Quantitative prediction of electronic properties in correlated materials requires simulations without empirical truncations and parameters. We present a method to achieve this goal through a new ab initio formulation of dynamical mean-field theory (DMFT). Instead of using small impurities defined in a low-energy subspace, which require complicated downfolded interactions which are often approximated, we describe a full cell $GW$+DMFT approach, where the impurities comprise all atoms in a unit cell or supercell of the crystal. Our formulation results in large impurity problems, which we treat here with efficient quantum chemistry impurity solvers that work on the real-frequency axis, combined with a one-shot $G_0W_0$ treatment of long-range interactions. We apply our full cell approach to bulk Si, two antiferromagnetic correlated insulators NiO and $α$-Fe$_2$O$_3$, and the paramagnetic correlated metal SrMoO$_3$, with impurities containing up to 10 atoms and 124 orbitals. We find that spectral properties, magnetic moments, and two-particle spin correlation functions are obtained in good agreement with experiments. In addition, in the metal oxide insulators, the balanced treatment of correlations involving all orbitals in the cell leads to new insights into the orbital character around the insulating gap.
We propose a self-consistent method for electronic structure calculations of correlated systems, which combines the local spin-density approximation (LSDA) and the dynamical mean field theory (DMFT). The LSDA part is based on the exact muffin-tin orbital approach, meanwhile the DMFT uses a perturbation scheme that includes the T matrix with fluctuation exchange approximation. The current LSDA+DMFT implementation fulfills both self-energy and charge self-consistency requirements. We present results on the electronic structure calculations for bulk 3d transition metals (Cr, Fe, and Ni) and for F…
We present an efficient ab initio dynamical mean-field theory (DMFT) implementation for quantitative simulations in solids. Our DMFT scheme employs ab initio Hamiltonians defined for impurities comprising the full unit cell or a supercell of atoms and for realistic quantum chemical basis sets. We avoid double counting errors by using Hartree-Fock as the low-level theory. Intrinsic and projected atomic orbitals (IAO+PAO) are chosen as the local embedding basis, facilitating numerical bath truncation. Using an efficient integral transformation and coupled-cluster Green's function (CCGF) impurity…
In this paper, we show how to calculate analytical atomic forces within self-consistent density functional theory + dynamical mean-field theory (DFT+DMFT) approach in the case when ultra-soft or norm-conserving pseudopotentials are used. We show how to treat the non-local projection terms arising within the pseudopotential formalism and circumvent the problem of non-orthogonality of the Kohn-Sham eigenvectors. Our approach is, in principle, independent of the DMFT solver employed, and here was tested with the Hubbard I solver. We benchmark our formalism by comparing against the forces calculat…
ComDMFT is a massively parallel computational package to study the electronic structure of correlated-electron systems (CES). Our approach is a parameter-free method based on ab initio linearized quasiparticle self-consistent GW (LQSGW) and dynamical mean field theory (DMFT). The non-local part of the electronic self-energy is treated within ab initio LQSGW and the local strong correlation is treated within DMFT. In addition to ab initio LQSGW+DMFT, charge self-consistent LDA+DMFT methodology is also implemented, enabling multiple methods in one open-source platform for the electronic structur…
We discuss the recently proposed LDA'+DMFT approach providing consistent parameter free treatment of the so called double counting problem arising within the LDA+DMFT hybrid computational method for realistic strongly correlated materials. In this approach the local exchange-correlation portion of electron-electron interaction is excluded from self consistent LDA calculations for strongly correlated electronic shells, e.g. d-states of transition metal compounds. Then the corresponding double counting term in LDA+DMFT Hamiltonian is consistently set in the local Hartree (fully localized limit -…
We review recent developments in electronic structure calculations that go beyond state-of-the-art methods such as density functional theory (DFT) and dynamical mean field theory (DMFT). Specifically, we discuss the following methods: GW as implemented in the Vienna {\it ab initio} simulation package (VASP) with the self energy on the imaginary frequency axis, GW+DMFT, and ab initio dynamical vertex approximation (D$Γ$A). The latter includes the physics of GW, DMFT and non-local correlations beyond, and allows for calculating (quantum) critical exponents. We present results obtained by the thr…
We present a joint implementation of dynamical-mean-field theory (DMFT) with the pseudopotential plane-wave approach, via Wannier functions, for the determination of the electronic properties of strongly correlated materials. The scheme uses, as input for the DMFT calculations, a tight-binding Hamiltonian obtained from the plane-wave calculations by projecting onto atomic-centered symmetry-constrained Wannier functions for the correlated orbitals. We apply this scheme to two prototype systems: a paramagnetic correlated metal, SrVO3, and a paramagnetic correlated system, V2O3, which exhibits a …
We propose a dynamical mean field approach for calculating the electronic structure of strongly correlated materials from first principles. The scheme combines the GW method with dynamical mean field theory, which enables one to treat strong interaction effects. It avoids the conceptual problems inherent to conventional ``LDA+DMFT'', such as Hubbard interaction parameters and double counting terms. We apply a simplified version of the approach to the electronic structure of nickel and find encouraging results.
