Testing the GFCCSD impurity solver on real materials within the self-energy embedding theory framework

TL;DR

This paper applies the GFCCSD impurity solver within the SEET framework to realistic strongly correlated materials, demonstrating its effectiveness for weakly to moderately correlated impurities and identifying limitations for strongly correlated cases.

Contribution

The study implements and evaluates GFCCSD as an impurity solver in SEET for real materials, highlighting its advantages and limitations compared to existing methods.

Findings

GFCCSD performs well for weakly and moderately correlated impurities.

Instabilities occur in GFCCSD for strongly correlated, larger impurities with degenerate orbitals.

Higher-order excitation methods are needed for reliable results in strongly correlated regimes.

Abstract

We apply the Green's function coupled cluster singles and doubles (GFCCSD) impurity solver to realistic impurity problems arising for strongly correlated solids within the self-energy embedding theory (SEET) framework. We describe the details of our GFCC solver implementation, investigate its performance, and highlight potential advantages and problems on examples of impurities created during the self-consistent SEET for antiferromagnetic MnO and paramagnetic SrMnO$_{3}$. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization (ED). However, our data also shows that when correlations become strong, the singles and doubles approximation used in GFCC could lead to instabilities in searching for the particle number present in impurity problems. These instabilities appears especially severe when the impurity size gets larger and multiple degenerate orbitals with strong correlations are present. We conclude that to fully check the reliability of GFCCSD results and use them in fully {\em ab initio} calculations in the absence of experiments, a verification from a GFCC solver with higher order excitations is necessary.