Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian
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. In conclusion, 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 themore »
 Authors:

^{[1]}
;
^{[1]}
;
^{[1]}
;
^{[1]};
^{[1]}
;
^{[1]};
^{[2]}
;
^{[1]}
 Rice Univ., Houston, TX (United States)
 CSIC, Madrid (Spain)
 Publication Date:
 Grant/Contract Number:
 FG0209ER16053; SC0001474
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Chemical Physics
 Additional Journal Information:
 Journal Volume: 146; Journal Issue: 5; Journal ID: ISSN 00219606
 Publisher:
 American Institute of Physics (AIP)
 Research Org:
 Rice Univ., Houston, TX (United States)
 Sponsoring Org:
 USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC22)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 74 ATOMIC AND MOLECULAR PHYSICS
 OSTI Identifier:
 1474111
 Alternate Identifier(s):
 OSTI ID: 1361758
WahlenStrothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, and Scuseria, Gustavo E.. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. United States: N. p.,
Web. doi:10.1063/1.4974989.
WahlenStrothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, & Scuseria, Gustavo E.. Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian. United States. doi:10.1063/1.4974989.
WahlenStrothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, and Scuseria, Gustavo E.. 2017.
"Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian". United States.
doi:10.1063/1.4974989. https://www.osti.gov/servlets/purl/1474111.
@article{osti_1474111,
title = {Merging symmetry projection methods with coupled cluster theory: Lessons from the Lipkin model Hamiltonian},
author = {WahlenStrothman, Jacob M. and Henderson, Thomas M. and Hermes, Matthew R. and Degroote, Matthias and Qiu, Yiheng and Zhao, Jinmo and Dukelsky, Jorge and Scuseria, Gustavo 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. In conclusion, 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 = {10.1063/1.4974989},
journal = {Journal of Chemical Physics},
number = 5,
volume = 146,
place = {United States},
year = {2017},
month = {2}
}