Bogoliubov many-body perturbation theory under constraint

Demol, Pepijn; Frosini, Mikaël; Tichai, Alexander; Somà, V.; Duguet, Thomas

doi:10.1016/j.aop.2020.168358

Cited by 39 publications

(69 citation statements)

References 105 publications

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“…Figure 9C shows the neutron-number dispersion σ ≡ A 2 − A 2 that grows with mass number. While the second-order contribution does not decrease yet the neutronnumber dispersion, one expects higher orders to do so [104]. In closed-shell systems, the particle-number dispersion is zero as a hallmark of the particle-number-conserving character of the wave function throughout the expansion.…”

Section: Low-order Calculations In Mid-mass Nucleimentioning

confidence: 99%

“…i.e., the computed average particle number does not match the targeted number A 0 of the physical system. This feature requires an iterative BMBPT scheme in order for the particle number to be correct at the working order, e.g., p ≥ 3, of interest [104]. To do so, one needs to rerun the HFB calculation with a p-dependent chemical potential such that, through a series of iterations, one eventually obtains, e.g., A (1) 0 + .…”

Section: Low Ordersmentioning

confidence: 99%

“…+ A (p) 0 = A 0 . Such a costly algorithm can fortunately be very well approximated by an a posteriori correction scheme that entirely bypasses the iterative scheme [104]. The third-order results presented in section 7.6.1 have been computed without any adjustment of the average particle number whereas the novel ones discussed in section 10.2 have been obtained on the basis of the a posteriori correction scheme.…”

Section: Low Ordersmentioning

confidence: 99%

“…In open-shell systems third-order partial sums are strongly contaminated due to a significant excess of neutrons brought by the third-order contribution to the average neutron number. As discussed earlier, calculations at third-order and beyond must eventually be done while constraining the average particle number to match the physical value [104]. This is reported on in section 10.2.…”

Section: Low-order Calculations In Mid-mass Nucleimentioning

confidence: 99%

“…A detailed study of the convergence characteristics of the BMBPT expansion via the calculation of high-order corrections similar to the ones presented in section 5 (section 6.4.1) for HF-MBPT (NCSM-PT) calculations of closed-shell (open-shell) nuclei has just be completed [104] and is thus not reported on here.…”

Section: Low-order Calculations In Mid-mass Nucleimentioning

confidence: 99%

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Many-Body Perturbation Theories for Finite Nuclei

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In recent years many-body perturbation theory encountered a renaissance in the field of ab initio nuclear structure theory. In various applications it was shown that perturbation theory, including novel flavors of it, constitutes a useful tool to describe atomic nuclei, either as a full-fledged many-body approach or as an auxiliary method to support more sophisticated non-perturbative many-body schemes. In this work the current status of many-body perturbation theory in the field of nuclear structure is discussed and novel results are provided that highlight its power as a efficient and yet accurate (pre-processing) approach to systematically investigate medium-mass nuclei. Eventually a new generation of chiral nuclear Hamiltonians is benchmarked using several state-of-the-art flavors of many-body perturbation theory.

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Section: Low-order Calculations In Mid-mass Nucleimentioning

confidence: 99%

Section: Low Ordersmentioning

confidence: 99%

Section: Low Ordersmentioning

confidence: 99%

Section: Low-order Calculations In Mid-mass Nucleimentioning

confidence: 99%

Section: Low-order Calculations In Mid-mass Nucleimentioning

confidence: 99%

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Many-Body Perturbation Theories for Finite Nuclei

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ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory

Arthuis

Duguet

Tichai

et al. 2019

Computer Physics Communications

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122

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We describe the first version (v1.0.0) of the code ADG that automatically (1) generates all valid Bogoliubov many-body perturbation theory (BMBPT) diagrams and (2) evaluates their algebraic expression to be implemented for numerical applications. This is achieved at any perturbative order p for a Hamiltonian containing both two-body (four-legs) and three-body (six-legs) interactions (vertices). The automated generation of BMBPT diagrams of order p relies on elements of graph theory, i.e., it is achieved by producing all oriented adjacency matrices of size (p + 1) × (p + 1) satisfying topological Feynman's rules. The automated evaluation of BMBPT diagrams of order p relies both on the application of algebraic Feynman's rules and on the identification of a powerful diagrammatic rule providing the result of the remaining p-tuple time integral. The diagrammatic rule in question constitutes a novel finding allowing for the straight summation of large classes of time-ordered diagrams at play in the time-independent formulation of BMBPT. Correspondingly, the traditional resolvent rule employed to compute time-ordered diagrams happens to be a particular case of the general rule presently identified. The code ADG is written in Python2.7 and uses the graph manipulation package NetworkX. The code is also able to generate and evaluate Hartree-Fock-MBPT (HF-MBPT) diagrams and is made flexible enough to be expanded throughout the years to tackle the diagrammatics at play in various many-body formalisms that already exist or are yet to be formulated. PROGRAM SUMMARYProgram Title: ADG Licensing provisions: GPLv3 Programming language: Python2.7 Nature of problem: As formal and numerical developments in many-bodyperturbation-theory-based ab initio methods make higher orders reachable, producing and evaluating all the diagrams become rapidly undoable on a handmade basis as both their number and complexity grows quickly, making it prone to mistakes and oversights. Solution method: BMBPT diagrams are encoded as square matrices known as oriented adjacency matrices in graph theory, and then turned into graph objects using the NetworkX package. Checks on the diagrams and evaluation of their time-integrated expression is then done on a purely diagrammatic basis. HF-MBPT diagrams are produced and evaluated as well using the same principle.

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Bogoliubov many-body perturbation theory under constraint

Cited by 39 publications

References 105 publications

Many-Body Perturbation Theories for Finite Nuclei

Many-Body Perturbation Theories for Finite Nuclei

Chiral Effective Field Theory after Thirty Years: Nuclear Lattice Simulations

ADG: Automated generation and evaluation of many-body diagrams I. Bogoliubov many-body perturbation theory

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