Ordering Phenomena in Transition Metal Oxides

Wannier functions and electronic correlation problems   

Coulomb interaction term of the Hubbard model (or more general Anderson lattice model) is written in a site-centered, localized atomic-like orbitals basis set which is not explicitly defined. Wannier functions (WF) are regarded as a best possible choice for these orbitals. We propose a method where Wannier functions are calculated in explicit form and ab-initio full-orbital Hamiltonian is projected on the Wannier function subspace defined for partially filled bands of interest. The calculated in this way few (Wannier) orbitals Hamiltonian together with Coulomb interaction term between Wannier orbitals (with interaction strength parameters computed in constrain calculations) is used as ab-initio set up of correlation problem that can be solved then by one of the methods developed in many-body community, for example by dynamical mean-field theory (DMFT). The self-energy operator obtained in such calculations is defined in Wannier functions basis and can be converted back into full-orbital Hilbert space, that in its turn can be used for calculation of the full-orbital interacting Green function . Using this Green function one can calculate the charge density changed by correlations together with a new set of Wannier functions and so to define a fully self-consistent scheme. The Green function can be also used to calculate spectral, magnetic and electronic properties of the system under investigation. The results obtained by this method for SrVO₃ and V₂O₃ are reported and compared with the previous results by more simple computation method and new bulk sensitive experimental spectroscopic data.