While second-order phase transitions always cause strong non-local fluctuations, their effect on spectral properties crucially depends on the dimensionality. For the important case of three dimensions, we show that the electron self-energy is well se
parable into a local dynamical part and static non-local contributions. In particular, our non-perturbative many-body calculations for the 3D Hubbard model at different fillings demonstrate that the quasi-particle weight remains essentially momentum-independent, also in the presence of overall large non-local corrections to the self-energy. Relying on this insight we propose a space-time-separated scheme for many-body perturbation theory that is up to ten times more efficient than current implementations. Besides these far-reaching implications for state-of-the-art electronic structure schemes, our analysis will also provide guidance to the quest of going beyond them.
We present an approach which is based on the one-particle irreducible (1PI) generating functional formalism and includes electronic correlations on all length-scales beyond the local correlations of dynamical mean field theory (DMFT). This formalism
allows us to unify aspects of the dynamical vertex approximation (DGammaA) and the dual fermion (DF) scheme, yielding a consistent formulation of non-local correlations at the one- and two-particle level beyond DMFT within the functional integral formalism. In particular, the considered approach includes one-particle reducible contributions from the three- and more-particle vertices in the dual fermion approach, as well as some diagrams not included in the ladder version of DGammaA. To demonstrate the applicability and physical content of the 1PI approach, we compare the diagrammatics of 1PI, DF and DGammaA, as well as the numerical results of these approaches for the half-filled Hubbard model in two dimensions.
Recently, dynamical mean field theory calculations have shown that kinks emerge in the real part of the self energy of strongly correlated metals close to the Fermi level. This gives rise to a similar behavior in the quasi-particle dispersion relatio
n as well as in the electronic specific heat. Since f-electron systems are even more strongly correlated than the -hitherto studied- d-electron systems we apply the dynamical mean field approach with the numerical renormalization group method as impurity solver to study whether there are kinks in the periodic Anderson model.
We have calculated the local magnetic susceptibility of one of the prototypical Fe-based superconductors (LaFeAsO) by means of the local density approximation + dynamical mean field theory as a function of both (imaginary) time and real frequencies w
ith and without vertex corrections. Vertex corrections are essential for obtaining the correct $omega$-dependence, in particular a pronounced low-energy peak at $omega sim 0.2 $eV, which constitutes the hallmark of the dynamical screening of a large instantaneous magnetic moment on the Fe atoms. In experiments, however, except for the case of x-ray absorption spectroscopy (XAS), the magnetic moment or the susceptibility represent typically the average over long time scales. In this respect, the frequency range of typical neutron experiments would be too limited to directly estimate the magnitude of the short-time moment.
We propose an approach for the ab initio calculation of materials with strong electronic correlations which is based on all local (fully irreducible) vertex corrections beyond the bare Coulomb interaction. It includes the so-called GW and dynamical m
ean field theory and important non-local correlations beyond, with a computational effort estimated to be still manageable.
By means of the dynamical vertex approximation (D$Gamma$A) we include spatial correlations on all length scales beyond the dynamical mean field theory (DMFT) for the half-filled Hubbard model in three dimensions. The most relevant changes due to non-
local fluctuations are: (i) a deviation from the mean-field critical behavior with the same critical exponents as for the three dimensional Heisenberg (anti)-ferromagnet and (ii) a sizable reduction of the Neel temperature ($T_N$) by $sim 30%$ for the onset of antiferromagnetic order. Finally, we give a quantitative estimate of the deviation of the spectra between D$Gamma$A and DMFT in different regions of the phase-diagram.
