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

Background: 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 arrangeme...

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Autores: Bally, Benajamin, Bender, Michael
Tipo de recurso: artículo
Fecha de publicación:2021
País:España
Institución:Universidad Autónoma de Madrid
Repositorio:Biblos-e Archivo. Repositorio Institucional de la UAM
Idioma:inglés
OAI Identifier:oai:repositorio.uam.es:10486/705251
Acceso en línea:http://hdl.handle.net/10486/705251
https://dx.doi.org/10.1103/PhysRevC.103.024315
Access Level:acceso abierto
Palabra clave:Bogoliubov Theory
Nuclear Properties
Isotopes
Física
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dc.title.none.fl_str_mv Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
title Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
spellingShingle Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
Bally, Benajamin
Bogoliubov Theory
Nuclear Properties
Isotopes
Física
title_short Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
title_full Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
title_fullStr Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
title_full_unstemmed Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
title_sort Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle states
dc.creator.none.fl_str_mv Bally, Benajamin
Bender, Michael
author Bally, Benajamin
author_facet Bally, Benajamin
Bender, Michael
author_role author
author2 Bender, Michael
author2_role author
dc.contributor.none.fl_str_mv Departamento de Física Teórica
Facultad de Ciencias
dc.subject.none.fl_str_mv Bogoliubov Theory
Nuclear Properties
Isotopes
Física
topic Bogoliubov Theory
Nuclear Properties
Isotopes
Física
description Background: 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. Purpose: The goal of this work is threefold. 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. Methods: Using the algebra of group representation theory, we introduce the projection method for the general symmetry group of a given Hamiltonian. For realistic examples built with either a pseudopotential-based energy density functional or a valence-space shell-model interaction, we then study the convergence and accuracy of the quadrature rules for the multidimensional integrals that have to be evaluated numerically and analyze the consequences of conserved subgroups of the broken symmetry groups. Results: The main results of this work are also threefold. First, we give a concise, but general, presentation of the projection method that applies to the most important potentially broken symmetries whose restoration is relevant for nuclear spectroscopy. Second, we demonstrate how to achieve high accuracy of the discretizations used to evaluate the multidimensional integrals appearing in the calculation of particle-number and angular-momentum projected matrix elements while limiting the order of the employed quadrature rules. Third, for the example of a point-group symmetry that is often imposed on calculations that describe collective phenomena emerging in triaxially deformed nuclei, we provide the group-theoretical derivation of relations between the intermediate matrix elements that are integrated, which permits a further significant reduction of the computational cost of the method. These simplifications are valid regardless of the number parity of the quasiparticle states and therefore can be used in the description of even-even, odd-mass, and odd-odd nuclei. Conclusions: The quantum-number projection technique is a versatile and efficient method that permits to restore the symmetry of any arbitrary many-body wave function. Its numerical implementation is relatively simple and accurate. In addition, it is possible to use the conserved symmetries of the reference states to reduce the computational burden of the method. More generally, the ever-growing computational resources and the development of nuclear ab-initio methods opens new possibilities of applications of the method
publishDate 2021
dc.date.none.fl_str_mv 2021
2021-02-15
dc.type.none.fl_str_mv research article
http://purl.org/coar/resource_type/c_2df8fbb1
VoR
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dc.type.openaire.fl_str_mv info:eu-repo/semantics/article
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dc.identifier.none.fl_str_mv http://hdl.handle.net/10486/705251
https://dx.doi.org/10.1103/PhysRevC.103.024315
url http://hdl.handle.net/10486/705251
https://dx.doi.org/10.1103/PhysRevC.103.024315
dc.language.none.fl_str_mv Inglés
eng
language_invalid_str_mv Inglés
language eng
dc.relation.none.fl_str_mv European Commission http://dx.doi.org/10.13039/501100000780 Horizon 2020 Framework Programme 839847
dc.rights.none.fl_str_mv open access
http://purl.org/coar/access_right/c_abf2
dc.rights.openaire.fl_str_mv info:eu-repo/semantics/openAccess
rights_invalid_str_mv open access
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eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:Biblos-e Archivo. Repositorio Institucional de la UAM
instname:Universidad Autónoma de Madrid
instname_str Universidad Autónoma de Madrid
reponame_str Biblos-e Archivo. Repositorio Institucional de la UAM
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spelling Projection on particle number and angular momentum: Example of triaxial Bogoliubov quasiparticle statesBally, BenajaminBender, MichaelBogoliubov TheoryNuclear PropertiesIsotopesFísicaBackground: 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. Purpose: The goal of this work is threefold. 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. Methods: Using the algebra of group representation theory, we introduce the projection method for the general symmetry group of a given Hamiltonian. For realistic examples built with either a pseudopotential-based energy density functional or a valence-space shell-model interaction, we then study the convergence and accuracy of the quadrature rules for the multidimensional integrals that have to be evaluated numerically and analyze the consequences of conserved subgroups of the broken symmetry groups. Results: The main results of this work are also threefold. First, we give a concise, but general, presentation of the projection method that applies to the most important potentially broken symmetries whose restoration is relevant for nuclear spectroscopy. Second, we demonstrate how to achieve high accuracy of the discretizations used to evaluate the multidimensional integrals appearing in the calculation of particle-number and angular-momentum projected matrix elements while limiting the order of the employed quadrature rules. Third, for the example of a point-group symmetry that is often imposed on calculations that describe collective phenomena emerging in triaxially deformed nuclei, we provide the group-theoretical derivation of relations between the intermediate matrix elements that are integrated, which permits a further significant reduction of the computational cost of the method. These simplifications are valid regardless of the number parity of the quasiparticle states and therefore can be used in the description of even-even, odd-mass, and odd-odd nuclei. Conclusions: The quantum-number projection technique is a versatile and efficient method that permits to restore the symmetry of any arbitrary many-body wave function. Its numerical implementation is relatively simple and accurate. In addition, it is possible to use the conserved symmetries of the reference states to reduce the computational burden of the method. More generally, the ever-growing computational resources and the development of nuclear ab-initio methods opens new possibilities of applications of the methodAmerican Physical SocietyDepartamento de Física TeóricaFacultad de Ciencias20212021-02-15research articlehttp://purl.org/coar/resource_type/c_2df8fbb1VoRhttp://purl.org/coar/version/c_970fb48d4fbd8a85info:eu-repo/semantics/articleapplication/pdfhttp://hdl.handle.net/10486/705251https://dx.doi.org/10.1103/PhysRevC.103.024315reponame:Biblos-e Archivo. Repositorio Institucional de la UAMinstname:Universidad Autónoma de MadridInglésengEuropean Commission http://dx.doi.org/10.13039/501100000780 Horizon 2020 Framework Programme 839847open accesshttp://purl.org/coar/access_right/c_abf2info:eu-repo/semantics/openAccessoai:repositorio.uam.es:10486/7052512026-06-23T12:46:27Z
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