We present a computational study of $L$-edge resonant inelastic x-ray scattering (RIXS) in correlated 3$d$ transition-metal oxides using an $ab$ $initio$ method based on local density approximation + dynamical mean-field theory (DMFT). The present method, building on Anderson impurity model with an optimized continuum bath within DMFT, is an extension of the cluster model to include unbound electron-hole pair excitations as well as material-specific charge-transfer excitations with less empirical parameters. We find a good agreement with available experimental data. The relationship between co…
We give a detailed description of a recently proposed first principles approach to the electronic structure of strongly correlated materials. The method combines the GW approximation with dynamical mean field theory. It is designed to describe Coulomb interactions and screening effects without adjustable parameters, thus avoiding the conceptual problems inherent to LDA+DMFT techniques.
We present a new open-source program, DCore, that implements dynamical mean-field theory (DMFT). DCore features a user-friendly interface based on text and HDF5 files. It allows DMFT calculations of tight-binding models to be performed on predefined lattices as well as \textit{ab initio} models constructed by external density functional theory codes through the Wannier90 package. Furthermore, DCore provides interfaces to many advanced quantum impurity solvers such as quantum Monte Carlo and exact diagonalization solvers. This paper details the structure and usage of DCore and shows some applic…
The LDA+DMFT approach merges conventional band structure theory in the local density approximation (LDA) with a state-of-the-art many-body technique, the dynamical mean-field theory (DMFT). This new computational scheme has recently become a powerful tool for ab initio investigations of real materials with strong electronic correlations. In this paper an introduction to the basic ideas and the set-up of the LDA+DMFT approach is given. Results for the photoemission spectra of the transition metal oxide La_{1-x}Sr_xTiO_3, obtained by solving the DMFT-equations by quantum Monte-Carlo (QMC) simula…
Dynamical Mean-Field Theory (DMFT) has opened new perspectives for the investigation of strongly correlated electron systems and greatly improved our understanding of correlation effects in models and materials. In contrast to Hartree-Fock-type approximations the mean field of DMFT is dynamical, whereby local quantum fluctuations are fully taken into account. DMFT becomes exact in the limit of high spatial dimensions or coordination number. Using DMFT the dynamics of correlated electron systems can be investigated non-perturbatively at all interaction strengths, electron densities and temperat…
Dynamical Mean Field Theory (DMFT) is a successful method to compute the electronic structure of strongly correlated materials, especially when it is combined with density functional theory (DFT). Here, we present an open-source computational package (and a library) combining DMFT with various DFT codes interfaced through the Wannier90 package. The correlated subspace is expanded as a linear combination of Wannier functions introduced in the DMFT approach as local orbitals. In particular, we provide a library mode for computing the DMFT density matrix. This library can be linked and then inter…
Phonons are fundamentally important for many materials properties, including thermal and electronic transport, superconductivity, and structural stability. Here, we describe a method to compute phonons in correlated materials using state-of-the-art DFT+DMFT calculations. Our approach combines a robust DFT+DMFT implementation to calculate forces with the direct method for lattice dynamics using nondiagonal supercells. The use of nondiagonal instead of diagonal supercells drastically reduces the computational expense associated with the DFT+DMFT calculations. We benchmark the method for typical …
We present a consistent way of treating a double counting problem unavoidably arising within the LDA+DMFT combined approach to realistic calculations of electronic structure of strongly correlated systems. The main obstacle here is the absence of systematic (e.g. diagrammatic) way to express LDA (local density approximation) contribution to exchange correlation energy appearing in the density functional theory. It is not clear then, which part of interaction entering DMFT (dynamical mean-field theory) is already taken into account through LDA calculations. Because of that, up to now there is n…
We have implemented the $GW$+dynamical mean field theory (DMFT) approach in the Vienna ab initio simulation package. Employing the interaction values obtained from the locally unscreened random phase approximation (RPA), we compare $GW$+DMFT and LDA+DMFT against each other and against experiment for SrVO$_3$. We observed a partial compensation of stronger electronic correlations due to the reduced $GW$ bandwidth and weaker correlations due to a larger screening of the RPA interaction, so that the obtained spectra are quite similar and well agree with experiment. Noteworthily, the $GW$+DMFT bet…
