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Register a new userAb initio calculations of quasiparticle band structure in correlated systems: LDA++ approach
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We discuss a general approach to a realistic theory of the electronic structure in materials containing correlated d- or f- electrons. The main feature of this approach is the taking into account the energy dependence of the electron self-energy with the momentum dependence being neglected (local approximation). In the case of strong interactions (U/W>>1 - rare-earth system) the Hubbard-I approach is the most suitable. Starting from an exact atomic Green function with the constrained density matrix the band structure problem is formulated as the functional problem on Nmm for f-electrons and the standard LDA-functional for delocalized electrons. In the case of moderate correlations (U/W=1 metal-insulator regime) we start from the dynamical mean field iterative perturbation scheme (IPS) of G. Kotliar et. al. and also make use of our multiband atomic Green function. Finally for the weak interactions (U/W<1 -transition metals) the self-consistent diagrammatic fluctuation- exchange (FLEX)-approach of N. Bickers and D. Scalapino is generalized to the realistic multiband case. We presents two-band, two-dimensional model calculations for all three regimes. A realistic calculation in Hubbard-I scheme with the exact solution of the on-site multielectron problem for f(d)- shells was performed for mixed-valence 4f compound TmSe, and for the classical Mott insulator NiO.
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We present the TRIQS/DFTTools package, an application based on the TRIQS library that connects this toolbox to realistic materials calculations based on density functional theory (DFT). In particular, TRIQS/DFTTools together with TRIQS allows an efficient implementation of DFT plus dynamical mean-field theory (DMFT) calculations. It supplies tools and methods to construct Wannier functions and to perform the DMFT self-consistency cycle in this basis set. Post-processing tools, such as band-structure plotting or the calculation of transport properties are also implemented. The package comes with a fully charge self-consistent interface to the Wien2k band structure code, as well as a generic interface that allows to use TRIQS/DFTTools together with a large variety of DFT codes. It is distributed under the GNU General Public License (GPLv3).
A novel approach to electronic correlations in magnetic crystals which takes into account a dynamical many-body effects is present. In order to to find a frequency dependence of the electron self energy, an effective quantum-impurity many-particle problem need to be solved within the dynamical mean-field theory. The numerically exact QMC-scheme and the spin-polarized fluctuation exchange approximation are used for the self-consistent solution of this single-site many-particle problem. The calculations of effective exchange interaction parameters based on the realistic electronic structure of correlated magnetic crystals have been discussed.
The LDA+DMFT method is a very powerful tool for gaining insight into the physics of strongly correlated materials. It combines traditional ab-initio density-functional techniques with the dynamical mean-field theory. The core aspects of the method are (i) building material-specific Hubbard-like many-body models and (ii) solving them in the dynamical mean-field approximation. Step (i) requires the construction of a localized one-electron basis, typically a set of Wannier functions. It also involves a number of approximations, such as the choice of the degrees of freedom for which many-body effects are explicitly taken into account, the scheme to account for screening effects, or the form of the double-counting correction. Step (ii) requires the dynamical mean-field solution of multi-orbital generalized Hubbard models. Here central is the quantum-impurity solver, which is also the computationally most demanding part of the full LDA+DMFT approach. In this chapter I will introduce the core aspects of the LDA+DMFT method and present a prototypical application.
Efficient ab initio calculations of correlated materials at finite temperature require compact representations of the Greens functions both in imaginary time and Matsubara frequency. In this paper, we introduce a general procedure which generates sparse sampling points in time and frequency from compact orthogonal basis representations, such as Chebyshev polynomials and intermediate representation (IR) basis functions. These sampling points accurately resolve the information contained in the Greens function, and efficient transforms between different representations are formulated with minimal loss of information. As a demonstration, we apply the sparse sampling scheme to diagrammatic $GW$ and GF2 calculations of a hydrogen chain, of noble gas atoms and of a silicon crystal.
A novel hybrid scheme is proposed. The {it ab initio} LDA calculation is used to construct the Wannier functions and obtain single electron and Coulomb parameters of the multiband Hubbard-type model. In strong correlation regime the electronic structure within multiband Hubbard model is calculated by the Generalized Tight-Binding (GTB) method, that combines the exact diagonalization of the model Hamiltonian for a small cluster (unit cell) with perturbation treatment of the intercluster hopping and interactions. For undoped La$_2$CuO$_4$ and Nd$_2$CuO$_4$ this scheme results in charge transfer insulators with correct values of gaps and dispersions of bands in agreement to the ARPES data.
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