Title: Tensor-decomposition techniques for ab initio nuclear structure calculations: From chiral nuclear potentials to ground-state energies

Abstract

The computational resources needed to generate the ab initio solution of the nuclear many-body problem for increasing mass number and/or accuracy necessitates innovative developments to improve upon (i) the storage of many-body operators and (ii) the scaling of many-body methods used to evaluate nuclear observables. The storing and efficient handling of many-body operators with high particle ranks is currently one of the major bottlenecks limiting the applicability range of ab initio studies with respect to mass number and accuracy. Recently, the application of tensor decomposition techniques to many-body tensors has proven highly beneficial to reduce the computational cost of ab initio calculations in quantum chemistry and solid-state physics. The impact of applying state-of-the-art tensor factorization techniques to modern nuclear Hamiltonians derived from chiral effective field theory is investigated. Subsequently, the error induced by the tensor decomposition of the input Hamiltonian on ground-state energies of closed-shell nuclei calculated via second-order many-body perturbation theory is benchmarked. The first proof-of-principles application of tensor-decomposition techniques to the nuclear Hamiltonian is performed. Two different tensor formats are investigated by systematically benchmarking the approximation error on matrix elements stored in various bases of interest. The analysis is achieved while including normal-ordered three-nucleon interactions that are nowadaysmore » used as input to the most advanced ab initio calculations in medium-mass nuclei. With the aid of the factorized Hamiltonian, the second-order perturbative correction to ground-state energies is decomposed and the scaling properties of the underlying tensor network are discussed. The employed tensor formats are found to lead to an efficient data compression of two-body matrix elements of the nuclear Hamiltonian. In particular, the sophisticated tensor hypercontraction scheme yields low tensor ranks with respect to both harmonic-oscillator and Hartree-Fock single-particle bases. It is found that the tensor rank depends on the two-body total angular momentum J for which one performs the decomposition, which is itself directly related to the sparsity of the corresponding tensor. Furthermore, including normal-ordered two-body contributions originating from three-body interactions does not compromise the efficient data compression. Ultimately, the use of factorized matrix elements authorizes controlled approximations of the exact second-order ground-state energy corrections. In particular, a small enough error is obtained from low-rank factorizations in He4,O16, and Ca40. It is presently demonstrated that tensor-decomposition techniques can be efficiently applied to systematically approximate the nuclear many-body Hamiltonian in terms of lower-rank tensors. Beyond the input Hamiltonian, tensor-decomposition techniques can be envisioned to scale down the cost of state-of-the-art nonperturbative many-body methods in order to extend ab initio studies to (i) higher precisions, (ii) larger masses, and (iii) nuclei of doubly open-shell character.« less

Authors:

Tichai, A. ^[1]; Schutski, R. ^[2]; Scuseria, G. E. ^[3]; Duguet, T. ^[4]

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+ Show Author Affiliations

1. Alternative Energies and Atomic Energy Commission (CEA), Saclay (France); Univ. Paris-Saclay, Gif-sur-Yvette (France). Dépt. de Physique Nucléaire
2. Rice Univ., Houston, TX (United States). Dept. of Chemistry, and Dept. of Physics and Astronomy; Skolkovo Inst. of Science and Technology, Moscow (Russia)
3. Rice Univ., Houston, TX (United States). Dept. of Chemistry, and Dept. of Physics and Astronomy
4. Alternative Energies and Atomic Energy Commission (CEA), Saclay (France); Univ. Paris-Saclay, Gif-sur-Yvette (France); Katholieke Univ. Leuven, Heverlee (Belgium). Inst. voor Kern- en Stralingsfysica

Publication Date:

Mon Mar 18 00:00:00 EDT 2019

Research Org.:

Energy Frontier Research Centers (EFRC) (United States). Center for Complex Materials from First Principles (CCM); Temple Univ., Philadelphia, PA (United States)

Sponsoring Org.:

USDOE Office of Science (SC), Basic Energy Sciences (BES)

OSTI Identifier:

1566691

Alternate Identifier(s):

OSTI ID: 1501692

Grant/Contract Number:  

SC0012575

Resource Type:

Accepted Manuscript

Journal Name:

Physical Review. C

Additional Journal Information:

Journal Volume: 99; Journal Issue: 3; Journal ID: ISSN 2469-9985

Publisher:

American Physical Society (APS)

Country of Publication:

United States

Language:

English

Subject:

73 NUCLEAR PHYSICS AND RADIATION PHYSICS; catalysis (heterogeneous); electrocatalysis; solar (photovoltaic); mechanical behavior; superconductivity; magnetism and spin physics; water; materials and chemistry by design; synthesis (novel materials)