Mutual Correlation

TL;DR

This paper introduces a new measure called mutual correlation to quantify nonadditive correlations in quantum many-body states, offering computational advantages and basis-independent insights for chemistry and physics.

Contribution

It presents a novel framework based on the Frobenius norm of the two-body cumulant, demonstrating its effectiveness and efficiency over entropy-based metrics.

Findings

Mutual correlation effectively quantifies nonadditive correlations.

It outperforms entropy-based metrics in benchmark studies.

Maximally correlated orbitals help identify basis-independent correlation partitions.

Abstract

Quantifying correlation and complexity in quantum many-body states is central to advancing theoretical and computational chemistry, physics, and quantum information science. This work introduces a novel framework, mutual correlation, based on the Frobenius norm squared of the two-body reduced density matrix cumulant. Through systematic partitioning of the cumulant norm, mutual correlation quantifies nonadditive correlations among interacting subsystems. Benchmark studies on model systems, including H$_{10}$, N$_{2}$, and p-benzyne, demonstrate its efficacy and computational advantage compared to entropy-based metrics such as orbital mutual information. Maximally correlated orbitals, obtained by maximizing a nonlinear cost function of the mutual correlation, are also considered to identify a basis-independent partitioning of correlation. This study suggests that mutual correlation is a broadly applicable metric, useful in active space selection and the interpretation of electronic states.