Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states

Abstract

Many quantal many-body methods that aim at the description of self-bound nuclear or mesoscopic electronic systems make use of auxiliary wave functions that break one or several of the symmetries of the Hamiltonian in order to include correlations associated with the geometrical arrangement of the system's constituents. Such reference states have been used already for a long time within self-consistent methods that are either based on effective valence-space Hamiltonians or energy density functionals, and they are presently also gaining popularity in the design of novel ab-initio methods. A fully quantal treatment of a self-bound many-body system, however, requires the restoration of the broken symmetries through the projection of the many-body wave functions of interest onto good quantum numbers. The goal of this work is three-fold. First, we want to give a general presentation of the formalism of the projection method starting from the underlying principles of group representation theory. Second, we want to investigate formal and practical aspects of the numerical implementation of particle-number and angular-momentum projection of Bogoliubov quasiparticle vacua, in particular with regard of obtaining accurate results at minimal computational cost. Third, we want to analyze the numerical, computational and physical consequences of intrinsic symmetries of the symmetry-breaking states when projecting them.

arXiv comment45 pages, 18 figures

References in corpus (76)

• The In-Medium Similarity Renormalization Group: A Novel Ab Initio Method for Nuclei
• Pairing gaps from nuclear mean-field models
• Microscopic justification of the Equal Filling approximation
• Mean field and beyond description of nuclear structure with the Gogny force: A review
• Global study of quadrupole correlation effects
• Triaxial Angular Momentum Projection and Configuration Mixing calculations with the Gogny force
• Particle number projection with effective forces
• Configuration mixing of angular-momentum and particle-number projected triaxial HFB states using the Skyrme energy density functional
• Variation after Angular Momentum Projection for the Study of Excited States Based on Antisymmetrized Molecular Dynamics
• Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ${}^{48}$Ca
• Shape and pairing fluctuations effects on neutrinoless double beta decay nuclear matrix elements
• Ab-initio Gorkov-Green's function calculations of open-shell nuclei
• Particle-Number Projection and the Density Functional Theory
• Particle-Number Restoration within the Energy Density Functional Formalism
• Configuration Mixing within the Energy Density Functional Formalism: Removing Spurious Contributions from Non-Diagonal Energy Kernels
• The sign of the overlap of HFB wave functions
• Ab Initio Multi-Reference In-Medium Similarity Renormalization Group Calculations of Even Calcium and Nickel Isotopes
• Particle-Number Restoration within the Energy Density Functional formalism: Nonviability of terms depending on noninteger powers of the density matrices
• Configuration mixing of angular momentum projected self-consistent mean-field states for neutron-deficient Pb isotopes
• Further explorations of Skyrme-Hartree-Fock-Bogoliubov mass formulas. III: Role of particle-number projection
• Beyond Mean-Field Calculations for Odd-A Nuclei
• Fixed-N Superconductivity: The Crossover from the Bulk to the Few-Electron Limit
• Beyond the relativistic mean-field approximation (II): configuration mixing of mean-field wave functions projected on angular momentum and particle number
• Symmetry-Projected Hartree-Fock-Bogoliubov Equations
• Configuration mixing of angular-momentum projected triaxial relativistic mean-field wave functions. II. Microscopic analysis of low-lying states in magnesium isotopes
• Ab initio Bogoliubov coupled cluster theory for open-shell nuclei
• Projected Coupled Cluster Theory
• State-of-the-art of beyond mean field theories with nuclear density functionals
• Symmetry broken and restored coupled-cluster theory I. Rotational symmetry and angular momentum
• Symmetry conserving configuration mixing method with cranked states
• Search for the Skyrme-Hartree-Fock Solutions for Chiral Rotation in N=75 Isotones
• Microscopic study of 240Pu, mean-field and beyond
• Collective and Single-particle Motion in Beyond Mean Field Approaches
• Microscopic description of quadrupole-octupole coupling in Sm and Gd isotopes with the Gogny Energy Density Functional
• Remarks on the use of projected densities in the density dependent part of Skyrme or Gogny functionals
• Particle-number projected Bogoliubov coupled cluster theory. Application to the pairing Hamiltonian
• Point symmetries in the Hartree-Fock approach: Densities, shapes and currents
• Beyond-mean-field study of the possible "bubble" structure of 34Si
• The intruder feature of 31Mg and the coexistence of many particle and many hole states
• Pairing-correlations and particle-number projection methods
• Toward global beyond-mean-field calculations of nuclear masses and low-energy spectra
• Angular momentum projection of cranked Hartree-Fock states: Application to terminating bands in A~44 nuclei
• Evaluation of overlaps between arbitrary Fermionic quasiparticle vacua
• Skyrme pseudo-potential-based EDF parametrisation for spuriousity-free MR-EDF calculations
• Isospin-symmetry restoration within the nuclear density functional theory: formalism and applications
• Numerical accuracy of mean-field calculations in coordinate space
• Point symmetries in the Hartree-Fock approach: Symmetry-breaking schemes
• Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part I: Energies, form factors, charge densities and mathematical sum rules
• Variation after full projection with triaxially deformed nuclear mean field
• Beyond mean-field study of elastic and inelastic electron scattering off nuclei
• Variational approximations to exact solutions in shell-model valence spaces: calcium isotopes in the pf-shell
• Symmetry restoration in the mean-field description of proton-neutron pairing
• Approximate particle number projection with density dependent forces: Superdeformed bands in the A=150 and A=190 regions
• A new and practical formulation for overlaps of Bogoliubov vacua
• Quantum number projection at finite temperature via thermofield dynamics
• Angular-momentum projection of cranked symmetry-unrestricted Slater determinants
• Symmetry-projected variational calculations with the numerical suite TAURUS I. Variation after particle-number projection
• Correlation energies by the generator coordinate method: computational aspects for quadrupolar deformations
• Projection of angular momentum via linear algebra
• Simple regularization scheme for multi-reference density functional theories
• On the norm overlap between many-body states. I. Uncorrelated overlap between arbitrary Bogoliubov product states
• Zero-pairing limit of Hartree-Fock-Bogoliubov reference states
• Lipkin method of particle-number restoration to higher orders
• Spherical Hartree-Fock calculations with linear momentum projection before the variation.Part II: Spectral functions and spectroscopic factors
• The union of rotational and vibrational modes in generator-coordinate-type calculations, with application to neutrinoless double-beta decay
• Why does the sign problem occur in evaluating the overlap of HFB wave functions?
• On the formulation of functional theory for pairing with particle number restoration
• Convergence and efficiency of angular momentum projection for many-body systems
• Beyond mean-field calculation for pairing correlation
• Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian
• Angular momentum projected multi-cranked configuration mixing for reliable calculation of high-spin rotational bands
• Density-matrix functionals for pairing in mesoscopic superconductors
• Particle-Number Projected Hartree-Fock-Bogoliubov Study with Effective Shell Model Interactions
• A variational approach to approximate particle number projection with effective forces
• Zero-pairing and zero-temperature limits of finite temperature Hartree-Fock-Bogoliubov theory
• Importance of multicranked configuration mixing for angular-momentum-projection calculations: Study of superdeformed rotational bands in ${}^{152}$Dy and ${}^{194}$Hg

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