# Projected Coupled Cluster Theory

## TL;DR

This paper introduces projected coupled cluster theory, combining symmetry projection with coupled cluster methods to better handle strong correlations, demonstrated on molecules and the Hubbard model.

## Contribution

It develops a disentanglement framework for applying symmetry projection to coupled cluster wavefunctions, improving accuracy in strongly correlated systems.

## Key findings

- Spin projection enhances unrestricted coupled cluster accuracy.
- Projected coupled cluster restores quantum numbers effectively.
- Energy convergence is slower than projected Hartree-Fock in the thermodynamic limit.

## Abstract

Coupled cluster theory is the method of choice for weakly correlated systems. But in the strongly correlated regime, it faces a symmetry dilemma, where it either completely fails to describe the system, or has to artificially break certain symmetries. On the other hand, projected Hartree-Fock theory captures the essential physics of many kinds of strong correlations via symmetry breaking and restoration. In this work, we combine and try to retain the merits of these two methods by applying symmetry projection to broken symmetry coupled cluster wavefunctions. The non-orthogonal nature of states resulting from the application of symmetry projection operators furnishes particle-hole excitations to all orders, thus creating an obstacle for the exact evaluation of overlaps. Here we provide a solution via a disentanglement framework theory that can be approximated rigorously and systematically. Results of projected coupled cluster theory are presented for molecules and the Hubbard model, showing that spin projection significantly improves unrestricted coupled cluster theory while restoring good quantum numbers. The energy of projected coupled cluster theory reduces to the unprojected one in the thermodynamic limit, albeit at a much slower rate than projected Hartree-Fock.