Diagrammatic extensions of dynamical mean field theory (DMFT) such as the dynamical vertex approximation (DΓA) allow us to include non-local correlations beyond DMFT on all length scales and proved their worth for model calculations. Here, we develop and implement an AbinitioDΓA approach for electronic structure calculations of materials. Starting point is the two-particle irreducible vertex in the two particle-hole channels which is approximated by the bare non-local Coulomb interaction and all local vertex corrections. From this we calculate the full non-local vertex and the non-local self-energy through the Bethe-Salpeter equation. The AbinitioDΓA approach naturally generates all local DMFT correlations and all non-local GW contributions, but also further non-local correlations beyond: mixed terms of the former two and non-local spin fluctuations. We apply this new methodology to the prototypical correlated metal SrVO3. arXiv:1610.02998v2 [cond-mat.str-el]
While key effects of the many-body problem-such as Kondo and Mott physics-can be understood in terms of onsite correlations, non-local fluctuations of charge, spin, and pairing amplitudes are at the heart of the most fascinating and unresolved phenomena in condensed matter physics. Here, we review recent progress in diagrammatic extensions to dynamical mean-field theory for ab initio materials calculations. We first recapitulate the quantum field theoretical background behind the two-particle vertex. Next we discuss latest algorithmic advances in quantum Monte Carlo simulations for calculating such two-particle quantities using worm sampling and vertex asymptotics, before giving an introduction to the ab initio dynamical vertex approximation (AbinitioDΓA). Finally, we highlight the potential of AbinitioDΓA by detailing results for the prototypical correlated metal SrVO 3 .
While the stoichiometric intermetallic compound FeAl is found to be paramagnetic in experiment, standard band-theory approaches predict the material to be ferromagnetic. We show that this discrepancy can be overcome by a better treatment of electronic correlations with density functional plus dynamical mean field theory. Our results show no ferromagnetism down to 100 K and since the susceptibility is decreasing at the lowest temperatures studied we also do not expect ferromagnetism at even lower temperatures. This behavior is found to originate from temporal quantum fluctuations that screen short-lived local magnetic moments of 1.6 $\mu_B$ on Fe
The ab initio extension of the dynamical vertex approximation (DΓA) method allows for realistic materials calculations that include non-local correlations beyond GW and dynamical mean-field theory. Here, we discuss the AbinitioDΓA algorithm, its implementation and usage in detail, and make the program package available to the scientific community.Keywords: Strongly correlated electron systems; dynamical mean-field theory; dynamical vertex approximation; electronic structure calculations PROGRAM SUMMARYProgram Title: AbinitioDΓA Licensing provisions: GNU General Public License (GPLv3) Operating system: Linux, Unix, macOS Programming language: Fortran95 and Python Required dependencies: MPI, LAPACK, BLAS, HDF5 (≥ 1.8.12), Python (≥ 2.7), h5py (≥ 2.5.0), numpy (≥ 1.9.1) Optional dependencies: pip, matplotlib (≥ 1.5.1), scipy (≥ 0.14.0) Supplementary material: Test case files and step-by-step instructions Nature of problem: Realistic materials calculations including non-local correlations beyond dynamical mean-field theory (DMFT) as well as non-local interactions. Solving the Bethe-Salpeter equation for multiple orbitals. Determining momentum-resolved susceptibilities in DMFT.Solution method: Ab initio dynamical vertex approximation: starting from the local two-particle vertex and constructing from it the local DMFT correlations, the GW diagrams, and further non-local correlations, e.g., spin fluctuations. Efficient solution of the Bethe-Salpeter equation, avoiding divergencies in the irreducible vertex in the particle-hole channel by reformulating the problem in terms of the full vertex. Parallelization with respect to the bosonic frequency and transferred momentum.Additional comments including Restrictions and Unusual features: As input, a Hamiltonian derived, e.g., from density functional theory and a DMFT solution thereof is needed including a local twoparticle vertex calculated at DMFT self-consistency. Hitherto the AbinitioDΓA program package is restricted to SU(2) symmetric problems. A so-called λ correction or self-consistency is not yet implemented in the AbinitioDΓA code. Susceptibilities are so far only calculated within DMFT, not the dynamical vertex approximation.
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