An effective recursive algorithm for generating many-body Hugenholtz and Goldstone diagrams

Csépes, Zoltán; Pipek, János

doi:10.1016/0021-9991(88)90153-2

Cited by 16 publications

(13 citation statements)

References 25 publications

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“…This translates into the difficulty to both generate all allowed diagrams at a given order without missing any and to evaluate their expression in a quick and errorsafe way. Consequently, the last tool introduced to tackle this difficulty consists of an automatized generation and evaluation of diagrams [88][89][90][91][92][93][94][95]. All these technical, yet crucial, aspects of MBPT are not addressed in the present article and the interested reader is referred to the references.…”

Section: Closed-shell Many-body Perturbation Theorymentioning

confidence: 99%

Many-Body Perturbation Theories for Finite Nuclei

2020

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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: Closed-shell Many-body Perturbation Theorymentioning

confidence: 99%

Many-Body Perturbation Theories for Finite Nuclei

2020

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“…Diagrammatics in CC theory was pioneered by Č ížek and Paldus 1,24,25 as well as Bartlett and co-workers. 26,27 Generation of MBPT 28,29 or CC diagrams 27,30 through infinite order is well documented. ͑For further references about diagrammatics see, e.g., Refs.…”

Section: Introductionmentioning

confidence: 99%

Higher excitations in coupled-cluster theory

Kállay¹,

Śurján²

2001

The Journal of Chemical Physics

721

448

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Articles you may be interested inInclusion of selected higher excitations involving active orbitals in the state-specific multireference coupledcluster theory J. Chem. Phys. 133, 234110 (2010); 10.1063/1.3515478Second-and third-order triples and quadruples corrections to coupled-cluster singles and doubles in the ground and excited states Extended benchmark studies of coupled cluster theory through triple excitations The viability of treating higher excitations in coupled-cluster theory is discussed. An algorithm is presented for solving coupled-cluster ͑CC͒ equations which can handle any excitation. Our method combines the formalism of diagrammatic many-body perturbation theory and string-based configuration interaction ͑CI͒. CC equations are explicitly put down in terms of antisymmetrized diagrams and a general method is proposed for the factorization of the corresponding algebraic expressions. Contractions between cluster amplitudes and intermediates are evaluated by a string-based algorithm. In contrast to our previous developments ͓J. Chem. Phys. 113, 1359 ͑2000͔͒ the operation count of this new method scales roughly as the (2nϩ2)nd power of the basis set size where n is the highest excitation in the cluster operator. As a by-product we get a completely new CI formalism which is effective for solving both truncated and full CI problems. Generalization for approximate CC models as well as multireference cases is also discussed.

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“…While in earlier works the working equations were derived by hand, the rising computational power and the development of computer-aided algebraic manipulation tools have facilitated the derivation of more advanced truncation schemes in modern many-body approaches, many of which have undergone their pioneering studies in quantum chemistry [38][39][40][41][42]. A shining example is the tensor contraction engine that was developed in close collaboration with computer scientists and has been one of the most powerful tools to extend quantum-chemistry calculations to higher accuracy by generating working equations and source code for large-scale distributed implementations [43].…”

Section: Introductionmentioning

confidence: 99%

Symmetry reduction of tensor networks in many-body theory

et al. 2020

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The ongoing progress in (nuclear) many-body theory is accompanied by an ever-rising increase in complexity of the underlying formalisms used to solve the stationary Schrödinger equation. The associated working equations at play in state-of-the-art ab initio nuclear many-body methods can be analytically reduced with respect to angular-momentum, i.e. SU(2), quantum numbers whenever they are effectively employed in a symmetry-restricted context. The corresponding procedure constitutes a tedious and error-prone but yet an integral part of the implementation of those many-body frameworks. Indeed, this symmetry reduction is a key step to advance modern simulations to higher accuracy since the use of symmetry-adapted tensors can decrease the computational complexity by orders of magnitude. While attempts have been made in the past to automate the (anti-) commutation rules linked to Fermionic and Bosonic algebras at play in the derivation of the working equations, there is no systematic account to achieve the same goal for their symmetry reduction. In this work, the first version of an automated tool performing graph-theory-based angular-momentum reduction is presented. Taking the symmetry-unrestricted expressions of a generic tensor network as an input, the code provides their angular-momentum-reduced form in an error-safe way in a matter of seconds. Several state-of-the-art many-body methods serve as examples to demonstrate the generality of the approach and to highlight the potential impact on the many-body community.

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An effective recursive algorithm for generating many-body Hugenholtz and Goldstone diagrams

Cited by 16 publications

References 25 publications

Many-Body Perturbation Theories for Finite Nuclei

Many-Body Perturbation Theories for Finite Nuclei

Higher excitations in coupled-cluster theory

Symmetry reduction of tensor networks in many-body theory

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