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

We report in detail our ab initio local density approximation (LDA)+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 LDA+Gutzwiller are in better agreement with existing experiments, suggesting significant improvements over LDA or LDA+U.