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

Paul A. Johnson

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arXiv · 2405.00279

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

Paul A. Johnson

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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.

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Paul A. Johnson. 2024-05-01. Beyond a Richardson-Gaudin mean-field: Slater-Condon rules and perturbation theory. https://arxiv.org/abs/2405.00279

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