# Projected Hartree-Fock as a Polynomial of Particle-Hole Excitations and Its Combination With Variational Coupled Cluster Theory

## TL;DR

This paper develops a novel approach combining projected Hartree-Fock and coupled cluster theories to accurately describe both strong and weak electron correlations, demonstrated on the Hubbard model and small molecules.

## Contribution

It introduces a variational formulation that unifies projected Hartree-Fock with coupled cluster theory, extending previous work to improve correlation descriptions.

## Key findings

- Effective description of strong and weak correlations
- Successful application to Hubbard Hamiltonian and small molecules
- Enhanced accuracy over individual methods

## Abstract

Projected Hartree-Fock theory provides an accurate description of many kinds of strong correlation but does not properly describe weakly correlated systems. Coupled cluster theory, in contrast, does the opposite. It therefore seems natural to combine the two so as to describe both strong and weak correlations with high accuracy in a relatively black-box manner. Combining the two approaches, however, is made more difficult by the fact that the two techniques are formulated very differently. In earlier work, we showed how to write spin-projected Hartree-Fock in a coupled-cluster-like language. Here, we fill in the gaps in that earlier work. Further, we combine projected Hartree-Fock and coupled cluster theory in a variational formulation and show how the combination performs for the description of the Hubbard Hamiltonian and for several small molecular systems.