Projection of angular momentum via linear algebra

Johnson, Calvin W.; O'Mara, Kevin D.

doi:10.1103/physrevc.96.064304

Cited by 29 publications

(33 citation statements)

References 27 publications

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“…In these calculations, the norm kernel, which is just the matrix element of the rotation operator Ψ|R(Ω)|Ψ , is significantly cheaper to compute than the Hamiltonian kernel Ψ|ĤR(Ω)|Ψ , especially as the model space increases in size [29]. There is however another way to project [29]. Before the integrals over the Euler angles in Eq.…”

Section: Two Methods For Angular Momentum Projectionmentioning

confidence: 99%

Convergence and efficiency of angular momentum projection

Johnson

Jiao

2018

J. Phys. G: Nucl. Part. Phys.

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In many so-called "beyond-mean-field" many-body methods, one creates symmetry-breaking states and then projects out states with good quantum number(s); the most important example is angular momentum. Motivated by the computational intensity of symmetry restoration, we investigate the numerical convergence of two competing methods for angular momentum projection with rotations over Euler angles, the textbook-standard projection through quadrature, and a recently introduced projection through linear algebra. We find well-defined patterns of convergence with increasing number of mesh points (for quadrature) and cut-offs (for linear algebra). Because the method of projection through linear algebra requires inverting matrices generated on a mesh of Euler angles, we discuss two methods for robustly reducing the number of required evaluations. Reviewing the literature, we find our inversion involving rotations about the zaxis is equivalent to trapezoidal 'quadrature' commonly used as well as Fomenko projection used for particle-number projection. The efficiency depends upon the number of angular momentum J to be projected, but in general inversion methods, including Fomenko projection/trapezoidal 'quadrature' dramatically improve the efficiency.

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Section: Two Methods For Angular Momentum Projectionmentioning

confidence: 99%

Convergence and efficiency of angular momentum projection

Johnson

Jiao

2018

J. Phys. G: Nucl. Part. Phys.

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“…In this work we allow for triaxial deformations. While there is extensive literature on the standard quadrature approach for angular momentum projection [2,[40][41][42], we adopt the recently developed "linear algebraic projection"(LAP) technique [35,36]. Although both approaches are based on standard quantum theory of angular momentum [43], i.e.…”

Section: A Angular Momentum Projectionmentioning

confidence: 99%

“…In any finite space the sums are not infinite but restricted to a maximum I, K, and in practice the coefficients c IK restricts the sum even further [35]. The projection operator P J M K picks out the (J, K) spherical tensor component and rotates it to a (J, M ) spherical tensor,…”

Section: A Angular Momentum Projectionmentioning

confidence: 99%

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Nuclear states projected from a pair condensate

Lu,

Lei,

Johnson

et al. 2021

Preprint

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Atomic nuclei exhibit deformation, pairing correlations, and rotational symmetries. To meet these competing demands in a computationally tractable formalism, we revisit the use of general pair condensates with good particle number as a trial wave function for even-even nuclei. After minimizing the energy of the condensate, we project out states with good angular momentum with a fast projection technique, allowing for general triaxial deformations. To show applicability, we present example calculations from pair condensates in several model spaces, and compare against projected Hartree-Fock and full configuration-interaction shell model calculations. This approach successfully generates spherical, vibrational and rotational spectra, demonstrating potential for modeling medium-to heavy-mass nuclei.

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“…We emphasize this difference is largely because our CHFB-GCM code has been highly optimized for nuclides with axially symmetric minima. We have investigated efficient projection methods [47,48] but have yet to implement them in projected HFB. Figure 1 shows the low-lying level spectra of 124 Sn, 124 Te, 130 Te, 130 Xe, 136 Xe, and 136 Ba, compared to the CHFB-GCM calculation [35], as well as the SM calculations [44,45].…”

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confidence: 99%

Union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double- β decay

Jiao

Johnson

2019

Phys. Rev. C

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Good many-body methods for medium and heavy nuclei are important. Here we combine rotational motion with vibrational modes in a novel generator-coordinate method (GCM): starting from a mean-field solution (Hartree-Fock-Bogoliubov), we create non-orthogonal reference states from low-lying quasiparticle Tamm-Dancoff modes, and then project onto states of good angular momentum and particle number. The results we benchmark against full shell model calculations. Even with just a few such modes we find improvement over standard GCM calculations in excitation spectra. We also find significant improvement in 0νββ nuclear matrix elements.

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Projection of angular momentum via linear algebra

Cited by 29 publications

References 27 publications

Convergence and efficiency of angular momentum projection

Convergence and efficiency of angular momentum projection

Nuclear states projected from a pair condensate

Union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double- β decay

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