Local density approximation combined with Gutzwiller method for correlated electron systems: Formalism and applications

We report in detail our ab initio local density approximation $\left(\text{LDA}\right)+\text{Gutzwiller}$ method, in which the Gutzwiller variational approach is naturally incorporated with the density-functional theory through the “Gutzwiller density-functional theory” (which is a generalization of original Kohn-Sham formalism). This method can be used for ground-state determination of electron systems ranging from weakly correlated metal to strongly correlated insulators with long-range ordering. We will show that its quality for ground state is as high as that by dynamic mean-field theory, and yet it is computationally much cheaper. In addition, the method is fully variational, the charge-density self-consistency can be naturally achieved, and the quantities, such as total energy and linear response, can be accurately obtained similarly as with LDA-type calculations. Applications on several typical systems are presented, and the characteristic aspects of this method are clarified. The obtained results using $\text{LDA}+\text{Gutzwiller}$ are in better agreement with existing experiments, suggesting significant improvements over LDA or $\text{LDA}+U$.

Figure 1

(Color online) Comparisons of calculated $Z$ factors, total energies, double occupancies, and kinetic energies of single-band Hubbard model with half filling. In GA the band renormalization factor and quasiparticle weight are coincident. $Z$ factor from DMFT denotes quasiparticle weight. Double occupancy is $⟨n_{\uparrow }{n}_{\downarrow }⟩$.

Figure 2

(Color online) Comparisons of calculated $Z$ factors, total energies, double occupancies, and kinetic energies of single-band Hubbard model with occupation number $n=0.9$.

Figure 3

(Color online) Comparisons of calculated $Z$ factors, total energies, double occupancies, and kinetic energies of single-band Hubbard model with occupation number $n=0.8$.

Figure 4

(Color online) Comparisons of calculated $Z$ factors, total energies, interaction energies, and kinetic energies of two-band Hubbard model with $\text{SU}\left(N\right)$ interaction.

Figure 5

Flow chart of self-consistent loops for $\text{LDA}+\text{Gutzwiller}$ method.

Figure 6

The calculated $Z$ factor as function of $U$ for ${\text{SrVO}}_3$ using $\text{LDA}+\text{G}$ method.

Figure 7

(Color online) The calculated density of states for ${\text{SrVO}}_3$ using LDA, $\text{LDA}+U$, and $\text{LDA}+\text{G}$ methods. We used the $U=5.0\text{eV}$ and $J=1.0\text{eV}$, and the electron DOS (rather than quasiparticle DOS) is shown, in the calculations of $\text{LDA}+\text{G}$.

Figure 8

(Color online) The calculated magnetic moment (per Fe) of bcc FM Fe as function of $U$ and $J$, by using different methods.

Figure 9

(Color online) The calculated DOSs of bcc FM Fe using different methods. The parameters $U=7.0\text{eV}$ and $J=1.0\text{eV}$ are used in these calculations.

Figure 10

(Color online) The calculated level splitting between the $a_{1g}$ and the $e_g^{\prime }$ states for ${\text{Na}}_{1-x}{\text{CoO}}_2$. The original figure is obtained from Ref. 29. The one-loop result corresponds to the calculation without charge-density self-consistency.