Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian

Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good q...

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Autores: Wahlen-Strothman, J. M., Henderson, T. M., Hermes, M. R., Degroote, M., Qiu, Y., Zhao, J., Dukelsky, Jorge, Scuseria, G. E.
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2017
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/161645
Acesso em linha:http://hdl.handle.net/10261/161645
Access Level:acceso abierto
Palavra-chave:Mean field theory
Coupled cluster
Wave functions
Parity
Excited states
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spelling Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model HamiltonianWahlen-Strothman, J. M.Henderson, T. M.Hermes, M. R.Degroote, M.Qiu, Y.Zhao, J.Dukelsky, JorgeScuseria, G. E.Mean field theoryCoupled clusterWave functionsParityExcited statesCoupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.This work was supported by the U.S. Department of Energy, Office of Basic Energy Sciences, Computational and Theoretical Chemistry Program under Award No. DE-FG02- 09ER16053. G.E.S. is a Welch Foundation Chair (No. C- 0036). Computational resources for this work were supported in part by the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award funded by NSF under Grant No. CNS- 1338099 and by Rice University. J.D. acknowledges support from the Spanish Ministry of Economy and Competitiveness and FEDER through Grant No. FIS2015-63770-P.Peer Reviewed10 pags., 6 figs., app.American Institute of PhysicsWelch FoundationNational Science Foundation (US)Rice UniversityMinisterio de Economía y Competitividad (España)Department of Energy (US)Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2018201820172018info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionhttp://hdl.handle.net/10261/161645reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/FIS2015-63770-Phttps://doi.org/10.1063/1.4974989Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/1616452026-05-22T06:33:51Z
dc.title.none.fl_str_mv Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
title Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
spellingShingle Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
Wahlen-Strothman, J. M.
Mean field theory
Coupled cluster
Wave functions
Parity
Excited states
title_short Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
title_full Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
title_fullStr Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
title_full_unstemmed Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
title_sort Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
dc.creator.none.fl_str_mv Wahlen-Strothman, J. M.
Henderson, T. M.
Hermes, M. R.
Degroote, M.
Qiu, Y.
Zhao, J.
Dukelsky, Jorge
Scuseria, G. E.
author Wahlen-Strothman, J. M.
author_facet Wahlen-Strothman, J. M.
Henderson, T. M.
Hermes, M. R.
Degroote, M.
Qiu, Y.
Zhao, J.
Dukelsky, Jorge
Scuseria, G. E.
author_role author
author2 Henderson, T. M.
Hermes, M. R.
Degroote, M.
Qiu, Y.
Zhao, J.
Dukelsky, Jorge
Scuseria, G. E.
author2_role author
author
author
author
author
author
author
dc.contributor.none.fl_str_mv Welch Foundation
National Science Foundation (US)
Rice University
Ministerio de Economía y Competitividad (España)
Department of Energy (US)
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Mean field theory
Coupled cluster
Wave functions
Parity
Excited states
topic Mean field theory
Coupled cluster
Wave functions
Parity
Excited states
description Coupled cluster and symmetry projected Hartree-Fock are two central paradigms in electronic structure theory. However, they are very different. Single reference coupled cluster is highly successful for treating weakly correlated systems but fails under strong correlation unless one sacrifices good quantum numbers and works with broken-symmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the mean-field level through multireference non-orthogonal configuration interaction wavefunctions, but unlike coupled cluster, it is neither size extensive nor ideal for treating dynamic correlation. We here examine different scenarios for merging these two dissimilar theories. We carry out this exercise over the integrable Lipkin model Hamiltonian, which despite its simplicity, encompasses non-trivial physics for degenerate systems and can be solved via diagonalization for a very large number of particles. We show how symmetry projection and coupled cluster doubles individually fail in different correlation limits, whereas models that merge these two theories are highly successful over the entire phase diagram. Despite the simplicity of the Lipkin Hamiltonian, the lessons learned in this work will be useful for building an ab initio symmetry projected coupled cluster theory that we expect to be accurate in the weakly and strongly correlated limits, as well as the recoupling regime.
publishDate 2017
dc.date.none.fl_str_mv 2017
2018
2018
2018
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/161645
url http://hdl.handle.net/10261/161645
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/MINECO/Plan Estatal de Investigación Científica y Técnica y de Innovación 2013-2016/FIS2015-63770-P
https://doi.org/10.1063/1.4974989
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv American Institute of Physics
publisher.none.fl_str_mv American Institute of Physics
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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score 15.81155

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