Variational method for integrability-breaking Richardson-Gaudin models

Claeys, Pieter W.; Caux, Jean-Sébastien; Neck, Dimitri Van; Baerdemacker, Stijn De

doi:10.1103/physrevb.96.155149

Cited by 17 publications

(17 citation statements)

References 110 publications

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“…RG states are also being employed in nuclear structure 34 and condensed matter theory. 35 Our results were promising, though we explicitly noted many issues to be addressed in upcoming contributions. In particular the energy functional was not optimal.…”

Section: Introductionmentioning

confidence: 67%

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis

Fecteau¹,

Fortin²,

Cloutier³

et al. 2020

Preprint

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Eigenvectors of the reduced Bardeen-Cooper-Schrieffer Hamiltonian have recently been employed as a variational wavefunction ansatz in quantum chemistry. This wavefunction is a mean-field of pairs of electrons (geminals). In this contribution we report optimal expressions for their reduced density matrices in both the original physical basis and the basis of the Richardson-Gaudin pairs. Physical basis expressions were originally reported by Gorohovsky and Bettelheim 1 . In each case, the expressions scale like O(N 4 ), with the most expensive step the solution of linear equations. Analytic gradients are also reported in the physical basis. These expressions are an important step towards practical mean-field methods to treat strongly-correlated electrons.

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Section: Introductionmentioning

confidence: 67%

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis

Fecteau¹,

Fortin²,

Cloutier³

et al. 2020

Preprint

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show abstract

“…For the purpose of this paper, it suffices to note that such computationally facile expressions exist. We refer to recent papers [41,42] for more technical details.…”

Section: Richardson-gaudin Modelmentioning

confidence: 99%

“…In a first step, we optimize the basis. This is done by means of a variational Richardson-Gaudin (varRG) calculation, as has been done before in the context of quantum chemistry [51,52] and integrability-breaking quantum dots [42]. Because of the integrability of the underlying Richardson-Gaudin model (1), the variationally obtained state not only gives an approximation of the ground state, but also a complete set of orthogonal basis states, used in the consecutive step.…”

Section: Richardson-gaudin Configuration Interactionmentioning

confidence: 99%

Richardson-Gaudin Configuration-Interaction for nuclear pairing correlations

Baerdemacker¹,

Claeys²,

Caux³

et al. 2017

Preprint

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Background: The nuclear many-body system is a strongly correlated quantum system, posing serious challenges for perturbative approaches starting from uncorrelated reference states. The last decade has witnessed considerable progress in the accurate treatment of pairing correlations, one of the major components in medium-sized nuclei, reaching accuracies below the 1% level of the correlation energy.Purpose: Development of a quantum many-body method for pairing correlations that is (a) competitive in the 1% error range, and (b) can be systematically improved with a fast (exponential) convergence rate.Method: The present paper capitalizes upon ideas from Richardson-Gaudin integrability. The proposed method is a two-step approach. The first step consists of the optimization of a Richardson-Gaudin ground state as variational trial state. At the second step, the complete set of excited states on top of this Richardson-Gaudin ground state is used as an optimal basis for a Configuration Interaction method in an increasingly large effective Hilbert space.Results: The performance of the variational Richardson-Gaudin (varRG) and Richardson-Gaudin Configuration Interaction (RGCI) method is benchmarked against exact results using an effective G-matrix interaction for the Sn region. The varRG already reaches accuracies around the 1% level of the correlation energies, and the RGCI step sees an additional improvement scaling exponentially with the size of the effective Hilbert space. Conclusions:The Richardson-Gaudin models of integrability provide an optimized complete basis set for pairing correlations.

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“…More recently, BA has been applied as an approximate solution to systems with broken integrability. [ 48,49 ]…”

Section: Introductionmentioning

confidence: 99%

Bethe ansatz of electrons as a mean‐field wavefunction for chemical systems

Carrier

Fecteau

Johnson

2020

Int J of Quantum Chemistry

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Eigenvectors of a Hamiltonian solvable by a Bethe ansatz (BA) are employed as a variational trial wavefunction for electrons. Energy expressions are developed showcasing the methods of BA. Numerical results are presented for atomic systems as well as molecular dissociations, which are numerically identical with the restricted Hartree‐Fock (HF) results. The present contribution serves as a bridge between HF and other BA wavefunctions to be employed as mean‐field methods for strongly correlated electrons.

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Variational method for integrability-breaking Richardson-Gaudin models

Cited by 17 publications

References 110 publications

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis

Reduced density matrices of Richardson-Gaudin states in the Gaudin algebra basis

Richardson-Gaudin Configuration-Interaction for nuclear pairing correlations

Bethe ansatz of electrons as a mean‐field wavefunction for chemical systems

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