Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
Abstract
Coupled cluster and symmetry projected HartreeFock 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 brokensymmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the meanfield level through multireference nonorthogonal 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 nontrivial 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 andmore »
 Authors:
 Rice Univ., Houston, TX (United States)
 Consejo Superior de Investigaciones Cientificas (CSIC), Madrid (Spain). Inst. de Estructura de la Materia
 Publication Date:
 Research Org.:
 Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
 Sponsoring Org.:
 USDOE
 OSTI Identifier:
 1416505
 Report Number(s):
 LLNLSR744060
 DOE Contract Number:
 AC5207NA27344
 Resource Type:
 Technical Report
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 74 ATOMIC AND MOLECULAR PHYSICS
Citation Formats
WahlenStrothman, J. M., Henderson, T. H., Hermes, M. R., Degroote, M., Qiu, Y., Zhao, J., Dukelsky, J., and Scuseria, G. E. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. United States: N. p., 2018.
Web. doi:10.2172/1416505.
WahlenStrothman, J. M., Henderson, T. H., Hermes, M. R., Degroote, M., Qiu, Y., Zhao, J., Dukelsky, J., & Scuseria, G. E. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. United States. doi:10.2172/1416505.
WahlenStrothman, J. M., Henderson, T. H., Hermes, M. R., Degroote, M., Qiu, Y., Zhao, J., Dukelsky, J., and Scuseria, G. E. 2018.
"Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian". United States.
doi:10.2172/1416505. https://www.osti.gov/servlets/purl/1416505.
@article{osti_1416505,
title = {Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian},
author = {WahlenStrothman, J. M. and Henderson, T. H. and Hermes, M. R. and Degroote, M. and Qiu, Y. and Zhao, J. and Dukelsky, J. and Scuseria, G. E.},
abstractNote = {Coupled cluster and symmetry projected HartreeFock 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 brokensymmetry wave functions, which is unphysical for finite systems. Symmetry projection is effective for the treatment of strong correlation at the meanfield level through multireference nonorthogonal 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 nontrivial 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.},
doi = {10.2172/1416505},
journal = {},
number = ,
volume = ,
place = {United States},
year = 2018,
month = 1
}

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