Dependence of $\mathrm{DFT}+\mathrm{DMFT}$ results on the construction of the correlated orbitals

The sensitivity of density functional theory plus dynamical mean field theory calculations to different constructions of the correlated orbitals is investigated via a detailed comparison of results obtained for the quantum material ${\mathrm{NdNiO}}_2$ using different Wannier and projector methods to define the correlation problem. Using the same interaction parameters we find that the different methods produce different results for the orbital and band basis mass enhancements and for the orbital occupancies, with differing implications regarding the importance of multiorbital effects and charge transfer physics. Using interaction parameters derived from the constrained random phase approximation enhances the difference in results. For the isostructural cuprate ${\mathrm{CaCuO}}_2$, the different methods give quantitatively different mass enhancements but still result in the same qualitative physics.

Figure 1

Energy bands obtained from diagonalizing the Wannier $H^{ab}\left(k\right)$ in the MLWF and SLWF methods. The color of the bands at each energy eigenvalue represents the amount of the $d_{x^2-y^2}$ Wannier function in the corresponding eigenvectors.

Figure 2

Uncorrelated DOS (per spin), obtained from the imaginary part of the local Green's function in the basis of localized orbitals using Wannier and projector methods without self-energy.

Figure 3

Negative imaginary part of the real frequency hybridization of the (a) $d_{x^2-y^2}$ and (b) $d_{z^2}$ orbitals. The inset of (a) shows the $d_{x^2-y^2}$ hybridization zoomed in on the window of $-7$ to $-2\mathrm{eV}$ and with a larger y axis to show the large hybridization to $\mathrm{O}\text{−}{p}_{\sigma }$.

Figure 4

Imaginary part of the Matsubara self-energy obtained from a DMFT solution for a two-orbital $\mathrm{Ni}\text{−}{e}_g$ model with a Kanamori Hamiltonian with $U=7\mathrm{eV}$ and $J=0.7\mathrm{eV}$ using the downfolding methods shown in the legends.

Figure 5

Pseudocolor plot of the quasiparticle mass enhancements in the band basis along a high-symmetry $k$ path. In the Wannier cases the bands plotted are the same in Fig. 1 and in the projector cases they are the wien2k DFT bands. The color corresponds to the mass enhancement of the DFT band determined from upfolding the self-energy to the band basis. The self-energy is obtained from a DMFT solution for a two-orbital $\mathrm{Ni}\text{−}{e}_g$ model with a Kanamori Hamiltonian with $U=7\mathrm{eV}$ and $J=0.7\mathrm{eV}$.

Figure 6

Momentum-integrated spectral functions per spin obtained from DMFT solutions for a two-orbital $\mathrm{Ni}\text{−}{e}_g$ model with a Kanamori Hamiltonian with $U=7\mathrm{eV}$ and $J=0.7\mathrm{eV}$ using the downfolding methods shown in the legends.

Figure 7

Pseudocolor plots of the momentum-resolved spectral functions $A(k,\omega )$ obtained from DMFT solutions for a two-orbital $\mathrm{Ni}\text{−}{e}_g$ model with a Kanamori Hamiltonian with $U=7\mathrm{eV}$ and $J=0.7\mathrm{eV}$.

Figure 8

Comparison of imaginary part of the Matsubara self-energy of the $d_{x^2-y^2}$ orbital obtained from two-orbital DMFT calculations (solid lines) to self-energy obtained from one-orbital DMFT calculation (dashed lines) with downfolding methods unchanged.

Figure 9

Uncorrelated density of states (per spin) of the $t_{2g}$ orbitals with the different methods.

Figure 10

Negative imaginary part of the real frequency hybridization of the $t_{2g}$ orbitals.

Figure 11

Comparison of the one-shot and FCSC $\mathrm{DFT}+\mathrm{DMFT}$ imaginary Matsubara self-energies for the case of projectors in the wide energy window from $-10$ to 10 eV.