Quasiparticle coupled cluster theory for pairing interactions

Henderson, Thomas M.; Scuseria, Gustavo E.; Dukelsky, J.; Signoracci, A.; Duguet, Thomas

doi:10.1103/physrevc.89.054305

Cited by 118 publications

(145 citation statements)

References 32 publications

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“…The effect of singles contributions, which have been excluded from the BCC calculations, is expected to remain on the order of 100 keV such that 2PA-EOM-CCSD is genuinely lower in energy. This is not surprising given that nuclei in the very vicinity of a closed shell are those for which the benefit provided by the breaking of U (1) symmetry is actually overtaken by the associated shortcoming of not having an exact eigenstate of the particle-number operator [30], i.e. this constitutes a regime for which the exact restoration of symmetry [42] is critical.…”

Section: B Resultsmentioning

confidence: 99%

“…translationally invariant, geometries [28,29]. Very recently, the BCS-based version of the BCC formalism developed in the present paper was applied, at the doubles level, to the attractive pairing Hamiltonian problem [30]. Near the transition point where particle-number symmetry is spontaneously broken, a high-quality reproduction of exact Richardson solutions [31,32] was obtained.…”

Section: Introductionmentioning

confidence: 99%

“…Near the transition point where particle-number symmetry is spontaneously broken, a high-quality reproduction of exact Richardson solutions [31,32] was obtained. The present work derives BCC theory and, encouraged by the results of Henderson et al [30], applies it for the first time to ab initio calculations of open-shell nuclei.…”

Section: Introductionmentioning

confidence: 99%

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Ab initioBogoliubov coupled cluster theory for open-shell nuclei

et al. 2015

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Background: Ab initio many-body methods have been developed over the past ten years to address closed-shell nuclei up to mass A ∼ 130 on the basis of realistic two-and three-nucleon interactions. A current frontier relates to the extension of those many-body methods to the description of open-shell nuclei.Purpose: Several routes to address open-shell nuclei are currently under investigation, including ideas which exploit spontaneous symmetry breaking. Singly open-shell nuclei can be efficiently described via the sole breaking of U (1) gauge symmetry associated with particle-number conservation, as a way to account for their superfluid character. While this route was recently followed within the framework of self-consistent Green's function theory, the goal of the present work is to formulate a similar extension within the framework of coupled cluster theory.Methods: We formulate and apply Bogoliubov coupled cluster (BCC) theory, which consists of representing the exact ground-state wavefunction of the system as the exponential of a quasiparticle excitation cluster operator acting on a Bogoliubov reference state. Equations for the ground-state energy and the cluster amplitudes are derived at the singles and doubles level (BCCSD) both algebraically and diagrammatically. The formalism includes three-nucleon forces at the normal-ordered two-body level. The first BCCSD code is implemented in m-scheme, which will permit the treatment of doubly open-shell nuclei via the further breaking of SU (2) symmetry associated with angular momentum conservation.Results: Proof-of-principle calculations in an Nmax = 6 spherical harmonic oscillator basis are performed for 16,18,20 O, 18 Ne, and 20 Mg in the BCCD approximation with a chiral two-nucleon interaction, comparing to results obtained in standard coupled cluster theory when applicable. The breaking of U (1) symmetry is monitored by computing the variance associated with the particle-number operator. Conclusions:The newly developed many-body formalism increases the potential span of ab initio calculations based on single-reference coupled cluster techniques tremendously, i.e. potentially to reach several hundred additional mid-mass nuclei. The new formalism offers a wealth of potential applications and further extensions dedicated to the description of ground-and excited-states of open-shell nuclei. Short-term goals include the implementation of three-nucleon forces at the normal-ordered two-body level. Mid-term extensions include the approximate treatment of triple corrections and the development of the equation-of-motion methodology to treat both excited states and odd nuclei. Long-term extensions include exact restoration of U (1) and SU (2) symmetries.