While the traditional local-density approximation (LDA) cannot describe Mott insulators, {\it ab-initio} determination of the Hubbard $U$, for example, limits LDA-plus dynamical mean field theory (DMFT) approaches. Here, we attempt to overcome these bottlenecks by achieving fusion of the quantum chemistry (QC) approach with DMFT. QC+DMFT supplants the LDA bandstructure by its QC counterpart as an input to DMFT. Using QC+DMFT, we show that undoped $La_{2}CuO_{4}$ is a $d$-Mott insulator, and qualitatively discuss the circulating current- and incoherent metal phase, at small but finite hole dopi…
We present an ab initio quantum theory of the finite temperature magnetism of iron and nickel. A recently developed technique which combines dynamical mean-field theory with realistic electronic structure methods, successfully describes the many-body features of the one electron spectra and the observed magnetic moments below and above the Curie temperature.
The spinless Falicov-Kimball model on the simple cubic lattice is analyzed in the Hubbard-I and dynamical mean field (DMFT) approximations. The Matsubara and real frequency itinerant electron Green's functions, the evolution of the system with doping, and the range of phase separation are found in two approximations. At large values of the on-site Coulomb repulsion both approximations give similar results. The phase separation can be also favorable for a more general model, where heavy electrons have a finite bandwidth. This indicates that the phase separation phenomenon is an inherent feature…
I present a critical overview of so-called "{\it ab initio}" DFT (density fuctional theory) based calculation schemes for the description of the electronic structure, energy spectrum, and optical response for strongly correlated 3$d$ oxides, in particular, crystal-field and charge transfer transitions as compared with an "old"\, cluster model that does generalize crystal-field and ligand-field theory. As a most instructive illustration of validity of numerous calculation techniques I address the prototypical 3$d$ insulator NiO predicted to be a metal in frames of a standard LDA (local density …
We present an ab initio quantum theory of the metal-insulator transition in Ti$_2$O$_3$. The recently developed cluster LDA+DMFT scheme is applied to describe the many-body features of this compound. The conventional single site DMFT cannot reproduce a low temperature insulating phase for any reasonable values of the Coulomb interaction. We show that the non-local Coulomb interactions and the strong chemical bonding within Ti-Ti pair is the origin of the small gap insulating ground state of Ti$_2$O$_3$.
Diagrammatic extensions of dynamical mean field theory (DMFT) such as the dynamical vertex approximation (D$Γ$A) 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 AbinitioD$Γ$A 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 se…
We investigate a photoinduced insulator-metal transition in the Falicov-Kimball model with the dynamical mean-field theory (DMFT) extended to nonequilibrium systems in periodic modulations in time. When the photon energy of the pump light is $Ω\approx U$ ($U$: the interaction strength), a Drude-like peak is found to grow in the optical conductivity spectrum, which is an evidence that the system is driven into a metallic state. During the transition, the band gap does not collapse, whereas the distribution function exhibits a non-monotonic behaviour away from the Fermi distribution. This indica…
We present a charge and self-energy self-consistent computational scheme for correlated systems based on the Korringa-Kohn-Rostoker (KKR) multiple scattering theory with the many-body effects described by the means of dynamical mean field theory (DMFT). The corresponding local multi-orbital and energy dependent self-energy is included into the set of radial differential equations for the single-site wave functions. The KKR Green's function is written in terms of the multiple scattering path operator, the later one being evaluated using the single-site solution for the $t$-matrix that in turn i…
The sensitivity of Density Functional Theory plus Dynamical Mean Field Theory calculations to different constructions of the correlated orbitals is investigated via a detailed comparison of results obtained for the quantum material NdNiO$_2$ using different Wannier and projector methods to define the correlation problem. Using the same interaction parameters we find that the different methods produce different results for the orbital and band basis mass enhancements and for the orbital occupancies, with differing implications regarding the importance of multiorbital effects and charge transfer…
The dynamical fluctuations in approaches such as dynamical mean-field theory (DMFT) allow for the self-consistent optimization of a local fragment, hybridized with a true correlated environment. We show that these correlated environmental fluctuations can instead be efficiently captured in a wave function perspective in a computationally cheap, frequency-independent, zero-temperature approach. This allows for a systematically improvable, short-time wave function analogue to DMFT, which entails a number of computational and numerical benefits. We demonstrate this approach to solve the correlate…
