Superconducting nickelates appear to be difficult to synthesize. Since the chemical reduction of ABO3 (A: rare earth; B transition metal) with CaH2 may result in both, ABO2 and ABO2H, we calculate the topotactic H binding energy by density functional theory (DFT). We find intercalating H to be energetically favorable for LaNiO2 but not for Sr-doped NdNiO2. This has dramatic consequences for the electronic structure as determined by DFT+dynamical mean field theory: that of 3d 9 LaNiO2 is similar to (doped) cuprates, 3d 8 LaNiO2H is a two-orbital Mott insulator. Topotactic H might hence explain why some nickelates are superconducting and others are not.

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 .

We present a dynamical mean-field study of dynamical susceptibilities in two-band Hubbard model. Varying the model parameters we analyze the two-particle excitations in the normal as well as in the ordered phase, an excitonic condensate. The two-particle DMFT spectra in the ordered phase reveal the gapless Goldstone modes arising from spontaneous breaking of continuous symmetries. We also observe gapped Higgs mode, characterized by vanishing of the gap at the phase boundary. Qualitative changes observed in the spin susceptibility can be used as an experimental probe to identify the excitonic condensation. arXiv:1808.08046v2 [cond-mat.str-el]

We derive the equations for calculating the high-frequency asymptotics of the local two-particle vertex function for a multi-orbital impurity model. These relate the asymptotics for a general local interaction to equal-time two-particle Green's functions, which we sample using continuoustime quantum Monte Carlo simulations with a worm algorithm. As specific examples we study the single-orbital Hubbard model and the three t2g orbitals of SrVO3 within dynamical mean field theory (DMFT). We demonstrate how the knowledge of the high-frequency asymptotics reduces the statistical uncertainties of the vertex and further eliminates finite box size effects. The proposed method benefits the calculation of non-local susceptibilities in DMFT and diagrammatic extensions of DMFT.

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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We derive equations of motion for Green's functions of the multi-orbital Anderson impurity model by differentiating symmetrically with respect to all time arguments. The resulting equations relate the one-and two-particle Green's function to correlators of up to six particles at four times. As an application we consider continuous-time quantum Monte Carlo simulations in the hybridization expansion, which hitherto suffered from notoriously high noise levels at large Matsubara frequencies.Employing the derived symmetric improved estimators overcomes this problem.

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