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 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.
Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.
Jacob M
0000000223798962
JM
Wahlen-Strothman
Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.
Thomas M
0000000243584312
TM
Henderson
Department of Chemistry, Rice University, Houston, Texas 77005, USA.
Matthew R
0000000178072950
MR
Hermes
Department of Chemistry, Rice University, Houston, Texas 77005, USA.
Matthias
M
Degroote
Department of Chemistry, Rice University, Houston, Texas 77005, USA.
Yiheng
0000000213486041
Y
Qiu
Department of Chemistry, Rice University, Houston, Texas 77005, USA.
Jinmo
J
Zhao
Instituto de Estructura de la Materia, CSIC, Serrano 123, E-28006 Madrid, Spain.
Jorge
0000000277155487
J
Dukelsky
Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA.
Gustavo E
GE
Scuseria