Exploring the exact limits of the real-time equation-of-motion coupled cluster cumulant Green's functions

TL;DR

This paper investigates the limits of the real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function method, proposes an improved ansatz for exactness, and introduces a cluster-analysis technique for spectral peak characterization, validated on impurity models.

Contribution

It introduces an enhanced double TDCC ansatz for exact expansion and a cluster-analysis method for spectral peak assignment in RT-EOM-CC Green's functions.

Findings

The enhanced ansatz achieves exactness in the expansion limit.

The cluster-analysis method effectively characterizes spectral peaks.

Numerical tests compare RT-EOM-CC with exact solutions on impurity models.

Abstract

In this paper, we analyze the properties of the recently proposed real-time equation-of-motion coupled-cluster (RT-EOM-CC) cumulant Green's function approach [J. Chem. Phys. 2020, 152, 174113]. We specifically focus on identifying the limitations of the original time-dependent coupled cluster (TDCC) ansatz and propose an enhanced double TDCC ansatz ensuring the exactness in the expansion limit. Additionally, we introduce a practical cluster-analysis-based approach for characterizing the peaks in the computed spectral function from the RT-EOM-CC cumulant Green's function approach, which is particularly useful for the assignments of satellite peaks when many-body effects dominate the spectra. Our preliminary numerical tests focus on reproducing, approximating, and characterizing the exact impurity Green's function of the three-site and four-site single impurity Anderson models using the RT-EOM-CC cumulant Green's function approach. The numerical tests allow us to have a direct comparison between the RT-EOM-CC cumulant Green's function approach and other Green's function approaches in the numerical exact limit.