Electronic structure of LaNiO2 and CaCuO2 from a self-consistent vertex-corrected

The electronic structure of one of the nickelates ($\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{2}$) and one of the cuprates ($\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_{2}$) is studied with three self-consistent $GW$-based methods: $\mathrm{sc}GW$, $\mathrm{sc}(GW+\text{vertex})$, and quasiparticle self-consistent $GW$. Low-energy features obtained in our study are in many respects similar to the features reported in previous density functional theory plus dynamical mean-field theory ($\mathrm{DFT}+\mathrm{DMFT}$) studies. Consistent with the $\mathrm{DFT}+\mathrm{DMFT}$ conclusion, we find $\mathrm{La}\mathrm{Ni}{\mathrm{O}}_{2}$ to be more correlated than $\mathrm{Ca}\mathrm{Cu}{\mathrm{O}}_{2}$. However, correlation effects included in our study change the DFT Fermi surface near the $\mathrm{\ensuremath{\Gamma}}$ point differently from that reported in DMFT studies. Features that are a few electronvolts away from the Fermi level are broader in our calculations than in the $\mathrm{DFT}+\mathrm{DMFT}$, which reflects the differences between the DFT and the $GW$ methods. Our results are in qualitative agreement with previous $G0W0$ results, but the self-consistency results in quantitative differences. Generally, correlation effects are found to be sufficiently weak in both materials, which allows one to use totally ab initio diagrammatic approaches such as $\mathrm{sc}(GW+\text{vertex})$ and to avoid the methods with adjustable parameters ($\mathrm{DFT}+\mathrm{U}$ or $\mathrm{DFT}+\mathrm{DMFT}$). However, the possibility of some strong correlations at low energy that cannot be captured by perturbative methods cannot be completely excluded. For instance, differences in the Fermi surface should be resolved, thus experimental studies are necessary.