Low-rank decomposition on the antisymmetric product of geminals for strongly correlated electrons

TL;DR

This paper introduces a low-rank decomposition approach for antisymmetric product of geminals (APG) wavefunctions, enabling efficient variational calculations for strongly correlated electrons by reducing the number of parameters.

Contribution

The authors propose a novel low-rank APG wavefunction method using Schur decomposition, significantly decreasing variational parameters while maintaining accuracy.

Findings

Few non-zero eigenvalues found in Schur decomposition.

Low-rank APG wavefunctions approximate full APG effectively.

Method reduces computational complexity for strongly correlated systems.

Abstract

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.