  State-of-the-art many-body wave function techniques rely on heuristics to
achieve high accuracy at an attainable cost to solve the many-body
Schr\"odinger 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, the authors 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 the evaluation of 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 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.
