Analysis of two-orbital correlations in wavefunctions restricted to electron-pair states

TL;DR

This paper investigates the capabilities and limitations of electron-pair wavefunctions, specifically AP1roG, in modeling strong electron correlation effects in model systems like the Hubbard model and hydrogen rings, using various correlation metrics.

Contribution

It provides a detailed analysis of the electron correlation effects captured by AP1roG and assesses its performance against DMRG reference data in strongly correlated systems.

Findings

AP1roG captures many correlation effects but misses contributions from singly occupied states in strong correlation regimes.

Orbital rotations within AP1roG influence orbital pair correlations.

Limitations of AP1roG are highlighted in the context of strong electron correlation.

Abstract

Wavefunctions constructed from electron-pair states can accurately model strong electron correlation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wavefunctions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong correlation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs.