Convergence and efficiency of angular momentum projection for many-body systems

Abstract

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 $z$-axis 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.

15 pages, 4 figures; conforms to published version

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Cited by in corpus (11)

• Symmetry restoration in mean-field approaches
• Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
• Beyond-mean-field approaches for nuclear neutrinoless double beta decay in the standard mechanism
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Nuclear states projected from a pair condensate
• Nucleon-pair coupling scheme in Elliott's SU(3) model
• Benchmarking projected Hartree-Fock as an approximation
• Nucleon-pair truncation of the shell model for medium-heavy nuclei
• A Pfaffian formulation for matrix elements of three-body operators in multiple quasi-particle configurations
• Exact sum rules with approximate ground states
• The pervasiveness of shape coexistence in nuclear pair condensates