Tensor decomposition methods for correlated electron pairs

TL;DR

This paper explores tensor decomposition techniques, specifically Waring decomposition, to improve the variational determination of ground states in strongly correlated electron systems, bridging geminal wave functions and full configuration interaction.

Contribution

It introduces the application of Waring tensor decomposition to efficiently represent correlated electron wave functions, enhancing understanding of molecular orbital theories.

Findings

Waring decomposition improves convergence speed of energy calculations.

The method bridges geminal product wave functions and full-CI.

Provides insights into hierarchy of electron pair theories.

Abstract

We analyze wave functions constructed as a sum of product of two-electron functions, or as a polynomial of geminals, to investigate their ability to represent the ground state of a strongly correlated few-body system. The known difficulty associated with variational determination of the total energy is overcome by applying a tensor decomposition method called Waring decomposition. Convergence speed of the total energy is compared for various polynomial types. The result provides information bridging between geminal product wave functions and the full-CI in the strongly correlated regime, thereby enriching knowledge on the hierarchy of molecular orbital theories of electron pairs.