Electronic structure of SrVO${}_3$ within $GW$+DMFT

We present a detailed calculation of the electronic structure of SrVO${}_3$ based on the $GW$+DMFT method. We show that a proper inclusion of the frequency-dependent Hubbard $U$ and the nonlocal self-energy via the $GW$ approximation, as well as a careful treatment of the Fermi level, are crucial for obtaining an accurate and coherent picture of the quasiparticle band structure and satellite features of SrVO${}_3$. The $GW$+DMFT results for SrVO${}_3$ are not attainable within the $GW$ approximation or the LDA+DMFT scheme. We also compare the results of $GW$+DMFT to DMFT calculations based on the $GW$ quasiparticle bands.

Figure 1

Upper panel: the quasiparticle band structure of SrVO${}_3$ within LDA, $GW$, LDA+DMFT, and $GW$+DMFT. Lower panel: To emphasize the kink structure near $\Gamma$, the $GW$+DMFT band is plotted against a renormalized $GW$ band.

Figure 2

$GW$ and $GW$+DMFT self-energies at the $\Gamma$ and $R$ points. The straight line is $\omega -{\varepsilon }_{\mathbf{k}n}$ where ${\varepsilon }_{\mathbf{k}n}$ is the LDA energy.

Figure 3

$\text{Im}\Sigma$ as a function of inverse temperature $\beta$ along the Matsubara axis.

Figure 4

The total spectral function within LDA, GWA, LDA+DMFT, and $GW$+DMFT.

Figure 5

The DMFT and $GW$ impurity self-energies and the vertex correction, which is the difference between the two self-energies.

Figure 6

Comparison of the spectral functions calculated with the full $GW$+DMFT scheme and the simplified scheme [Eq. (6)].

Figure 7

Quasiparticle band structures calculated with the simplified scheme. The label “DCC” denotes the double-counting correction. The results obtained with LDA, $GW$, and the full $GW$+DMFT are also shown for comparison.