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

Abstract

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. 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 » weakly and strongly correlated limits, as well as the recoupling regime.« less

Authors:
ORCiD logo [1]; ORCiD logo [1]; ORCiD logo [1];  [1]; ORCiD logo [1];  [1]; ORCiD logo [2];  [1]
  1. Rice Univ., Houston, TX (United States)
  2. CSIC, Madrid (Spain)
Publication Date:
Research Org.:
Rice Univ., Houston, TX (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)
OSTI Identifier:
1474111
Alternate Identifier(s):
OSTI ID: 1361758
Grant/Contract Number:  
FG02-09ER16053; SC0001474
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 146; Journal Issue: 5; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Wahlen-Strothman, 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., 2017. Web. doi:10.1063/1.4974989.
Wahlen-Strothman, 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.
Wahlen-Strothman, Jacob M., Henderson, Thomas M., Hermes, Matthew R., Degroote, Matthias, Qiu, Yiheng, Zhao, Jinmo, Dukelsky, Jorge, and Scuseria, Gustavo E. Tue . "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 = {Wahlen-Strothman, 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 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. 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 = {Tue Feb 07 00:00:00 EST 2017},
month = {Tue Feb 07 00:00:00 EST 2017}
}

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