2024/10/09 by Airi Kawasaki, Kawasaki, Airi, Naoki Nakatani +1 · 1 citation
Computer Science · Materials Science · Mathematics · #Chemical Physics (physics.chem-ph) #FOS: Physical sciences #Finite Group Theory Research #Matrix Theory and Algorithms #Strongly Correlated Electrons (cond-mat.str-el) #X-ray Diffraction in Crystallography
paper · pdf · doi:10.48550/arxiv.2410.06666
openalex publication_date 2024/10/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigated some variational methods to compute a wavefunction based on antisymmetric product of geminals (APG). The Waring decomposition on the APG wavefunction leads a finite sum of antisymmetrized geminal power (AGP) wavefunctions, each for which the variational principle can be applied. We call this as AGP-CI method which provides a variational solution of the APG wavefunction efficiently. However, number of AGP wavefunctions in the exact AGP-CI formalism become exponentially large in case of many-electron systems. Therefore, we also investigate the low-rank APG wavefunction, in which the geminal matrices are factorized by the Schur decomposition. Interestingly, only a few non-zero eigenvalues (up to half number of electrons) were found from the Schur decomposition on the APG wavefunction. We developed some methods to approximate the APG wavefunction by lowering the ranks of geminal matrices, and demonstrate their performance. Our new geminal method based on the low-rank decomposition can drastically reduce the number of variational parameters, although there is no efficient algorithm so far, due to some mathematical complications.