First-principles Wannier functions and effective lattice fermion models for narrow-band compounds

We propose a systematic procedure for constructing effective lattice fermion models for narrow-band compounds on the basis of first-principles electronic-structure calculations. The method is illustrated for the series of transition-metal (TM) oxides: SrVO₃, YTiO₃, V₂O₃, and Y₂Mo₂O₇, whose low-energy properties are linked exclusively to the electronic structure of an isolated t₂₆ band. The method consists of three parts, starting from the electronic structure in the local-density approximation (LDA). (i) Construction of the kinetic-energy Hamiltonian using formal downfolding method. It allows us to describe the band structure close to the Fermi level in terms of a limited number of (unknown yet) Wannier functions (WFs), and eliminate the rest of the basis states. (ii) Solution of an inverse problem and construction of WFs for the given kinetic-energy Hamiltonian. Here, we closely follow the construction of the basis functions in the liner-muffin-tin-orbital (LMTO) method, and enforce the orthogonality of WFs to other bands. In this approach, one can easily control the contributions of the kinetic-energy term to the WFs. (iii) Calculation of screened Coulomb interactions in the basis of auxiliary WFs. The latter are defined as the WFs for which the kinetic-energy term is set to be zero. Meanwhile, the hybridization between TM d and other atomic states is preserved by the orthogonality condition to other bands. The use of auxiliary WFs is necessary in order to avoid the double counting of the kinetic-energy term, which is included explicitly in the model Hamiltonian. In order to calculate the screened Coulomb interactions we employed a hybrid approach. First, we evaluate the screening caused by the change of occupation numbers and the relaxation of the LMTO basis functions, using the conventional constraint-LDA approach, where all matrix elements of hybridization connecting the TM d orbitals and other orbitals are set to be zero. Then, we switch on the hybridization and evaluate the screening of on-site Coulomb interactions associated with the change of this hybridization in the random-phase approximation. The second channel of screening appears to be very important, and results in relatively small values of effective Coulomb interactions in the t₂₆ band (of the order of 2--30. 3em{0ex}eV, depending on the material). We discuss details of this screening and consider its band-filling dependence, frequency dependence, influence of the lattice distortion, proximity of other bands, as well as the effect of dimensionality of the model Hamiltonian.