Beyond a Richardson-Gaudin mean-field: Slater-Condon rules and perturbation theory

TL;DR

This paper extends Richardson-Gaudin mean-field theory by deriving efficient transition density matrix expressions, establishing Slater-Condon-like rules, and developing a perturbation method that rivals configuration interaction in accuracy for strongly correlated electrons.

Contribution

It introduces optimal transition density matrix formulas, identifies Slater-Condon analogues based on singular value analysis, and proposes a perturbative approach comparable to configuration interaction.

Findings

Transition density matrices can be computed efficiently with costs similar to reduced density matrices.

Slater-Condon rules are extended to Richardson-Gaudin states based on singular value analysis.

A perturbation method achieves accuracy close to configuration interaction, with feasible computational cost.

Abstract

Richardson-Gaudin states provide a basis of the Hilbert space for strongly correlated electrons. In this study, optimal expressions for the transition density matrix elements between Richardson-Gaudin states are obtained with a cost comparable with the corresponding reduced density matrix elements. Analogues of the Slater-Condon rules are identified based on the number of near-zero singular values of the RG state overlap matrix. Finally, a perturbative approach is shown to be close in quality to a configuration interaction of Richardson-Gaudin states while being feasible to compute.