Combining DFT and Many-body Methods to Understand Correlated Materials

Electronic and magnetic properties of strongly-correlated systems are typically controlled by a limited number of electronic states, located near the Fermi level and well isolated from the rest of the spectrum. This opens a formal way for combining the first-principles methods of electronic structure calculations, based on the density-functional theory (DFT), with model many- body methods, formulated in a restricted Hilbert space of states near the Fermi level. The core of this project is the construction of ``\textit{ab initio} model Hamiltonians'', which would incorporate the physics of on-site Coulomb correlations and provide a transparent physical picture for the low-energy properties of strongly- correlated systems. First, I will describe a systematic procedure for constructing such an effective Hubbard-type model, which consists of three major steps, starting from the electronic structure in the local- density approximation.$^1$ (i) Construction of the kinetic-energy part using an exact version of the downfolding method;$^{1,2}$ (ii) Construction of the Wannier functions; (iii) Calculation of screened Coulomb interactions using a hybrid approach, which combines the random phase approximation with the constraint DFT.$^{1,3}$ Then, I will illustrate abilities of this method for resolving a number of controversial issues, related with the interplay of the experimental lattice distortion and magnetic properties of four narrow $t_{2g}$ band perovskite oxides (YTiO$_3$, LaTiO$_3$, YVO$_3$, and LaVO$_3$), for which the obtained Hamiltonian was solved using a number of techniques, including the Hartree-Fock (HF) approximation,$^4$ the second-order perturbation theory and the $t$-matrix approach for the correlation energy,$^ {4,5}$ and a variational superexchange theory, which takes into account the multiplet structure of the atomic states.$^4$ I will argue that the crystal distortion imposes a severe constraint on the form of the possible orbital states, which favors the formation of experimental magnetic structures in YTiO$_3$, YVO$_3$, and LaVO$_3$, even at the level of HF approximation. The correlation effects systematically improve the agreement with the experimental data and additionally stabilize the experimentally observed G- and C-type antiferromagnetic states in YVO$_3$ and LaVO$_3$. The role of relativistic spin-orbit interaction will be also discussed. \newline $^1$ I.~V.~Solovyev, Phys.~Rev.~B~\textbf{73}, 155117 (2006). \newline $^2$ I.~V.~Solovyev, Z.~V.~Pchelkina, and V.~I.~Anisimov, cond- mat/0608528. \newline $^3$ I.~V.~Solovyev and M.~Imada, Phys.~Rev.~B~\textbf{71}, 045103 (2005). \newline $^4$ I.~V.~Solovyev, Phys.~Rev.~B~\textbf{74}, 054412 (2006). \newline $^5$ I.~V.~Solovyev, cond-mat/0608625.