Predicting the compositional phase stability of strongly correlated electron materials is an outstanding challenge in condensed matter physics, requiring precise computations of total energies. In this work, we employ the density functional theory plus dynamical mean-field theory (DFT+DMFT) formalism to address local correlations due to transition metal d electrons on compositional phase stability in the prototype rechargeable battery cathode material LixCoO2, and detailed comparisons are made with the simpler DFT+U approach (i.e. the Hartree-Fock solution of the DMFT impurity problem). Local …
This review is devoted to generalization of dynamical mean-field theory (DMFT) for strongly correlated electronic systems towards the account of different types of additional interactions, necessary for correct physical description of many experimentally observed phenomena in such systems. As additional interactions we consider: (1) interaction of electrons with antiferromagnetic (or charge) fluctuations of order parameter in high-Tc superconductors leading to the formation of pseudogap state, (2) scattering of electrons on static disorder and its role in general picture of Anderson-Hubbard me…
The correlated Kondo insulator state of the plutonium monochalcogenides is investigated using the dynamical mean field theory (DMFT) and the local density approximation +U (LDA+U). The DMFT-dynamical fluctuations lead to a correlated insulator state at elevated temperature, in sharp contrast to the static LDA+U approach that fails to reproduce both the insulating behavior and anomalous lattice constant. The DMFT conversely predicts the experimentally observed anomalous increase of the gap with pressure and explains the lattice constant very well.
Materials with correlated electrons often respond very strongly to external or internal influences, leading to instabilities and states of matter with broken symmetry. This behavior can be studied theoretically either by evaluating the linear response characteristics, or by simulating the ordered phases of the materials under investigation. We developed the necessary tools within the dynamical mean-field theory (DMFT) to search for electronic instabilities in materials close to spin-state crossovers and to analyze the properties of the corresponding ordered states. This investigation, motivate…
We implemented the derivative of the free energy functional with respect to the atom displacements, so called force, within the combination of Density Functional Theory and the Embedded Dynamical Mean Field Theory. We show that in combination with the numerically exact quantum Monte Carlo (MC) impurity solver, the MC noise cancels to a great extend, so that the method can be used very efficiently for structural optimization of correlated electron materials. As an application of the method, we show how strengthening of the fluctuating moment in FeSe superconductor leads to a substantial increas…
We present a solution for the nonequilibrium dynamics of an interacting disordered system. The approach adapts the combination of the equilibrium dynamical mean field theory (DMFT) and the equilibrium coherent potential approximation (CPA) methods to the nonequilibrium many-body formalism, using the Kadanoff-Baym-Keldysh complex time contour, for the dynamics of interacting disordered systems away from equilibrium. We use our time domain solution to obtain the equilibrium density of states of the disordered interacting system described by the Anderson-Hubbard model, bypassing the necessity for…
We introduce natural atomic orbitals as the local projector to define the correlated subspace for DFT + DMFT (density functional theory plus dynamical mean-field theory) calculation. The natural atomic orbitals are found to be stably constructed against the number and the radius of basis orbitals. It can also be self-consistently updated inside the DFT+DMFT loop. The spatial localization, electron occupation and the degree of correlation are investigated and compared with other conventional techniques. As a `natural' choice to describe the electron numbers, adopting natural atomic orbitals has…
We propose to combine the Floquet formalism for systems in ac fields with the dynamical mean-field theory to study correlated electron systems periodically driven out of equilibrium by external fields such as intense laser light. This approach has a virtue that we can nonperturbatively include both the correlation effects and nonlinear effects due to the driving field, which is imperative in analyzing recent experiments for photoinduced phase transitions. In solving the problem, we exploit a general theorem that the Hamiltonian in a Floquet matrix form can be exactly diagonalized for single-ba…
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale via a (momentum dependent) ``external'' self-energy Σ_k. This external self-energy describes non-local dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT+Σ_k approach is used for the numerical solution of the weakly doped one--band Hubbard model with repulsive…
Ab initio calculation of the electronic properties of materials is a major challenge for solid state theory. Whereas the experience of forty years has proven density functional theory (DFT) in a suitable, e.g. local approximation (LDA) to give a satisfactory description in case electronic correlations are weak, materials with strongly correlated, say d- or f-electrons remain a challenge. Such materials often exhibit colossal responses to small changes of external parameters such as pressure, temperature, and magnetic field, and are therefore most interesting for technical applications. Encoura…
