Tensor product expansions for correlation in quantum many-body systems

TL;DR

This paper introduces a tensor product approximation framework for the two-body density matrix in quantum many-body systems, analyzing its physical implications and comparing it to existing theories like Hartree-Fock.

Contribution

It proposes a new tensor product-based approximation method for the two-body density matrix and examines its physical properties and accuracy in modeling electron correlations.

Findings

Single tensor product predicts near-zero dynamical correlation in homogeneous electron gas.

Tensor product of both dynamical and statistical correlations aligns with natural orbital functional.

The theory's accuracy is comparable to Hartree-Fock for typical valence densities.

Abstract

We explore a new class of computationally feasible approximations of the two-body density matrix as a finite sum of tensor products of single-particle operators. Physical symmetries then uniquely determine the two-body matrix in terms of the one-body matrix. Representing dynamical correlation alone as a single tensor product results in a theory which predicts near zero dynamical correlation in the homogeneous electron gas at moderate to high densities. But, representing both dynamical and statistical correlation effects together as a tensor product leads to the recently proposed ``natural orbital functional.'' We find that this latter theory has some asymptotic properties consistent with established many-body theory but is no more accurate than Hartee-Fock in describing the homogeneous electron gas for the range of densities typically found in the valence regions of solids. PACS 71.10.-w 71.15.Mb, Accepted for publication in Physical Review B