Low-rank compression of two-electron reduced density matrices

TL;DR

This paper presents a low-rank compression method for two-electron reduced density matrices (2RDMs) that significantly reduces storage costs while preserving essential physical properties, enabling more efficient electronic structure calculations.

Contribution

The authors introduce a simple protocol to compress 2RDMs into a lower-rank form that maintains physical symmetries and structure, improving scalability in correlated electronic state computations.

Findings

Achieves approximately 99% compression of 2RDMs for octane while retaining chemical accuracy.

Reduces memory scaling from quartic to quadratic with controlled error per electron.

Enables application of 2RDMs in large-scale nonadiabatic molecular dynamics simulations.

Abstract

Two-body reduced density matrices (2RDMs) encode the essential two-electron physics of electronic states, but their quartic storage cost poses a major limitation in practical workflows. We investigate a simple protocol to compress both transition and non-transition 2RDMs into a lower-rank representation that preserves their wedge-product structure and physical symmetries under truncation. The resulting decomposition couples Coulomb and exchange channels through a common set of low-rank factors, yielding a more compact rank-sparse representation than single-channel factorizations. For correlated states, the effective rank scales linearly with system size, achieving a $\sim99$\% compression for the coupled-cluster 2RDM of octane while retaining chemical accuracy. We apply this to the recently introduced {\em ab initio} eigenvector continuation workflows, where many-body wave functions are interpolated across nuclear geometries with mean-field cost. Here, 2RDMs between training states act as projectors into a subspace but their memory scaling limits applications to larger systems. The compression scheme reduces the memory cost from quartic to quadratic for a fixed error per electron. Metrics to systematically control the decomposition are investigated, enabling statistically resolved structural, dynamical and spectroscopic observables from nonadiabatic molecular dynamics simulations of photoexcited H$_{28}$ chains, interpolating from compressed near-exact DMRG training data. This establishes these structure-preserving compressed intermediates for practical correlated electronic structure workflows.