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

Wahlen-Strothman, Jacob M.; Henderson, Thomas M.; Hermes, Matthew R.; Degroote, Matthias; Qiu, Yiheng; Zhao, Jinmo; Dukelsky, Jorge; Scuseria, Gustavo E.

doi:10.1063/1.4974989

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

Journal Article · Tue Feb 07 00:00:00 EST 2017 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.4974989· OSTI ID:1474111

^[1]; ^[2]; ^[2]; Degroote, Matthias ^[2]; ^[2]; Zhao, Jinmo ^[2]; ^[3]; Scuseria, Gustavo E. ^[2]

Rice Univ., Houston, TX (United States); Department of Physics and Astronomy, Rice University, Houston, Texas 77005
Rice Univ., Houston, TX (United States)
CSIC, Madrid (Spain)

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.

View Accepted Manuscript (DOE)

Research Organization:: Rice Univ., Houston, TX (United States)

Sponsoring Organization:: USDOE; USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: SC0001474

OSTI ID:: 1474111

Alternate ID(s):: OSTI ID: 1361758

Journal Information:: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 5 Vol. 146; ISSN 0021-9606

Publisher:: American Institute of Physics (AIP)Copyright Statement

Country of Publication:: United States

Language:: English

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On the difference between variational and unitary coupled cluster theories Harsha, Gaurav; Shiozaki, Toru; Scuseria, Gustavo E. The Journal of Chemical Physics, Vol. 148, Issue 4 https://doi.org/10.1063/1.5011033	journal	January 2018
Orbital-invariant spin-extended approximate coupled-cluster for multi-reference systems Tsuchimochi, Takashi; Ten-no, Seiichiro L. The Journal of Chemical Physics, Vol. 149, Issue 4 https://doi.org/10.1063/1.5036542	journal	July 2018
Projected coupled cluster theory: Optimization of cluster amplitudes in the presence of symmetry projection Qiu, Yiheng; Henderson, Thomas M.; Zhao, Jinmo The Journal of Chemical Physics, Vol. 149, Issue 16 https://doi.org/10.1063/1.5053605	journal	October 2018
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