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Register a new userComparing $GW$+DMFT and LDA+DMFT for the testbed material SrVO$_3$
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We have implemented the $GW$+dynamical mean field theory (DMFT) approach in the Vienna ab initio simulation package. Employing the interaction values obtained from the locally unscreened random phase approximation (RPA), we compare $GW$+DMFT and LDA+DMFT against each other and against experiment for SrVO$_3$. We observed a partial compensation of stronger electronic correlations due to the reduced $GW$ bandwidth and weaker correlations due to a larger screening of the RPA interaction, so that the obtained spectra are quite similar and well agree with experiment. Noteworthily, the $GW$+DMFT better reproduces the position of the lower Hubbard side band.
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LDA+DMFT, the merger of density functional theory in the local density approximation and dynamical mean-field theory, has been mostly employed to calculate k-integrated spectra accessible by photoemission spectroscopy. In this paper, we calculate k-resolved spectral functions by LDA+DMFT. To this end, we employ the Nth order muffin-tin (NMTO) downfolding to set up an effective low-energy Hamiltonian with three t_2g orbitals. This downfolded Hamiltonian is solved by DMFT yielding k-dependent spectra. Our results show renormalized quasiparticle bands over a broad energy range from -0.7 eV to +0.9 eV with small ``kinks, discernible in the dispersion below the Fermi energy.
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.
Ab initio calculation of the electronic properties of materials is a major challenge for solid state theory. Whereas the experience of forty years has proven density functional theory (DFT) in a suitable, e.g. local approximation (LDA) to give a satisfactory description in case electronic correlations are weak, materials with strongly correlated, say d- or f-electrons remain a challenge. Such materials often exhibit colossal responses to small changes of external parameters such as pressure, temperature, and magnetic field, and are therefore most interesting for technical applications. Encouraged by the success of dynamical mean field theory (DMFT) in dealing with model Hamiltonians for strongly correlated electron systems, physicists from the bandstructure and many-body communities have joined forces and have developed a combined LDA+DMFT method for treating materials with strongly correlated electrons ab initio. As a function of increasing Coulomb correlations, this new approach yields a weakly correlated metal, a strongly correlated metal, or a Mott insulator. In this paper, we introduce the LDA+DMFT by means of an example, LaMnO_3 . Results for this material, including the colossal magnetoresistance of doped manganites are presented. We also discuss advantages and disadvantages of the LDA+DMFT approach.
The electronic spectrum, energy gap and local magnetic moment of paramagnetic NiO are computed by using the local density approximation plus dynamical mean-field theory (LDA+DMFT). To this end the noninteracting Hamiltonian obtained within the local density approximation (LDA) is expressed in Wannier functions basis, with only the five anti-bonding bands with mainly Ni 3d character taken into account. Complementing it by local Coulomb interactions one arrives at a material-specific many-body Hamiltonian which is solved by DMFT together with quantum Monte-Carlo (QMC) simulations. The large insulating gap in NiO is found to be a result of the strong electronic correlations in the paramagnetic state. In the vicinity of the gap region, the shape of the electronic spectrum calculated in this way is in good agreement with the experimental x-ray-photoemission and bremsstrahlung-isochromat-spectroscopy results of Sawatzky and Allen. The value of the local magnetic moment computed in the paramagnetic phase (PM) agrees well with that measured in the antiferromagnetic (AFM) phase. Our results for the electronic spectrum and the local magnetic moment in the PM phase are in accordance with the experimental finding that AFM long-range order has no significant influence on the electronic structure of NiO.
We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as implemented in the Vienna {it ab initio} simulation package (VASP) with the self energy on the imaginary frequency axis, GW+DMFT, and ab initio dynamical vertex approximation (D$Gamma$A). The latter includes the physics of GW, DMFT and non-local correlations beyond, and allows for calculating (quantum) critical exponents. We present results obtained by the three methods with a focus on the benchmark material SrVO$_3$.
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