Orbital entanglement and correlation from pCCD-tailored coupled cluster wave functions

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 analyze 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 the periodic boundary condition as well as the N-2 and F-2 molecules against density matrix renormalization group 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.

Automated summary

Wave functions based on electron-pair states provide reliable models for describing quantum many-body problems with strongly correlated electrons, especially when broken-pair states are corrected appropriately. The study analyzes the performance of electron-pair methods in predicting orbital-based correlation spectra, focusing on the pCCD-LCC ansatz. It is found that pCCD-LCC accurately reproduces orbital-pair correlation patterns in weak correlation limits and for molecules close to their equilibrium structure.