Structure of the number-projected BCS wave function

Dukelsky, J.; P̧ittel, S.; Esebbag, C.

doi:10.1103/physrevc.93.034313

Cited by 24 publications

(36 citation statements)

References 23 publications

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“…The error on the correlation energy is now lower than 0.1 % for all g, which is almost one order of magnitude lower than our original goal. Our results compare very favorably with PoST methods [58,59]. Once again, projected 2qp configurations are redundant and can actually be omitted.…”

Section: B Full Ansatzsupporting

confidence: 70%

“…Second-order results are displayed in Fig. 1 for N = 20 and compared with VAP-BCS results [58]. Three main lessons can be learnt from these calculations 1.…”

Section: Truncated CI Calculations a Perturbation Theorymentioning

confidence: 99%

“…3-12 builds in the breaking of the U (1) symmetry prior to performing its exact restoration. As such, each state |Φkl [58]. For g < g c , however, the BCS vacuum actually reduces to the HF reference state such that each state |Φkl ... N (g) identifies with one n-particle/n-hole (np-nh) excitation on top of it belonging to H N 8 .…”

Section: Formalism a Basis Constructionmentioning

confidence: 99%

“…[58,59]. Reconciling the performance of CC doubles in the normal phase with the merit of VAP-BCS in the strongly interacting regime, this method, coined as polynomial similarity transformation (PoST), reaches less than 1 % error…”

Section: Introductionmentioning

confidence: 99%

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Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

et al. 2017

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Background: Ab initio many-body methods have been developed over the past ten years to address mid-mass nuclei. In their best current level of implementation, their accuracy is of the order of a few per cent error on the ground-state correlation energy. Recently implemented variants of these methods are operating a breakthrough in the description of medium-mass open-shell nuclei at a polynomial computational cost while putting state-of-the-art models of inter-nucleon interactions to the test.Purpose: As progress in the design of inter-nucleon interactions is made, and as questions one wishes to answer are refined in connection with increasingly available experimental data, further efforts must be made to tailor many-body methods that can reach an even higher precision for an even larger number of observable/quantum states/nuclei. It is the objective of the present work to contribute to such a quest by designing and testing a new many-body scheme. Methods:We formulate a truncated configuration interaction method that consists of diagonalizing the Hamiltonian in a highly truncated subspace of the total N -body Hilbert space. The reduced Hilbert space is generated via the particle-number projected BCS state along with projected seniority-zero two and four quasi-particle excitations. Furthermore, the extent by which the underlying BCS state breaks U (1) symmetry is optimized in presence of the projected two and four quasi-particle excitations. This constitutes an extension of the so-called restricted variation after projection method in use within the frame of multi-reference energy density functional calculations. The quality of the newly designed method is tested against exact solutions of the so-called attractive pairing Hamiltonian problem.Results: By construction, the method reproduce exact results for N = 2 and N = 4. For N = (8,16,20), the error on the ground-state correlation energy is less than (0.006, 0.1, 0.15) % across the entire range of inter-nucleon coupling defining the pairing Hamiltonian and driving the normal-to-superfluid quantum phase transition. The presently proposed method offers the advantage to automatically access the low-lying spectroscopy, which it does with high accuracy. Conclusions:The numerical cost of the newly designed variational method is polynomial (N 6 ) in system size. It achieves an unprecedented accuracy on the ground-state correlation energy, effective pairing gap and onebody entropy as well as on the excitation energy of low-lying states of the attractive pairing Hamiltonian. This constitutes a strong enough motivation to envision its application to realistic nuclear Hamiltonians in view of providing a complementary, accurate and versatile ab initio description of mid-mass open-shell nuclei in the future.

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Section: B Full Ansatzsupporting

confidence: 70%

“…Second-order results are displayed in Fig. 1 for N = 20 and compared with VAP-BCS results [58]. Three main lessons can be learnt from these calculations 1.…”

Section: Truncated CI Calculations a Perturbation Theorymentioning

confidence: 99%

Section: Formalism a Basis Constructionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

et al. 2017

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“…We have recently explored the possibility of interpolating between projected mean-field and CCSD for the attractive pairing ("reduced BCS") model exhibiting meanfield number symmetry breaking [23,24], as well as explicitly combining the two approximations for molecules exhibiting mean-field spin symmetry breaking [25]. In a previous work [26], we used the Lipkin model [27][28][29] as a testbed to develop projected restricted coupled cluster (PRCC), projected quasirestricted coupled cluster (PQCC), and projected unrestricted coupled cluster (PUCC).…”

Section: Introductionmentioning

confidence: 99%

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

2017

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The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected meanfield wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.

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Richardson-Gaudin states

Johnson

2024

Advances in Quantum Chemistry

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Structure of the number-projected BCS wave function

Cited by 24 publications

References 23 publications

Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

Combining symmetry breaking and restoration with configuration interaction: A highly accurate many-body scheme applied to the pairing Hamiltonian

Combining symmetry collective states with coupled-cluster theory: Lessons from the Agassi model Hamiltonian

Richardson-Gaudin states

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