Multi-reference many-body perturbation theory for nuclei

Frosini, Mikaël; Duguet, Thomas; Ebran, J.-P.; Bally, B.; Mongelli, Tobias; Rodrı́guez, T.; Roth, Robert; Somà, V.

doi:10.1140/epja/s10050-022-00693-y

Cited by 36 publications

(24 citation statements)

References 65 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where the symbol µ is introduced to distinguish basis function of the space for the irrep. The projection operator (27) has the following properties…”

Section: The Löwdin Methodsmentioning

confidence: 99%

“…A detailed introduction to symmetry breaking in nuclear mean fields and the restoration of broken symmetries with projection techniques can be found in textbooks [17,18], and in recent review papers [19,20] and the references therein. Recently, this idea has also been implemented into ab initio studies of atomic nuclei based on the many-body expansion methods, including the symmetry broken and restored coupled-cluster theory [21,22,23,24], in-medium generator coordinate method (IM-GCM) [25,26] -a new variant of IMSRG method [2], and many-body perturbation theory (MBPT) [27,28,29].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Symmetry restoration methods

Yao¹

2022

Preprint

View full text Add to dashboard Cite

Symmetry techniques based on group theory play a prominent role in the analysis of nuclear phenomena, and in particular in the understanding of observed regular patterns in nuclear spectra and selection rules for electromagnetic transitions. A variety of symmetry-based nuclear models have been developed in nuclear physics, providing efficient tools of choice to interpret nuclear spectroscopic data. This chapter provides a pedagogical introduction to the basic idea of symmetrybreaking mechanism and symmetry-restoration methods in modeling atomic nuclei.

show abstract

“…where the symbol µ is introduced to distinguish basis function of the space for the irrep. The projection operator (27) has the following properties…”

Section: The Löwdin Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetry restoration methods

Yao¹

2022

Preprint

View full text Add to dashboard Cite

show abstract

“…Otherwise, solve the HWG equation [Eq. (12)] by diagonalizing (without truncations related with ε λ ) the corresponding N nat × N nat Hamiltonian matrix.…”

Section: A Solution Of the Hill-wheeler-griffin Equationmentioning

confidence: 99%

“…Such an implementation has been used in different contexts. Hence, with energy density functionals (EDFs) it is often referred as multireference EDF (MR-EDF) or symmetry conserving configuration mixing (SCCM) [4][5][6][7][8]; with valence-space Hamiltonians it is known as projected-GCM (PGCM) [9][10][11][12][13], discretized nonorthogonal shell model (DNO-SM) [14], or Monte Carlo shell model (MCSM) [15]. All of these methods are very similar and they subtly differ by the definition of the intrinsic states, the generating coordinates used, the nuclear interaction, the selection of the states and/or a combination of the aforementioned.…”

Section: Introductionmentioning

confidence: 99%

Optimization of the number of intrinsic states included in the discrete generator coordinate method

Jaime

Rodrı́guez

2022

Phys. Rev. C

View full text Add to dashboard Cite

We present a mechanism to efficiently preselect the number of intrinsic many-body states that are used to define the many-body wave functions within the discrete generator coordinate method (GCM). This procedure, based on the proper definition of a natural basis of orthonormal states, does not require the evaluation of the nondiagonal Hamiltonian kernels to do the selection and helps to reduce the numerical instabilities. The performance of the method is analyzed in detail in the ground state and 0 + excited states of some selected nuclei computed with the Gogny energy density functional.

show abstract

“…The latter are vital for interpreting and planning the current-and next-generation tonne-scale experiments for 0νββ decays (see the recent reviews [28][29][30]). GCM calculations most frequently use modern energy density functionals (EDFs) and effective Hamiltonians as inputs, but there have been several works that employ nuclear forces from chiral Effective Field Theory (EFT) in recent years, as the GCM has attracted interest as an pathway for extending nuclear ab initio calculations to deformed nuclei [26,27,[31][32][33][34][35].…”

Section: Introductionmentioning

confidence: 99%

Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation

Zhang¹,

Lin²,

M.³

et al. 2022

Preprint

View full text Add to dashboard Cite

Background: The generator coordinate method (GCM) is an important tool of choice for modeling large-amplitude collective motion in atomic nuclei. Recently, it has attracted increasing interest as it can be exploited to extend ab initio methods to the description of collective excitations of medium-mass and heavy deformed nuclei, as well as the nuclear matrix elements (NME) of candidates for neutrinoless double-beta (0νββ) decay.Purpose: The computational complexity of the GCM increases rapidly with the number of collective coordinates. It imposes a strong restriction on the applicability of the method. We aim to exploit machine learning (ML) algorithms to speed up GCM calculations and ultimately provide a more efficient description of nuclear energy spectra and other observables such as the NME of 0νββ decay without loss of accuracy.Method: To speed up GCM calculations, we propose a subspace reduction algorithm that employs optimized ML models as surrogates for exact quantum-number projection calculations for norm and Hamiltonian kernels. The model space of the original GCM is reduced to a subspace relevant for nuclear low energy spectra and the NME of ground state to ground state 0νββ decay based on the orthogonality condition (OC) and the energy transition-orthogonality procedure (ENTROP), respectively. Nuclear energy spectra are determined by the GCM through the configuration mixing within this subspace. For simplicity, a polynomial regression algorithm is used to learn the norm and Hamiltonian kernels. The efficiency and accuracy of this algorithm are illustrated for Ge 76 and Se 76 by comparing results obtained using the ML models to direct GCM calculations. The popular non-relativistic and relativistic EDFs, a valence-space shell-model Hamiltonian, and a modern nuclear interaction derived from chiral effective field theory are employed. Results:The low-lying energy spectra of 76 Ge and 76 Se, as well as the 0νββ-decay NME between their ground states, are computed. The results show that the performance of the GCM+OC/ENTROP+ML is more robust than that of the GCM+ML alone, and the former can reproduce the results of the original GCM calculation rather accurately with a significantly reduced computational cost.Conclusions: ML algorithms, when implemented properly, can accelerate GCM calculations without loss of accuracy. In applications with axially deformed configurations, the computation time can be reduced by a factor of three to nine for energy spectra and NMEs, respectively. This factor is expected to increase significantly with the number of employed generator coordinates.

show abstract

Multi-reference many-body perturbation theory for nuclei

Cited by 36 publications

References 65 publications

Symmetry restoration methods

Symmetry restoration methods

Optimization of the number of intrinsic states included in the discrete generator coordinate method

Optimization of generator coordinate method with machine-learning techniques for nuclear spectra and neutrinoless double-beta decay: ridge regression for nuclei with axial deformation

Contact Info

Product

Resources

About