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

TL;DR

This paper explores combining symmetry projection methods with coupled cluster theory using the Lipkin model to address their individual limitations in treating strong and weak correlations, aiming to develop a more universally accurate approach.

Contribution

It demonstrates how merging symmetry projection with coupled cluster doubles improves accuracy across different correlation regimes in the Lipkin model.

Findings

Symmetry projection and coupled cluster doubles fail individually in certain correlation regimes.

Merging these methods yields high accuracy across the entire phase diagram.

Lessons from the Lipkin model guide future development of ab initio symmetry projected coupled cluster theory.

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 over 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 over the weakly and strongly correlated limits, as well as the recoupling regime.