Confirmed Participants: Thomas Ayral, Arjan Berger, Silke Biermann, Fabio Caruso, Michele Casula, Pierluigi Cudazzo, Kay Dewhurst, Matteo Gatti, Hardy Gross, Matteo Guzzo, Philipp Hansmann, Federico Iori, Igor Krivenko, Nganba Meetei, Lucia Reining, Ambroise van Roekeghem, Pina Romaniello, Claudia Rödl, Francesco Sottile, Lorenzo Sponza, Adrian Stan, Falk Tandetzky, Loig Vaugier
DISCUSSION
MONDAY 04-06-2012
Falk Tandetzky: Multiple Solutions of GW-Type approximations
We show that the equations underlying the GW approximation have a large number of solutions. This raises the question: which is the physical solution? We provide two theorems which explain why the methods currently in use do, in fact, find the correct solution. These theorems are general enough to cover a large class of similar algorithms. See also arXiv:1205.4274v1
Fabio Caruso: How accurate is the GW approximation for ground-state properties?
Fully self-consistent GW (sc-GW) -- based on the iterative solution of the Dyson equation -- incorporates many-body correlation effects in the electronic ground state, providing a recipe to consistently describe ground and excited states on the same quantum mechanical level. To assess the quality of sc-GW ground-state we studied the potential energy curve of diatomic hydrogen. While equilibrium total energy is in excellent agreement with full configuration-interaction (CI), the sc-GW dissociation limit considerably deviates from the reference data. For H2, we compared sc-GW with the self-consistent random-phase approximation (sc-RPA) -- in which a local exchange-correlation potential is derived from the GW self-energy within the optimized effective potential framework. Although in sc-RPA and sc-GW the exchange and correlation energy are described through topologically identical Feynman diagrams, large qualitative differences in the description of the potential energy curve of H2 are observed. These discrepancies arise from different ways of accounting for static correlation in many-body perturbation theory and in Kohn-Sham density functional theory.
Pina Romaniello: A family of generalized one-body Green’s functions and exact constraints to determine the physical solution
In this talk we go beyond the standard methods to calculate G, which are plagued by various shortcomings, and we use an approximate set of functional differential equations relating the one-particle Green's function to its functional derivative with respect to an external perturbing potential. We show that this set of equations has, in principle, multiple solutions, but only one is well-behaved, which is the perturbative one. We give the formally exact family of solution, which depends on an auxiliary quantity q, which must fulfills stringent exact constraints. We give the exact solution of the equations within a space/spin decoupling approximation (continuous time framework) and we show that once q is known, the solution is uniquely fixed by the vanishing Coulomb interaction limit. This gives suggestions for the full functional case.
Lorenzo Sponza: Dynamical screening in optical absorption
Solving the Bethe-Salpeter equation (BSE) for cubic $SrTiO_3$ give rise to an extremely strong and sharp excitonic peak around 6.4 eV, far from the absorption onset (3.75 eV). We decomposed the BSE peak in single-particle transitions and we compared the analysis with the independent-quasiparticle spectrum (IQ-RPA). Moreover, by a selective reduction of both the number bands and the k-points included in the calculation, we were finally able to identify intial and final states of the single-particle transitions mixed by BSE that produce the strong excitonic peak at 6.4 eV. The strongly localised nature of such transitions make the inclusion of out-diagonal elements of $W_{GG'}$ important in solving the BSE for this material.
TUESDAY 05-06-2012:
Loig Vaugier: Effective Coulomb interactions from first principles
Determining the Coulomb interactions in real materials presents a serious challenge for first principles approaches. In 2004, a systematic way - called constrained-RPA (cRPA) - of calculating the Hubbard U and Hund's rule J parameters from first-principles has been proposed by Aryasetiawan and coworkers [1]. We have implemented the cRPA method in the framework of the Full Potential Linear Augmented Plane Waves method as implemented in the Wien2k code [2]. Our scheme permits us to calculate the Hubbard interactions in the same basis in which combined LDA+DMFT calculations are performed within the implementation of [3], yielding a fully consistent first-principles scheme. As an application of cRPA, we have calculated Hubbard U's and Hund J's for cubic 3d and 4d transition metal perovskites [4], and for iron-based pnictides. In contrast to what is usually assumed, the trend for the perovskite oxides is not necessarily monotonic, depending on the screening strength and the localization of the wave functions. Our work emphasizes the dependence of U and J on the choice of the one- electron part of the Hamiltonian. [1] Aryasetiawan, Imada, Georges, Kotliar, Biermann and Liechtenstein, PRB 70, 195104 (2004) [2] Blaha, Schwarz, Madsen, Kvasnicka and Luitz, Wien2k, An Augmented Plane Wave+Local Orbitals Program for Calculating Crystal Properties, Tech. Universität Wien, Austria, (2001) [3] Aichhorn, Pourovskii, Vildosola, Ferrero, Parcollet, Miyake, Georges and Biermann, PRB 80, 085101 (2009) [4] Vaugier, Jiang and Biermann, arXiv 1206.3533.v1
Philipp Hansmann: Adatoms on semiconductor surfaces: Mott or not
For quite some time now the so called alpha-phases of group IV adatom systems on silicon and germanium 111 surfaces have been under experimental and theoretical investigation. Specifically the role played by electron-electron correlations and their complex interplay with lattice degrees of freedom has been under controversial debate. It will be discussed how we can tackle the problem by means of state-of-the-art ab initio + many body approaches like e.g. density functional + dynamical mean field theory (LDA+DMFT). It will be shown how we can reach a truly ab initio treatment by calculating also the interaction parameters for the effective low energy models with the recently developed constrained random phase approximation (cRPA). Knowing the correct interaction parameters for the respective models will give extremely valuable information even before solving the complex many body problem and we can estimate for example if interaction effects can be approximated by a purely local term or if intersite interactions will contribute significantly. Recent results for said silicon adatom systems will be presented and possible consequences for the subsequent theoretical treatment will be discussed.
Federico Iori: Non-local exchange in TMOs
We present a systematic theoretical study of the electronic structure of several prototypical correlated transition-metal oxides. In all the materials that we have considered, density-functional theory in the local-density approximation (LDA) yields a metallic band structure for the low-temperature insulating phases. In the past, following the spirit of the Hubbard model, several corrections to LDA have been proposed to improve the description of the local correlation. Here we make use of hybrid functionals (specifically in the HSE06 parametrization) that mix a portion of non-local Fock exchange with LDA (and are not supposed to improve the description of electronic correlation). We thus show that non-local exchange is an essential ingredient to cure the LDA error. In fact, without invoking strong correlation effects, using HSE we find an insulating band structure for all the considered compounds, in qualitative agreement with photoemission results. Moreover, HSE describes correctly the metal-insulator transitions in the all the materials.