Transition density matrices of Richardson–Gaudin states

Johnson, Paul A.; Fortin, Hubert; Cloutier, Samuel; Fecteau, Charles‐Émile

doi:10.1063/5.0041051

Cited by 16 publications

(22 citation statements)

References 59 publications

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“…The labelling of the states suggests an aufbau principle, though as curves cross, the ordering of states does not respect the principle at all couplings. As we have shown, 78 the dominant couplings between two RG states occur for "single-pair" excitations, with double-pair excitations having non-zero contributions. Past doubles, the couplings go to zero quite quickly.…”

Section: Introductionmentioning

confidence: 64%

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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Section: Introductionmentioning

confidence: 64%

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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“…Since we are interested in systems that are well-described by pairing wavefunctions (14), we need Hamiltonians whose eigenstates are of this form. One such Hamiltonian is the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian [18][19][20][21]47,48 , ĤBCS = 1 2…”

Section: Rg States: On-shell Bethe Vectors Of the Reduced Bcs Hamilto...mentioning

confidence: 99%

“…In our previous work [11][12][13][14][15][16] we have chosen wavefunctions that are eigenvectors of a model Hamiltonian,…”

Section: Introductionmentioning

confidence: 99%

Bivariational Principle for an Antisymmetrized Product of Nonorthogonal Geminals Appropriate for Strong Electron Correlation

Johnson¹,

Ayers²,

Baerdemacker³

et al. 2022

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We develop a bivariational principle for an antisymmetric product of nonorthogonal geminals. Special cases reduce to the antisymmetric product of strongly-orthogonal geminals (APSG), the generalized valence bond-perfect pairing (GVB-PP), and the antisymmetrized geminal power (AGP) wavefunctions. The presented method employs wavefunctions of the same type as Richardson-Gaudin (RG) states, but which are not eigenvectors of a model Hamiltonian which would allow for more freedom in the mean-field. The general idea is to work with the same state in a primal picture in terms of pairs, and in a dual picture in terms of pair-holes. This leads to an asymmetric energy expression which may be optimized bivariationally, and is strictly variational when the two representations are consistent. The general approach may be useful in other contexts, such as for computationally feasible variational coupledcluster methods.

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“…Recently [48][49][50][51] we have employed the eigenvectors of the reduced Bardeen-Cooper-Schrieffer (BCS) Hamiltonian 33,34 ĤBCS = 1 2…”

Section: Closed-shell Pairs: Su(2)mentioning

confidence: 99%

Density Matrices of Seniority-Zero Geminal Wavefunctions

Moisset,

Fecteau,

Johnson

2022

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Scalar products and density matrix elements of closed-shell pair geminal wavefunctions are evaluated directly in terms of the pair amplitudes, resulting in an analogue of Wick's theorem for fermions or bosons. This expression is in general intractable, but it is shown how it becomes feasible in three distinct ways for Richardson-Gaudin (RG) states, the antisymmetrized geminal power, and the antisymmetrized product of strongly-orthogonal geminals. Dissociation curves for hydrogen chains are computed with off-shell RG states and the antisymmetrized product of interacting geminals.Both are near exact suggesting that the incorrect results observed with ground state RG states are fixable using a different RG state.

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Transition density matrices of Richardson–Gaudin states

Cited by 16 publications

References 59 publications

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

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

Bivariational Principle for an Antisymmetrized Product of Nonorthogonal Geminals Appropriate for Strong Electron Correlation

Density Matrices of Seniority-Zero Geminal Wavefunctions

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