Configuration interaction extension of AGP for incorporating inter-geminal correlations

TL;DR

This paper introduces an extended AGP-CI wavefunction method that incorporates inter-geminal correlations, improving accuracy for strongly correlated systems like molecules and the Hubbard model.

Contribution

The authors develop a computationally efficient AGP-CI wavefunction extension using a linear combination of AGPs with a small deformation parameter.

Findings

Achieves high accuracy in Hubbard model and small molecules

Outperforms previous LC-AGP approach in correlated regimes

Effective for systems with many electrons

Abstract

In this paper, we develop a class of antisymmetrized geminal power configuration interaction (AGP-CI) wave functions that extend the AGP framework by incorporating inter-geminal correlations through a CI expansion. To make these wavefunctions computationally tractable, we evaluate them by rewriting the AGP-CI ansatz as a linear combination of AGPs (LC-AGP), for which overlaps and Hamiltonian matrix elements can be computed with standard AGP machinery. Motivated by border-rank decompositions, we further reorganize this ansatz into a compact linear combination of AGPs depending on a small deformation parameter $\tau$, which controls how closely the truncated expansion approximates the full AGP-CI state. Benchmark applications to the Hubbard model and to the small molecules H$_2$O and N$_2$ demonstrate that the proposed wavefunctions achieve consistently high accuracy and outperform the LC-AGP, particularly for systems with more electrons and in strongly correlated regimes.