGP.

Area of Science:

• Quantum Chemistry
• Computational Physics

Background:

• The antisymmetrized geminal power (AGP) wave function has historical significance and is recognized under various names in physics and chemistry.
• Recent research highlights AGP's potential as a foundational approach for studying strongly correlated electrons.

Purpose of the Study:

• To demonstrate the equivalence of various AGP-based correlator representations within a seniority-conserving framework.
• To introduce and evaluate a novel AGP-based correlation method, J-CI, for accurate energy calculations.

Main Methods:

• Investigated the equivalence of AGP-based correlator representations, including those derived from algebra generators, killing operators, and geminal replacement operators.
• Implemented a specific AGP representation utilizing number operators as correlators, featuring linearly independent curvilinear metrics to differentiate Hilbert space regions.

Main Results:

• Established the equivalence of diverse AGP-based correlator representations under seniority conservation.
• The developed J-CI method, employing number operators and distinct curvilinear metrics, achieved high accuracy in energy predictions for the pairing Hamiltonian.

Conclusions:

• The J-CI method, an AGP-based approach, provides a robust and accurate means for calculating energies in strongly correlated systems.
• The equivalence of different AGP representations simplifies theoretical treatments and implementation strategies for these systems.