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Register a new userAb initio calculations with the dynamical vertex approximation
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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 mean field theory and important non-local correlations beyond, with a computational effort estimated to be still manageable.
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We characterize experimentally and theoretically the high-energy dielectric screening properties of the prototypical correlated metal SrVO$_3$. The dynamical structure factor measured by inelastic x-ray scattering spectroscopy as a function of momentum transfer is in very good agreement with first-principles calculations in the adiabatic local density approximation to time-dependent density-functional theory. Our results reveal the crucial importance of crystal local fields in the charge response function of correlated materials: They lead to depolarization effects for localised excitations and couple spectra from different Brillouin zones.
In this work, we adapt the formalism of the dynamical vertex approximation (D$Gamma$A), a diagrammatic approach including many-body correlations beyond the dynamical mean-field theory, to the case of attractive onsite interactions. We start by exploiting the ladder approximation of the D$Gamma$A scheme, in order to derive the corresponding equations for the non-local self-energy and vertex functions of the attractive Hubbard model. Second, we prove the validity of our derivation by showing that the results obtained in the particle-hole symmetric case fully preserve the exact mapping between the attractive and the repulsive models. It will be shown, how this property can be related to the structure of the ladders, which makes our derivation applicable for any approximation scheme based on ladder diagrams. Finally, we apply our D$Gamma$A algorithm to the attractive Hubbard model in three dimensions, for different fillings and interaction values. Specifically, we focus on the parameters region in the proximity of the second-order transition to the superconducting and charge-density wave phases, respectively, and calculate (i) their phase-diagrams, (ii) their critical behavior, as well as (iii) the effects of the strong non-local correlations on the single-particle properties.
Electronic structure calculations on the low dimensional spin-1/2 compound TiOCl were performed at several pressures in the orthorhombic phase, finding that the structure is quasi-one-dimensional. The Ti3+ (d1) ions have one t2g orbital occupied (dyz) with a large hopping integral along the b direction of the crystal. The most important magnetic coupling is Ti-Ti along the b axis. The transition temperature (Tc) has a linear evolution with pressure, and at about 10 GPa this Tc is close to room temperature, leading to a room temperature spin-Peierls insulator-insulator transition, with an important reduction of the charge gap in agreement with the experiment. On the high-pressure monoclinic phase, TiOCl presents two possible dimerized structures, with a long or short dimerization. Long dimerized state occurs above 15 GPa, and below this pressure the short dimerized structure is the more stable phase.
We show, by means of ab-initio calculations, that electron-electron correlations play an important role in potassium-doped picene ($K_x$-picene), recently characterized as a superconductor with $T_c = 18K$. The inclusion of exchange interactions by means of hybrid functionals reproduces the correct gap for the undoped compound and predicts an antiferromagnetic state for $x=3$, where superconductivity has been observed. The latter finding is compatible with a sizable value of the correlation strength, in agreement with simple estimates. Our results highlight the similarity between potassium-doped picene and alkali-doped fulleride superconductors.
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.
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