Quantification of electron correlation for approximate quantum calculations

TL;DR

This paper introduces a new way to measure electron correlation using von Neumann entropy of the 1-RDM, providing deeper insights into correlation effects beyond total energy, with an efficient algorithm for quantum Monte Carlo calculations.

Contribution

It presents a novel entropy-based metric for electron correlation and a circle reject algorithm that significantly enhances computational efficiency in quantum Monte Carlo methods.

Findings

von Neumann entropy distinguishes dynamic and static correlation

Efficient evaluation of entropy with the circle reject method

Correlation differences confirmed between CI and Slater-Jastrow wave functions

Abstract

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.