We study the expansion of single-particle and two-particle imaginary-time Matsubara Green's functions of quantum impurity models in the basis of Legendre orthogonal polynomials. We discuss various applications within the dynamical mean-field theory (DMFT) framework. The method provides a more compact representation of the Green's functions than standard Matsubara frequencies and therefore significantly reduces the memory-storage size of these quantities. Moreover, it can be used as an efficient noise filter for various physical quantities within the continuous-time quantum Monte Carlo impurity solvers recently developed for DMFT and its extensions. In particular, we show how to use it for the computation of energies in the context of realistic DMFT calculations in combination with the local density approximation to the density functional theory (LDA+DMFT) and for the calculation of lattice susceptibilities from the local irreducible vertex function.PACS numbers: 71.27.+a, 71.10.Fd In recent years, significant progress has been made in the study of strongly-correlated fermionic quantum systems with the development of methods combining systematic analytical approximations and modern numerical algorithms. The Dynamical Mean-Field Theory (DMFT) (for a review see Ref. 1) and its various extensions. 2-6serve as successful examples for this theoretical advance. On the technical side, important progress was made in the solution of quantum impurity problems, i.e. local quantum systems coupled to a bath (self-consistently determined in the DMFT formalism). In particular, a new generation of continuous-time quantum Monte Carlo (CTQMC) impurity solvers 7-10 has emerged that provide unprecedented efficiency and accuracy (for a recent review, see Ref. 11).In practice, several important technical issues still remain. Firstly, while the original DMFT formalism is expressed in terms of single-particle quantities (Green's function and self-energy), two-particle quantities play a central role in the formulation of some DMFT extensions (e.g. dual-fermions 4,12-14 , DΓA 3 ) and in susceptibility and transport computations in DMFT itself. They typically depend on three independent times or frequencies, and spatial indices. Therefore, they are quite large objects that are hard to store, manipulate and analyze, even with modern computing capabilities. Developing more compact representations of these objects and using them to solve, e.g., the Bethe-Salpeter equations is therefore an important challenge.A natural route is to use an orthogonal polynomial representation of the imaginary-time dependence of these objects. While the application of orthogonal polynomials has had productive use in other approaches to correlated electrons, 15,16 in this paper we show how to use Legendre polynomials to represent various imaginary-time Green's functions in a more compact way and show their usefulness in some concrete calculations.A second aspect is that modern CTQMC impurity solvers still have limitations. One well-known problem is the high-fre...

We discuss a parameter-free and computationally efficient ab initio simulation approach for moderately and strongly correlated materials, the multitier self-consistent GW +EDMFT method. This scheme treats different degrees of freedom, such as high-energy and low-energy bands, or local and nonlocal interactions, within appropriate levels of approximation, and provides a fully self-consistent description of correlation and screening effects in the solid. The ab initio input is provided by a one-shot G 0 W 0 calculation, while the strong-correlation effects originating from narrow bands near the Fermi level are captured by a combined GW plus extended dynamical mean-field (EDMFT) treatment. We present the formalism and technical details of our implementation and discuss some general properties of the effective EDMFT impurity action. In particular, we show that the retarded impurity interactions can have non-causal features, while the physical observables, such as the screened interactions of the lattice system, remain causal. As a first application, we present ab initio simulation results for SrMoO3, which demonstrate the existence of prominent plasmon satellites in the spectral function not obtainable within LDA+DMFT, and provide further support for our recent re-interpretation of the satellite features in the related cubic perovskite SrVO3. We then turn to stretched sodium as a model system to explore the performance of the multitier self-consistent GW +EDMFT method in situations with different degrees of correlation. While the results for the physical lattice spacing a0 show that the scheme is not very accurate for electron-gas like systems, because nonlocal corrections beyond GW are important, it does provide physically correct results in the intermediate correlation regime, and a Mott transition around a lattice spacing of 1.5a0. Remarkably, even though the Wannier functions in the stretched compound are less localized, and hence the bare interaction parameters are reduced, the self-consistently computed impurity interactions show the physically expected trend of an increasing interaction strength with increasing lattice spacing.