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Section: B Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Ab initioBogoliubov coupled cluster theory for open-shell nuclei

et al. 2015

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“…We should note here that the coincidence between pCCD and DOCI has been established for systems with repulsive two-body interactions, as we consider here, but seems to break down in systems with attractive two-body interactions. [39] To what extent the poor results of pCCD for attractive systems is relevant for realistic, repulsive Hamiltonians is an open question.…”

Section: Energy Comparison Between Doci and Pccdmentioning

confidence: 99%

Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

Shepherd

Henderson

Scuseria

2016

The Journal of Chemical Physics

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Over the past few years pair coupled cluster doubles (pCCD) has shown promise for the description of strong correlation. This promise is related to its apparent ability to match results from doubly occupied configuration interaction (DOCI), even though the latter method has exponential computational cost. Here, by modifying the full configuration interaction quantum Monte Carlo (FCIQMC) algorithm to sample only the seniority zero sector of Hilbert space, we show that the DOCI and pCCD energies are in agreement for a variety of 2D Hubbard models, including for systems well out of reach for conventional configuration interaction algorithms. Our calculations are aided by the sign problem being much reduced in the seniority zero space compared with the full space. We present evidence for this, and then discuss the sign problem in terms of the wave function of the system which appears to have a simplified sign structure.

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“…A different, computationally feasible approach suitable for strongly-correlated systems uses seniority-zero wavefunctions to describe the static/nondynamic part of the electron correlation en-ergy. [31][32][33][34][35][36][37][38][39][40][41][42][43][44] The missing dynamic electron correlation effects are included a posteriori in these ansätze using, for instance, many-body perturbation theory [45][46][47], coupled-cluster theory [48][49][50][51][52], extended random phase approximation [53], and density functional theory (DFT) corrections [54,55].…”

Section: Introductionmentioning

confidence: 99%

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

Boguslawski

Tecmer

2017

J. Chem. Theory Comput.

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Wavefunctions restricted to electron-pair states are promising models to describe static/nondynamic electron correlation effects encountered, for instance, in bond-dissociation processes and transition-metal and actinide chemistry. To reach spectroscopic accuracy, however, the missing dynamic electron correlation effects that cannot be described by electron-pair states need to be included a posteriori. In this article, we extend the previously presented perturbation theory models with an Antisymmetric Product of 1-reference orbital Geminal (AP1roG) reference function that allow us to describe both static/nondynamic and dynamic electron correlation effects. Specifically, our perturbation theory models combine a diagonal and off-diagonal zero-order Hamiltonian, a single-reference and multi-reference dual state, and different excitation operators used to construct the projection manifold. We benchmark all proposed models as well as an a posteriori linearized coupled cluster correction on top of AP1roG against CR-CCSD(T) reference data for reaction energies of several closed-shell molecules that are extrapolated to the basis set limit. Moreover, we test the performance of our new methods for multiple bond breaking processes in the N2, C2, and BN dimers against MRCI-SD and MRCI-SD+Q reference data. Our numerical results indicate that the best performance is obtained from a linearized coupled cluster correction as well as second-order perturbation theory corrections employing a diagonal and off-diagonal zero-order Hamiltonian and a single-determinant dual state. These dynamic corrections on top of AP1roG allow us to reliably model molecular systems dominated by static/nondynamic as well as dynamic electron correlation.

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Quasiparticle coupled cluster theory for pairing interactions

Cited by 118 publications

References 32 publications

Ab initioBogoliubov coupled cluster theory for open-shell nuclei

Ab initioBogoliubov coupled cluster theory for open-shell nuclei

Using full configuration interaction quantum Monte Carlo in a seniority zero space to investigate the correlation energy equivalence of pair coupled cluster doubles and doubly occupied configuration interaction

Benchmark of Dynamic Electron Correlation Models for Seniority-Zero Wave Functions and Their Application to Thermochemistry

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