# Coupled Cluster as an impurity solver for Green's function embedding methods

## TL;DR

This paper evaluates a Green's function coupled cluster (CCSD) method as an impurity solver in embedding techniques, demonstrating its efficiency and accuracy across different correlated regimes and models.

## Contribution

It introduces a frequency-independent CCSD Green's function solver using a non-hermitian Lanczos algorithm for embedding methods.

## Key findings

- Excellent agreement with FCI in 1D Hubbard model across all interactions.
- Some discrepancies observed in 2D Hubbard model in strongly correlated regime.
- Performance analysis of CCSD solver within SEET on ammonia cluster.

## Abstract

We investigate the performance of Green's function coupled cluster singles and doubles (CCSD) method as a solver for Green's function embedding methods. To develop an efficient CC solver, we construct the one-particle Green's function from the coupled cluster (CC) wave function based on a non-hermitian Lanczos algorithm. The major advantage of this method is that its scaling does not depend on the number of frequency points. We have tested the applicability of the CC Green's function solver in the weakly to strongly correlated regimes by employing it for a half-filled 1D Hubbard model projected onto a single site impurity problem and a half-filled 2D Hubbard model projected onto a 4-site impurity problem. For the 1D Hubbard model, for all interaction strengths, we observe an excellent agreement with the full configuration interaction (FCI) technique, both for the self-energy and spectral function. For the 2D Hubbard, we have employed an open-shell version of the current implementation and observed some discrepancies from FCI in the strongly correlated regime. Finally, on an example of a small ammonia cluster, we analyze the performance of the Green's function CCSD solver within the self-energy embedding theory (SEET) with Hartee-Fock (HF) and Green's function second order (GF2) for the treatment of the environment.