Richardson–Gaudin mean-field for strong correlation in quantum chemistry

Johnson, Paul A.; Fecteau, Charles‐Émile; Berthiaume, Frédéric; Cloutier, Samuel; Carrier, Laurie; Gratton, Marianne; Bultinck, Patrick; Baerdemacker, Stijn De; Neck, Dimitri Van; Limacher, Peter A.; Ayers, Paul W.

doi:10.1063/5.0022189

Cited by 53 publications

(55 citation statements)

References 83 publications

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“…[22][23][24] Exact ground states of the reduced BCS Hamiltonian have recently been appiled to the molecular Hamiltonian. [25][26][27] Although simplistic, this Hamiltonian shows non-trivial physics in the attractive regime, 28 which traditional quantum chemistry methods fail to describe. [28][29][30] In contrast, AGP and AGP-based methods are able to capture most of the correlation energies systematically.…”

Section: Lc-agpmentioning

confidence: 99%

Construction of linearly independent non-orthogonal AGP states

Dutta,

Chen,

Henderson

et al. 2021

Preprint

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We show how to construct a linearly independent set of antisymmetrized geminal power (AGP) states, which allows us to rewrite our recently introduced geminal replacement (GR) models as linear combinations of non-orthogonal AGPs. This greatly simplifies the evaluation of matrix elements and permits us to introduce an AGP-based selective configuration interaction (SCI) method, which can reach arbitrary excitation levels relative to a reference AGP, balancing accuracy and cost as we see fit.

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Section: Lc-agpmentioning

confidence: 99%

Construction of linearly independent non-orthogonal AGP states

Dutta,

Chen,

Henderson

et al. 2021

Preprint

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“…Scalar products and reduced density matrices (RDM) of RG states are easily evaluated, and thus variational optimizations with RG states are feasible. Recently, 59 we performed variational calculations for Hydrogen chain dissociations using RG ground states. We observed un-physical behaviour which was quite disappointing.…”

Section: Introductionmentioning

confidence: 99%

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

Fecteau,

Cloutier,

Moisset

et al. 2022

Preprint

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Eigenvectors of the reduced Bardeen-Cooper-Schrieffer 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 un-physical behaviour but in this contribution it is shown that with only the variational solution for the ground state, all the seniority-zero states are quite well approximated.The difficulty is in choosing the correct RG state. The systems studied showed a clear choice and we expect it should always be possible to reason physically which state to choose.

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“…In particular we are using the algebraic Bethe ansatz (ABA) 35,36 solution to the reduced Bardeen-Cooper-Schrieffer Hamiltonian, 37,38 which we refer to as Richardson-Gaudin (RG) [39][40][41][42][43] states, as a mean-field geminal wavefunction. [44][45][46][47] The ABA is an approach capable of solving a large class of models both in quantum mechanics, 48 and in 2-dimensional classical statistical mechanics. 49 We are studying RG states as the general mean-field for pairs of electrons, the so-called antisymmetric product of interacting geminals (APIG), is intractable to compute whereas RG states have polynomial cost and may be improved upon systematically.…”

Section: Introductionmentioning

confidence: 99%