Quantification of electron correlation for approximate quantum calculations

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrodinger equation. By far, the most common property used to assess accuracy has been the total energy; however, total energies do not give a complete picture of electron correlation. In this work, we assess the von Neumann entropy of the one-particle reduced density matrix (1-RDM) to compare selected configuration interaction (CI), coupled cluster, variational Monte Carlo, and fixed-node diffusion Monte Carlo for benchmark hydrogen chains. A new algorithm, the circle reject method, is presented, which improves the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo by several orders of magnitude. The von Neumann entropy of the 1-RDM and the eigenvalues of the 1-RDM are shown to distinguish between the dynamic correlation introduced by the Jastrow and the static correlation introduced by determinants with large weights, confirming some of the lore in the field concerning the difference between the selected CI and Slater-Jastrow wave functions. Published under an exclusive license by AIP Publishing.

Automated summary

State-of-the-art many-body wave function techniques rely on heuristics to achieve high accuracy at an attainable computational cost to solve the many-body Schrodinger equation. In this work, the von Neumann entropy of the one-particle reduced density matrix (1-RDM) is used to compare different wave function methods for benchmark hydrogen chains. A new algorithm called the circle reject method is presented to improve the efficiency of evaluating the von Neumann entropy using quantum Monte Carlo. The results show that the von Neumann entropy and eigenvalues of the 1-RDM can distinguish between dynamic and static correlation.