# Combining symmetry collective states with coupled cluster theory: Lessons from the Agassi model Hamiltonian

## TL;DR

This paper develops a combined symmetry-projected coupled cluster approach to accurately model strongly correlated systems, demonstrated on the Agassi Hamiltonian with two broken symmetries, improving correlation energy calculations.

## Contribution

It introduces a novel merger of symmetry projection with coupled cluster theory, extending previous simple model work to the complex Agassi Hamiltonian.

## Key findings

- Effective in capturing correlation energies across the phase diagram.
- Successfully models order parameters in strongly correlated regimes.
- Addresses symmetry breaking in coupled cluster methods.

## Abstract

The failures of single-reference coupled cluster for strongly correlated many-body systems is flagged at the mean-field level by the spontaneous breaking of one or more physical symmetries of the Hamiltonian. Restoring the symmetry of the mean-field determinant by projection reveals that coupled cluster fails because it factorizes high-order excitation amplitudes incorrectly. However, symmetry-projected mean-field wave functions do not account sufficiently for dynamic (or weak) correlation. Here we pursue a merger of symmetry projection and coupled cluster theory, following previous work along these lines that utilized the simple Lipkin model system as a testbed [J. Chem. Phys. 146, 054110 (2017)]. We generalize the concept of a symmetry-projected mean-field wave function to the concept of a symmetry projected state, in which the factorization of high-order excitation amplitudes in terms of low-order ones is guided by symmetry projection and is not exponential, and combine them with coupled cluster theory in order to model the ground state of the Agassi Hamiltonian. This model has two separate channels of correlation and two separate physical symmetries which are broken under strong correlation. We show how the combination of symmetry collective states and coupled cluster is effective in obtaining correlation energies and order parameters of the Agassi model throughout its phase diagram.