Comparing quasiparticle $GW$+DMFT and LDA+DMFT for the test bed material SrVO${}_3$

We have implemented the quasiparticle $GW$+dynamical mean field theory (DMFT) approach in the Vienna ab initio simulation package. To this end, a quasiparticle Hermitization of the $G_0{W}_0$ self-energy a lá Kotani-Schilfgaarde is employed, and the interaction values are obtained from the locally unscreened random phase approximation (RPA) using a projection onto Wannier orbitals. We compare quasiparticle $GW$+DMFT and local density approximation (LDA)+DMFT against each other and against experiment for SrVO${}_3$. We observe a partial compensation of stronger electronic correlations due to the reduced $GW$ bandwidth and weaker correlations due to a larger screening of the RPA interaction, so that the obtained spectra are quite similar and agree well with experiment. Noteworthy, the quasiparticle $GW$+DMFT better reproduces the position of the lower Hubbard side band.

Figure 1

Upper panel: $G_0{W}_0$ quasiparticle bands (red, gray) in comparison to LDA (black). The Fermi level sets our zero of energy and is marked as a line. Lower panel: Wannier projected $t_{2g}$ band structure from $G_0{W}_0$ (red, gray) and LDA (black). The $t_{2g}$ target bands bandwidth is reduced by $\sim$$0.7$ eV in $GW$.

Figure 2

Comparison of the imaginary part of the DMFT $t_{2g}$ self-energies $\Sigma$ vs (Matsubara) frequency $\omega$ for SrVO${}_3$ at inverse temperature $\beta =40$ eV${}^{-1}$ as computed in five different ways: employing qp$GW$ and LDA Wannier bands, the locally unscreened RPA interaction ${\overline{U}}^{\mathrm{DMFT}}=2.49$ eV and the cLDA ${\overline{U}}^{\mathrm{cLDA}}=3.55$ eV, as well as the ${\mathcal{Z}}_B=0.7$ renormalization.[23]

Figure 3

Spectral function for SrVO${}_3$ ($t_{2g}$ orbitals only) computed in five different ways as in Fig. 2. At lower temperatures the central peak gets only slightly sharper and higher, although the temperature effects from $\beta =25$ to 40 eV${}^{-1}$ are small.

Figure 4

Comparison of LDA+DMFT$@U^{\mathrm{cLDA}}$, qp$GW$+DMFT$@U^{\mathrm{DMFT}}$ (without and with Bose renormalization ${\mathcal{Z}}_B=0.7$), and experiment. The position of the lower Hubbard band is better reproduced in qp$GW$+DMFT, whereas the central peak is similar in LDA+DMFT and qp$GW$+DMFT. The Bose renormalization qp$GW$+DMFT differs considerably (photoemission spectra reproduced from Ref. 21).