Testing the Green's function coupled cluster singles and doubles impurity solver on real materials within the framework of self-energy embedding theory

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 $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$. GFCCSD provides satisfactory descriptions for weakly and moderately correlated impurities with sizes that are intractable by existing accurate impurity solvers such as exact diagonalization. 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 appear 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 ab initio calculations in the absence of experiments, a verification from a GFCC solver with higher order excitations is necessary.

Figure 1

Workflows of SEET with and without the outer-loop self-consistency. The details of the inner loop are shown in Fig. 2. ${\mathcal{F}}_{\text{Dyson}}$ represents the Dyson equation solver which is a functional of self-energy $\mathrm{\Sigma }$ and ${\mathcal{F}}_{GW}$ is the $GW$ solver which is a functional of Green's function $G$. Details of ${\mathcal{F}}_{\text{Dyson}}$ and ${\mathcal{F}}_{GW}$ can be found in Ref. [5].

Figure 2

Schematic view of the inner loop and GFCCSD solver. Particle sector search and GFCCSD construction sections pertain to the solver, and the rest of the steps are general to the SEET scheme.

Figure 3

Impurity self-energy $\mathrm{\Sigma }$ comparison between ED and GFCCSD on imaginary frequency axis for the MnO crystal. $GW$ label is used to denote the double counting contribution coming from performing one iteration of $GW$ in the impurity orbital subset.

Figure 4

Orbital-resolved local DOS for the MnO crystal from $\mathrm{SEET}(GW$/CCSD) and $\mathrm{SEET}(GW$/ED). The impurity choices from the first to second row correspond to A and B in Table 1. Solid lines in both right and left panels are from $\mathrm{SEET}(GW$/CCSD) and $\mathrm{SEET}(GW$/ED) data, respectively. Dashed lines are photoemission data from Ref. [42]. The dotted lines correspond to the orbitally resolved $\mathrm{sc}GW$ calculation.

Figure 5

Orbital-resolved local DOS of MnO from $\mathrm{SEET}(GW$/CCSD) for impurity setup C (see Table 1). Solid lines are from $\mathrm{SEET}(GW$/CCSD) data, dashed lines are photoemission data from Ref. [42], and the dotted lines correspond to the orbitally resolved $\mathrm{sc}GW$ calculation.

Figure 6

Impurity self-energy $\mathrm{\Sigma }$ comparison between ED and GFCCSD solvers on the imaginary frequency axis for the $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$ crystal. $GW$ label is used to denote the double counting contribution coming from performing one iteration of $GW$ in the impurity orbital subset.

Figure 7

Orbital-resolved local DOS for the $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$ crystal from $\mathrm{SEET}(GW$/CCSD) and $\mathrm{SEET}(GW$/ED). The impurity choices from the first to third row correspond to A, B, and C in Table 2. Dashed line are photoemission data from Ref. [51]. The dotted lines correspond to the orbitally resolved $\mathrm{sc}GW$ calculation.

Figure 8

Orbital-resolved local DOS of $\mathrm{Sr}\mathrm{Mn}{\mathrm{O}}_3$ from $\mathrm{SEET}(GW$/CCSD) for impurity setup D (see Table 2). Dashed lines are photoemission data from Ref. [51]. The dotted lines correspond to the orbitally resolved $\mathrm{sc}GW$ calculation.