Electrostatic Mapping of Nuclear Pairing

Dukelsky, J.; Esebbag, C.; P̧ittel, S.

doi:10.1103/physrevlett.88.062501

Cited by 62 publications

(72 citation statements)

References 10 publications

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“…While the solution to this problem has been found using standard techniques [36], larger systems would require more sophisticated methods [32] to avoid the singularities.…”

Section: Bcs-like Modelsmentioning

confidence: 99%

Exactly-solvable models derived from a generalized Gaudin algebra

et al. 2005

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We introduce a generalized Gaudin Lie algebra and a complete set of mutually commuting quantum invariants allowing the derivation of several families of exactly solvable Hamiltonians. Different Hamiltonians correspond to different representations of the generators of the algebra. The derived exactly-solvable generalized Gaudin models include the Hamiltonians of Bardeen-Cooper-Schrieffer, Suhl-Matthias-Walker, Lipkin-Meshkov-Glick, the generalized Dicke and atom-molecule, the nuclear interacting boson model, a new exactly-solvable Kondo-like impurity model, and many more that have not been exploited in the physics literature yet.

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“…While the solution to this problem has been found using standard techniques [36], larger systems would require more sophisticated methods [32] to avoid the singularities.…”

Section: Bcs-like Modelsmentioning

confidence: 99%

Exactly-solvable models derived from a generalized Gaudin algebra

et al. 2005

Self Cite

View full text Add to dashboard Cite

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“…Racah's seniority scheme, however, is badly broken by single-particle energies [244]. Nonetheless, for non-degenerate single-particle energies exact solutions to the pairing problem have been derived by Richardson and Gaudin [223][224][225], with further extensions based on the algebraic Bethe ansatz [227,228,235,[245][246][247][248]. For all these algebraic Bethe ansatz approaches, the solutions are provided by a set of highly non-linear Bethe Ansatz Equations (BAEs).…”

Section: Seniority Scheme and Exact Pairing Theorymentioning

confidence: 99%

Symmetry-guided large-scale shell-model theory

Launey

Dytrych

Draayer

2016

Progress in Particle and Nuclear Physics

127

173

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In this review, we present a symmetry-guided strategy that utilizes exact as well as partial symmetries for enabling a deeper understanding of and advancing ab initio studies for determining the microscopic structure of atomic nuclei. These symmetries expose physically relevant degrees of freedom that, for large-scale calculations with QCD-inspired interactions, allow the model space size to be reduced through a very structured selection of the basis states to physically relevant subspaces. This can guide explorations of simple patterns in nuclei and how they emerge from first principles, as well as extensions of the theory beyond current limitations toward heavier nuclei and larger model spaces. This is illustrated for the ab initio symmetry-adapted no-core shell model (SA-NCSM) and two significant underlying symmetries, the symplectic Sp(3, R) group and its deformation-related SU(3) subgroup. We review the broad scope of nuclei, where these symmetries have been found to play a key role -from the light p-shell systems, such as 6 Li, 8 B, 8 Be, 12 C, and 16 O, and sd-shell nuclei exemplified by 20 Ne, based on first-principle explorations; through the Hoyle state in 12 C and enhanced collectivity in intermediate-mass nuclei, within a no-core shell-model perspective; up to strongly deformed species of the rare-earth and actinide regions, as investigated in earlier studies. A complementary picture, driven by symmetries dual to Sp(3, R), is also discussed. We briefly review symmetry-guided techniques that prove useful in various nuclear-theory models, such as Elliott model, ab initio SA-NCSM, symplectic model, pseudo-SU(3) and pseudo-symplectic models, ab initio hyperspherical harmonics method, ab initio lattice effective field theory, exact pairing -plusshell model approaches, and cluster models, including the resonating-group method. Important implications of these approaches that have deepened our understanding of emergent phenomena in nuclei, such as enhanced collectivity, giant resonances, pairing, halo, and clustering, are discussed, with a focus on emergent patterns in the framework of the ab initio SA-NCSM with no a priori assumptions.

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“…We will call the variables E α pairons 26 . Equation (9) does not depend on the parameters i , which means that the eigenstates given by Eq.…”

Section: A the Generalized Gaudin Algebramentioning

confidence: 99%

Quantum phase diagram of the integrablepx+ipyfermionic superfluid

2010

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We determine the zero temperature quantum phase diagram of a px + ipy pairing model based on the exactly solvable hyperbolic Richardson-Gaudin model. We present analytical and large-scale numerical results for this model. In the continuum limit, the exact solution exhibits a third-order quantum phase transition, separating a strong-pairing from a weak-pairing phase. The mean field solution allows to connect these results to other models with px + ipy pairing order. We define an experimentally accessible characteristic length scale, associated with the size of the Cooper pairs, that diverges at the transition point, indicating that the phase transition is of a confinementdeconfinement type without local order parameter. We show that this phase transition is not limited to the px + ipy pairing model, but can be found in any representation of the hyperbolic RichardsonGaudin model and is related to a symmetry that is absent in the rational Richardson-Gaudin model.

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Electrostatic Mapping of Nuclear Pairing

Cited by 62 publications

References 10 publications

Exactly-solvable models derived from a generalized Gaudin algebra

Exactly-solvable models derived from a generalized Gaudin algebra

Symmetry-guided large-scale shell-model theory

Quantum phase diagram of the integrablepx+ipyfermionic superfluid

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