Orbital entanglement and correlation from pCCD-tailored Coupled Cluster wave functions

TL;DR

This paper evaluates the effectiveness of pCCD-tailored coupled cluster wave functions in predicting orbital entanglement and correlation, demonstrating accuracy in weakly correlated regimes and limitations in strongly correlated cases.

Contribution

It provides a detailed analysis of orbital-based correlation measures derived from pCCD wave functions and benchmarks the LCC correction against DMRG for various systems.

Findings

pCCD-LCC accurately captures orbital-pair correlations near equilibrium.

The method overestimates correlations in strongly correlated regimes.

Benchmarking shows good agreement with DMRG in weak correlation limit.

Abstract

Wave functions based on electron-pair states provide inexpensive and reliable models to describe quantum many-body problems containing strongly-correlated electrons, given that broken-pair states have been appropriately accounted for by, for instance, a posteriori corrections. In this article, we analyse the performance of electron-pair methods in predicting orbital-based correlation spectra. We focus on the (orbital-optimized) pair-coupled cluster Doubles (pCCD) ansatz with a linearized coupled-cluster (LCC) correction. Specifically, we scrutinize how orbital-based entanglement and correlation measures can be determined from a pCCD-tailored CC wave function. Furthermore, we employ the single-orbital entropy, the orbital-pair mutual information, and the eigenvalue spectra of the two-orbital reduced density matrices to benchmark the performance of the LCC correction for the one-dimensional Hubbard model with periodic boundary condition as well as the N$_2$ and F$_2$ molecules against DMRG reference calculations. Our study indicates that pCCD-LCC accurately reproduces the orbital-pair correlation patterns in the weak-correlation limit and for molecules close to their equilibrium structure. Hence, we can conclude that pCCD-LCC predicts reliable wave functions in this regime. In the strong-correlation limit and for molecules with stretched bonds, the LCC correction, generally, overestimates orbital-pair correlations.