Pertubative corrections for Hartree-Fock-like algebraic Bethe ansatz analogue

Moisset, Jean-David; Carrier, Laurie; Johnson, Paul A.

doi:10.1007/s10910-022-01385-0

Cited by 2 publications

(3 citation statements)

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“…For H 8 this does happen, and is so disastrous the curve will not be presented. Such failure was also observed for RSPT corrections to RG states for individual electrons. , …”

Section: Resultsmentioning

confidence: 79%

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Beyond a Richardson–Gaudin Mean-Field: Slater–Condon Rules and Perturbation Theory

Johnson

2024

J. Phys. Chem. A

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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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“…For H 8 this does happen, and is so disastrous the curve will not be presented. Such failure was also observed for RSPT corrections to RG states for individual electrons. , …”

Section: Resultsmentioning

confidence: 79%

“…Such failure was also observed for RSPT corrections to RG states for individual electrons. 97,98 A much better treatment is obtained by defining H ̂0 in terms of the expected values of the target H ̂C…”

Section: ■ Results and Discussionmentioning

confidence: 99%

Beyond a Richardson–Gaudin Mean-Field: Slater–Condon Rules and Perturbation Theory

Johnson

2024

J. Phys. Chem. A

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“…[65][66][67] An introduction in terms of electrons is presented in refs. 68,69 Our approach is to use RG states as a variational Ansatz. To do so, we optimize the parameters {ε} and g defining the reduced BCS Hamiltonian.…”

Section: Theorymentioning

confidence: 99%

Near-exact treatment of seniority-zero ground and excited states with a Richardson–Gaudin mean-field

Fecteau

Cloutier

Moisset

et al. 2022

The Journal of Chemical Physics

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Eigenvectors of the reduced Bardeen–Cooper–Schrieffer (BCS) Hamiltonian, Richardson–Gaudin (RG) states, are used as a variational wavefunction ansatz for strongly correlated electronic systems. These states are geminal products whose coefficients are solutions of non-linear equations. Previous results showed an un-physical apparent avoided crossing in ground state dissociation curves for hydrogen chains. In this paper, it is shown that each seniority-zero state of the molecular Coulomb Hamiltonian corresponds directly to an RG state. However, the seniority-zero ground state does not correspond to the ground state of a reduced BCS Hamiltonian. The difficulty is in choosing the correct RG state. The systems studied showed a clear choice, and we expect that it should always be possible to reason physically which state to choose.

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Pertubative corrections for Hartree-Fock-like algebraic Bethe ansatz analogue

Cited by 2 publications

References 50 publications

Beyond a Richardson–Gaudin Mean-Field: Slater–Condon Rules and Perturbation Theory

Beyond a Richardson–Gaudin Mean-Field: Slater–Condon Rules and Perturbation Theory

Near-exact treatment of seniority-zero ground and excited states with a Richardson–Gaudin mean-field

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