Symmetry-projected variational calculations with the numerical suite TAURUS

Bally, B.; Sánchez-Fernández, Adrián; Rodrı́guez, T.

doi:10.1140/epja/s10050-021-00369-z

Cited by 20 publications

(43 citation statements)

References 90 publications

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“…[11] for testing purposes. To construct the basis states and solve the resulting eigenvalue problem, we use the FORTRAN program TAURUS [22,23]. Fig.…”

Section: A Shell-model Testmentioning

confidence: 99%

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

et al. 2021

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The generator coordinate method begins with the variational construction of a set of non-orthogonal meanfield states that span a subspace of the full many-body Hilbert space. These states are then often projected onto states with good quantum numbers to restore symmetries, leading to a set with members that can be similar to one another, and it is sometimes possible to reduce this set without greatly affecting results. Here we propose a greedy algorithm that we call the energy-transition-orthogonality procedure (ENTROP) to select subsets of important states. As applied here, the approach selects on the basis of diagonal energy, orthogonality, and contribution to the matrix element that governs neutrinoless double-β. We present both shell-model and preliminary ab initio calculations of this matrix element for the decay of 76 Ge, with quadrupole deformation parameters and the isoscalar pairing strength as generator coordinates. ENTROP converges quickly, significantly reducing the number of basis states needed for an accurate calculation.

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“…[11] for testing purposes. To construct the basis states and solve the resulting eigenvalue problem, we use the FORTRAN program TAURUS [22,23]. Fig.…”

Section: A Shell-model Testmentioning

confidence: 99%

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

et al. 2021

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“…The first code is restricted to spherical symmetry and is based on the actual diagonalization of the HFB matrix [33]. The second code, named TAURUS vap , solves HFB or variation after particle-number projection (VAPNP) equations for symmetry-unrestricted (real) Bogoliubov quasi-particle states [34], thus allowing for spatially deformed solutions. Employing a gradient method, the code can actually solve the variational equations under a large variety of con-straints and was recently used to perform first practical calculations [35].…”

Section: A Numerical Set Upmentioning

confidence: 99%

Zero-pairing limit of Hartree-Fock-Bogoliubov reference states

Duguet,

Bally,

Tichai

2020

Preprint

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Background:The variational Hartree-Fock-Bogoliubov (HFB) mean-field theory is the starting point of various (ab initio) many-body methods dedicated to superfluid systems. In this context, pairing correlations may be driven towards zero either on purpose via HFB calculations constrained on, e.g., the particle-number variance or simply because inter-nucleon interactions cannot sustain pairing correlations in the first place in, e.g., closed-shell systems. While taking this limit constitutes a text-book problem when the system is of closed-(sub)shell character, it is typically, although wrongly, thought to be ill-defined whenever the naive filling of single-particle levels corresponds to an open-shell system. Purpose:The present work demonstrates that the zero-pairing limit of an HFB state is well-defined independently of the average particle number A it is constrained to. Still, the nature of the limit state is shown to depend of the regime, i.e., on whether the nucleus characterizes as a closed-(sub)shell or an open-shell system when taking the limit. Finally, the consequences of the zero-pairing limit on Bogoliubov many-body perturbation theory (BMBPT) calculations performed on top of the HFB reference state are illustrated.Methods: The zero-pairing limit of a HFB state constrained to carry an arbitrary (integer) number of particles A on average is worked out analytically and realized numerically using a two-nucleon interaction derived within the frame of chiral effective field theory.Results: The zero-pairing limit of the HFB state is mathematically well-defined, independently of the closedor open-shell character of the system in the limit. Still, the nature of the limit state strongly depends on the underlying shell structure and on the associated naive filling reached in the zero-pairing limit for the particle number A of interest. First, the text-book situation is recovered for closed-(sub)shell systems, i.e., the limit state is reached for a finite value of the inter-nucleon interaction (the well-known BCS collapse) and takes the form of a single Slater determinant displaying (i) zero pairing energy, (ii) non-degenerate elementary excitations and (iii) zero particle-number variance. Contrarily, a non-standard situation is obtained for open-shell systems, i.e., the limit state is only reached for a zero value of the pairing interaction (no BCS collapse) and takes the form of a specific finite linear combination of Slater determinants displaying (a) a non-zero pairing energy, (b) degenerate elementary excitations and (c) a non-zero particle-number variance for which an analytical formula is derived. This non-zero particle-number variance acts as a lower bound that depends in a specific way on the number of valence nucleons and on the degeneracy of the valence shell. The fact that a given nucleus does belong to one category or the other, i.e., closed-(sub)shell or open shell, in the pairing limit may depend on the self-consistent spatial symmetry assumed in the calculation. All these findings are confirmed and ...

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“…The precise impact, however, needs to be checked in actual EDF theory calculations. An extension to handle nuclear Hamiltonians -instead of functionals -where proton-neutron pairing can be accommodated explicitly has been proposed recently (Bally et al, 2021).…”

Section: Energy-density Functional Theorymentioning

confidence: 99%

Toward the discovery of matter creation with neutrinoless double-beta decay

Agostini¹,

Benato²,

Detwiler³

et al. 2022

Preprint

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The discovery of neutrinoless double-beta decay could soon be within reach. This hypothetical ultra-rare nuclear decay is a portal to new physics beyond the Standard Model. Its observation would constitute the discovery of a matter-creating process, corroborating leading theories of why the universe contains more matter than antimatter, and how the forces unify at high energy scales. It would also prove that neutrinos and antineutrinos are not two distinct particles, but can transform into each other, generating their own mass in the process. The recognition that neutrinos are not massless necessitates an explanation and has boosted interest in neutrinoless double-beta decay. The field is now at a turning point. A new round of experiments is currently being prepared for the next decade to cover an important region of parameter space. Advancements in nuclear theory are laying the groundwork to connect the nuclear decay with the underlying new physics. Meanwhile, the particle theory landscape continues to find new motivations for neutrinos to be their own antiparticle. This review brings together the experimental, nuclear theory, and particle theory aspects connected to neutrinoless double-beta decay, to explore the path toward -and beyond -its discovery.

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Symmetry-projected variational calculations with the numerical suite TAURUS

Cited by 20 publications

References 90 publications

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

Application of an efficient generator-coordinate subspace-selection algorithm to neutrinoless double- β decay

Zero-pairing limit of Hartree-Fock-Bogoliubov reference states

Toward the discovery of matter creation with neutrinoless double-beta decay

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