The cubic perovskite SrVO 3 is generally considered to be a prototype strongly correlated metal with a characteristic three-peak structure of the d-electron spectral function, featuring a renormalized quasiparticle band in between pronounced Hubbard sidebands. Here we show that this interpretation, which has been supported by numerous "ab initio" simulations, has to be reconsidered. Using a fully self-consistent GW + extended dynamical mean-field theory calculation we find that the screening from nonlocal Coulomb interactions substantially reduces the effective local Coulomb repulsion, and at the same time leads to strong plasmonic effects. The resulting effective local interactions are too weak to produce pronounced Hubbard bands in the local spectral function, while prominent plasmon satellites appear at energies which agree with those of the experimentally observed sidebands. Our results demonstrate the important role of nonlocal interactions and dynamical screening in determining the effective interaction strength of correlated compounds. DOI: 10.1103/PhysRevB.94.201106 SrVO 3 has been considered a prototype strongly correlated metal ever since photoemission and inverse photoemission experiments 20 years ago [1] showed features at energies well outside the renormalized quasiparticle band. These satellites have been explained as Hubbard bands, because they appear in combined density functional + dynamical mean-field theory (LDA+DMFT) [2] simulations when the local Coulomb repulsion is chosen such that the experimentally observed mass renormalization is reproduced (see, e.g., Refs. [3][4][5]). Comparable values for the "Hubbard U " on the order of 5 eV were obtained by constrained local density approximation (LDA) [6,7] and used in DMFT calculations with static local interactions. The constrained random phase approximation (cRPA) [8] provides a systematic way of computing the dynamically screened interaction parameters consistent with the LDA band structure, and the resulting local U (ω) of the DMFT auxiliary system can be efficiently handled by state-of-the-art impurity solvers [9]. These more realistic calculations, however, produce a too strong renormalization of the quasiparticle band [10]. The missing ingredients in the LDA+DMFT + U (ω) approach are the nonlocal self-energy and polarization effects, and the additional screening of the U (ω) resulting from nonlocal Coulomb interactions within the low-energy subspace.A promising scheme, which can treat all these effects in a consistent manner, is the combination of the GW ab initio method [11] and extended DMFT (EDMFT) [12,13]. While this GW + EDMFT formalism has been tested on simple one-band Hubbard models [14][15][16][17], and several simplified versions have been applied to SrVO 3 [7,10,18,19], a fully self-consistent implementation in an ab initio setting has so far been hampered by the challenges of solving the bosonic selfconsistency loop for multiorbital systems and nontrivial issues related to a proper embedding of the EDMFT calculations into a ...

In electronic systems with long-range Coulomb interaction, the nonlocal Fock-exchange term has a bandwidening effect. While this effect is included in combined many-body perturbation theory and dynamical mean field theory (DMFT) schemes, it is not taken into account in standard extended DMFT (EDMFT) calculations. Here, we include this instantaneous term in both approaches and investigate its effect on the phase diagram and dynamically screened interaction. We show that the largest deviations between previously presented EDMFT and GW +EDMFT results originate from the nonlocal Fock term, and that the quantitative differences are especially large in the strong-coupling limit. Furthermore, we show that the charge-ordering phase diagram obtained in GW +EDMFT methods for moderate interaction values is very similar to the one predicted by dual-boson methods that include the fermion-boson or four-point vertex. DOI: 10.1103/PhysRevB.95.245130 Dynamical mean field theory (DMFT) [1] self-consistently maps a correlated Hubbard lattice problem with local interactions onto an effective impurity problem consisting of a correlated orbital hybridized with a noninteracting fermionic bath. If the bath is integrated out, one obtains an impurity action with retarded hoppings. Extended dynamical mean field theory [2-10] (EDMFT) extends the DMFT idea to systems with long-range interactions. It does so by mapping a lattice problem with long-range interactions onto an effective impurity model with self-consistently determined fermionic and bosonic baths, or, in the action formulation, an impurity model with retarded hoppings and retarded interactions.While EDMFT captures dynamical screening effects and charge-order instabilities, it has been found to suffer from qualitative shortcomings in finite dimensions. For example, the charge susceptibility computed in EDMFT does not coincide with the derivative of the average charge with respect to a small applied field [11], nor does it obey local charge conservation rules [12] essential for an adequate description of collective modes such as plasmons.The EDMFT formalism has an even more basic deficiency: since it is based on a local approximation to the self-energy, it does not include even the first-order nonlocal interaction term, the Fock term. The combined GW +EDMFT [13][14][15] scheme corrects this by supplementing the local self-energy from EDMFT with the nonlocal part of the GW diagram, where G is the interacting Green's function and W the fully screened interaction. Indeed, the nonlocal Fock term [Gv] nonloc is included in the nonlocal [GW ] nonloc diagram. As described in more detail in Ref. [15] (see also the appendix of Ref.[16]), the GW +EDMFT method is formally obtained by constructing an energy functional of G and W , the Almbladh [17] functional , and by approximating as a sum of two terms, one containing all local diagrams (corresponding to EDMFT) and the other containing the simplest nonlocal correction (corresponding to the GW approximation [18]). This functional construct...