Quantification of electron correlation for approximate quantum calculations.

Many-body quantum systems are often divided into “strongly correlated” and “weakly correlated.” In strongly correlated systems, the determinant expansion of eigenstates includes several determinants with large weights, while in weakly correlated systems, the expansion is instead dominated by a single determinant. What sort of correlation is present can strongly affect the efficiency of a given approximate wave function method. For example, according to lore in the field, selected configuration interaction methods are efficient when there are just a few determinants with large weights. On the contrary, Slater-Jastrow wave functions are efficient for weakly correlated systems.

In this study, we assess several methods of quantifying electron correlation across quantum chemistry and quantum Monte Carlo methods, applied to a model hydrogen chain system, in particular the von Neumann entropy of the one-particle reduced density matrix. As part of the work, we present a new method to diagonalize matrices with stochastic noise. We confirm the ideas from lore above and show how different methods converge to the exact ground state quite differently on an energy-entropy plot.