Many-body theories such as dynamical mean field theory (DMFT) have enabled the description of the electron exchange-correlation interactions that are missing in current density functional theory (DFT) calculations. However, there has been relatively little focus on the wavefunctions from these theories. We present the methodology of the newly developed Elk-TRIQS interface and how to calculate the DFT with DMFT (DFT+DMFT) wavefunctions, which can be used to calculate DFT+DMFT wavefunction dependent quantities. We illustrate this by calculating the electron localized function (ELF) in monolayer …
We give a summary of recent progress in the field of electronic structure calculations for materials with strong electronic Coulomb correlations. The discussion focuses on developments beyond the by now well established combination of density functional and dynamical mean field theory dubbed "LDA+DMFT". It is organized around the description of dynamical screening effects in the solid. Indeed, screening in the solid gives rise to dynamical local Coulomb interactions U(w) (Aryasetiawan et al 2004 Phys. Rev. B 70 195104), and this frequency-dependence leads to effects that cannot be neglected in…
We generalize the dynamical-mean field (DMFT) approximation by including into the DMFT equations some length scale via a momentum dependent ``external'' self-energy S(k). This external self-energy describes non-local dynamical correlations induced by short-ranged collective SDW-like antiferromagnetic spin (or CDW-like charge) fluctuations. At high enough temperatures these fluctuations can be viewed as a quenched Gaussian random field with finite correlation length. This generalized DMFT+Sk approach is used for the numerical solution of the weakly doped one-band Hubbard model with repulsive Co…
We analyze a correlated system in equilibrium with special emphasis on non-Hermitian topology inducing a skin effect. The pseudo-spectrum, computed by the real-space dynamical mean-field theory, elucidates that additional pseudo-eigenstates emerge for the open boundary condition in contrast to the dependence of the density of states on the boundary condition. We further discuss how the line-gap topology, another type of non-Hermitian topology, affects the pseudo-spectrum. Our numerical simulation clarifies that while the damping of the quasi-particles induces the non-trivial point-gap topology…
The electronic properties of paramagnetic V_2O_3 are investigated by the ab-initio computational scheme LDA+DMFT(QMC). This approach merges the local density approximation (LDA) with dynamical mean-field theory (DMFT) and uses numerically exact quantum Monte Carlo simulations (QMC) to solve the effective Anderson impurity model of DMFT. Starting with the crystal structure of metallic V_2O_3 and insulating (V_{0.962}Cr_{0.038})_2O_3 we find a Mott-Hubbard metal-insulator-like transition at a Coulomb interaction U\approx 5eV. The calculated spectrum is in very good agreement with experiment. Fur…
The description of realistic strongly correlated systems has recently advanced through the combination of density functional theory in the local density approximation (LDA) and dynamical mean field theory (DMFT). This LDA+DMFT method is able to treat both strongly correlated insulators and metals. Several interfaces between LDA and DMFT have been used, such as (N-th order) Linear Muffin Tin Orbitals or Maximally localized Wannier Functions. Such schemes are however either complex in use or additional simplifications are often performed (i.e., the atomic sphere approximation). We present an alt…
Dynamical mean field theory (DMFT) combined with the local density approximation (LDA) is widely used in solids to predict properties of correlated systems. In this paper, its application to one of the simplest strongly correlated systems, the hydrogen molecule H$_2$, is demonstrated to develop a parameter-free LDA+DMFT framework. We propose a method to calculate the exact intersection of LDA and DMFT that leads to highly accurate subtraction of the doubly counted correlation in both methods. When the exact double-counting treatment and a good projector to the correlated subspace are used, LDA…
We present a fully self-consistent combined GW and dynamical mean field (GW+DMFT) study of the spectral properties of the extended two-dimensional Hubbard model. The inclusion of the local dynamical vertex stemming from the DMFT self-energy and polarization is shown to cure the problems of self-consistent GW in the description of spectral properties. We calculate the momentum-resolved spectral functions, the two-particle polarization and electron loss spectra, and show that the inclusion of GW in extended DMFT leads to a narrowing of the quasi-particle width and more pronounced Hubbard bands i…
We develop, clarify and test various aspects of cluster methods dynamical mean field methods using a soluble toy model as a benchmark. We find that the Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and compare its convergence properties with those of the Dynamical Cluster Approximation (DCA). We propose and test improved estimators for the lattice self energy within C-DMFT.
The development of polynomial cost solvers for correlated quantum impurity models, with controllable errors, is a central challenge in quantum many-body physics, where these models find applications ranging from nano-science to the dynamical mean-field theory (DMFT). Here we describe how configuration interaction (CI) approximations to exact diagonalization (ED) may be used as solvers in DMFT. CI approximations retain the main advantages of ED, such as the ability to treat general interactions and off-diagonal hybridizations and to obtain real spectral information, but are of polynomial cost. …
We consider a doped Mott insulator in the large dimensionality limit within both the recently developed Extremely Correlated Fermi Liquid (ECFL) theory and the Dynamical Mean-Field Theory (DMFT). We show that the general structure of the ECFL sheds light on the rich frequency-dependence of the DMFT self-energy. Using the leading Fermi-liquid form of the two key auxiliary functions introduced in the ECFL theory, we obtain an analytical ansatz which provides a good quantitative description of the DMFT self-energy down to hole doping level 0.2. In particular, the deviation from Fermi-liquid behav…
The use of effective local Coulomb interactions that are dynamical, that is, frequency-dependent, is an efficient tool to describe the effect of long-range Coulomb interactions and screening thereof in solids. The dynamical character of the interaction introduces the coupling to screening degrees of freedom such as plasmons or particle-hole excitations into the many-body description. We summarize recent progress using these concepts, putting emphasis on dynamical mean field theory (DMFT) calculations with dynamical interactions ("doubly dynamical mean field theory"). We discuss the relation to…
We shed light on the interplay between structure and many-body effects relevant for itinerant ferromagnetism in LaAlO$_3$/SrTiO$_3$ heterostructures. The realistic correlated electronic structure is studied by means of the (spin-polarized) charge self-consistent combination of density functional theory (DFT) with dynamical mean-field theory (DMFT) beyond the realm of static correlation effects. Though many-body behavior is also active in the defect-free interface, a ferromagnetic instability occurs only with oxygen vacancies. A minimal Ti two-orbital $e_g$-$t_{2g}$ description for the correlat…
The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applicat…
We derive a dynamical mean-field theory for mixtures of interacting bosons and fermions on a lattice (BF-DMFT). The BF-DMFT is a comprehensive, thermodynamically consistent framework for the theoretical investigation of Bose-Fermi mixtures and is applicable for arbitrary values of the coupling parameters and temperatures. It becomes exact in the limit of high spatial dimensions d or coordination number Z of the lattice. In particular, the BF-DMFT treats normal and condensed bosons on equal footing and thus includes the effects caused by their dynamic coupling. Using the BF-DMFT we investigate …
These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field theory (DMFT) are then briefly reviewed. I emphasize the formal analogies with classical mean-field theory and density functional theory, through the construction of free-energy functionals of a local observable. I review the application of DMFT to the Mott transition, and compare to recent spectroscopy and transport experiments. The key role of the quasipart…
The nonequilibrium Green's functions (NEGF) approach is a versatile theoretical tool, which allows to describe the electronic structure, spectroscopy and dynamics of strongly correlated systems. The applicability of this method is, however, limited by its considerable computational cost. Due to the treatment of the full two-time dependence of the NEGF the underlying equations of motion involve a long-lasting non-Markovian memory kernel that results in at least a $N^3_t$ scaling in the number of time points $N_t$. The system's memory time is, however, reduced in the presence of a thermalizing b…
The LDA+DMFT (local density approximation combined with dynamical mean-field theory) computation scheme has been used to study spectral and magnetic properties of FeSi and Fe$_{1-x}$Co$_{x}$Si. Having compared different models we conclude that a correlated band insulator scenario in contrast to Kondo insulator model agrees with FeSi band structure as well as experimental data. Coulomb correlation effects lead to band narrowing of the states near the Fermi level with mass renormalization parameter $m^*\approx 2$ in agreement with the results of angle-resolved photoemission spectroscopy (ARPES).…
