Consistent LDA’ + DMFT—an unambiguous way to avoid double counting problem: NiO test

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 no accepted unique expression for the double counting correction in LDA + DMFT. To avoid this problem we propose here the consistent LDA’ + DMFT approach, where LDA exchange correlation contribution is explicitly excluded for correlated states (bands) during self-consistent band structure calculations. What is left out of Coulomb interaction for those strongly correlated states (bands) is its non-local part, which is not included in DMFT, and the local Hartreelike contribution. Then the double counting correction is uniquely reduced to the local Hartree contribution. Correlations for strongly correlated states are then directly accounted for via the standard DMFT. We further test the consistent LDA’ + DMFT scheme and compare it with conventional LDA + DMFT calculating the electronic structure of NiO. Opposite to the conventional LDA + DMFT our consistent LDA’ + DMFT approach unambiguously produces the insulating band structure in agreement with experiments.     

Computation of electronic structure and magnetic properties of strongly correlated materials with LDA+DMFT method

In this review, we describe general ideas of the LDA+DMFT method which merges dynamical mean-field theory (DMFT) and density functional theory (in particular the local density approximation (LDA)). Nowadays, the LDA+DMFT computational scheme is the most powerful numerical tool for studying physical properties of real materials and chemical compounds. It incorporates the advantage of DMFT to treat the full range of local dynamical Coulomb correlations and the ability of band methods to describe material-specific band dispersion caused by the lattice periodicity. We briefly discuss underlying physical ideas of LDA+DMFT and its mathematical implementation. Then different algorithms applied to solution of the DMFT impurity problem are briefly described. We then give examples of successful applications of the LDA+DMFT method to study spectral and magnetic properties of recently synthesized compounds like pnictide superconductors as well as classic charge-transfer systems NiO and MnO.     

面心立方金属铈的高压电子结构研究

本文简要介绍了我们开发的基于密度泛函理论和动力学平均场理论(DFT+DMFT)的全自洽的的计算程序,并运用该程序研究了面心立方金属铈的等结构相变.动力学平均场采用的是目前公认的最为准确和高效的连续时间蒙特卡罗方法作为杂质求解器.我们首先分别计算了γ和α相的电子态密度,该结果可以正确的描述两个相的电子结构特征.然后计算了不同温度下的相变前后的电子结构,从中可以得到电子结构在不同温度下的相变过程,与之前的实验结果一致.这一工作为以后进一步的金属铈的等结构相变研究打下了基础.     

Electronic structure calculations using dynamical mean field theory

The calculation of the electronic properties of materials is an important task of solid-state theory, albeit particularly difficult if electronic correlations are strong, e.g., in transition metals, their oxides and in f-electron systems. The standard approach to material calculations, the density functional theory in its local density approximation (LDA), incorporates electronic correlations only very rudimentarily and fails if the correlations are strong. Encouraged by the success of dynamical mean field theory (DMFT) in dealing with strongly correlated model Hamiltonians, physicists from the bandstructure and the many-body communities have joined forces and developed a combined LDA + DMFT method recently. Depending on the strength of electronic correlations, this new approach yields a weakly correlated metal as in the LDA, a strongly correlated metal or a Mott insulator. This approach is widely regarded as a breakthrough for electronic structure calculations of strongly correlated materials. We review this LDA + DMFT method and also discuss alternative approaches to employ DMFT in electronic structure calculations, e.g., by replacing the LDA part with the so-called GW approximation. Different methods to solve the DMFT equations are introduced with a focus on those that are suitable for realistic calculations with many orbitals. An overview of the successful application of LDA + DMFT to a wide variety of materials, ranging from Pu and Ce, to Fe and Ni, to numerous transition metal oxides, is given.     

面心立方金属铈的高压电子结构研究

本文简要介绍了我们开发的基于密度泛函理论和动力学平均场理论（DFT+DMFT）的全自洽的的计算程序,并运用该程序研究了面心立方金属铈的等结构相变. 动力学平均场采用的是目前公认的最为准确和高效的连续时间蒙特卡罗方法作为杂质求解器. 我们首先分别计算了 和 相的电子态密度,该结果可以正确的描述两个相的电子结构特征. 然后计算了不同温度下的相变前后的电子结构,从中可以得到电子结构在不同温度下的相变过程,与之前的实验结果一致. 这一工作为以后进一步的金属铈的等结构相变研究打下了基础.     

Consistent LDA’ + DMFT approach to the electronic structure of transition metal oxides: Charge transfer insulators and correlated metals

We discuss the recently proposed LDA’ + DMFT approach providing a 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 the 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 the LDA’ + DMFT Hamiltonian is consistently set in the local Hartree (fully localized limit, FLL) form of the Hubbard model interaction term. We present the results of extensive LDA’ + DMFT calculations of densities of states, spectral densities, and optical conductivity for most typical representatives of two wide classes of strongly correlated systems in the paramagnetic phase: charge transfer insulators (MnO, CoO, and NiO) and strongly correlated metals (SrVO₃ and Sr₂RuO₄). It is shown that for NiO and CoO systems, the LDA’ + DMFT approach qualitatively improves the conventional LDA + DMFT results with the FLL type of double counting, where CoO and NiO were obtained to be metals. Our calculations also include transition-metal 4s-states located near the Fermi level, missed in previous LDA + DMFT studies of these monoxides. General agreement with optical and the X-ray experiments is obtained. For strongly correlated metals, the LDA’ + DMFT results agree well with the earlier LDA + DMFT calculations and existing experiments. However, in general, LDA’ + DMFT results give better quantitative agreement with experimental data for band gap sizes and oxygen-state positions compared to the conventional LDA + DMFT method.     

Mott-hubbard metal-insulator transition in paramagnetic V2O3: an LDA+DMFT(QMC) study

The electronic properties of paramagnetic V2O3 are investigated by the computational scheme LDA+DMFT(QMC). This approach merges the local density approximation (LDA) with dynamical mean-field theory (DMFT) and uses quantum Monte Carlo simulations (QMC) to solve the effective Anderson impurity model of DMFT. Starting with the crystal structure of metallic V2O3 and insulating (V0.962Cr0.038)2O3 we find a Mott-Hubbard transition at a Coulomb interaction U approximately 5 eV. The calculated spectrum is in very good agreement with experiment. Furthermore, the orbital occupation and the spin state S = 1 determined by us agree with recent polarization dependent x-ray-absorption experiments.     

Calculation of photoemission spectra of the doped Mott insulator using LDA+DMFT(QMC)

The spectral properties of La_1–xSr_xTiO₃, a doped Mott insulator with strong Coulomb correlations, are calculated with the ab initio computational scheme LDA+DMFT(QMC). It starts from the non-interacting electronic band structure as calculated by the local density approximation (LDA), and introduces the missing correlations by the dynamical mean-field theory (DMFT), using numerically exact quantum Monte-Carlo (QMC) techniques to solve the resulting self-consistent multi-band single-impurity problem. The results of the LDA+DMFT(QMC) approach for the photoemission spectra of La_1–xSr_xTiO₃ are in good agreement with experiment and represent a considerable qualitative and quantitative improvement on standard LDA calculations. Received 20 May 2000 and Received in final form 27 July 2000     

Orbital switching and the first-order insulator-metal transition in paramagnetic V2O3

The first-order metal-insulator transition (MIT) in paramagnetic V2O3 is studied within the ab initio scheme LDA+DMFT, which merges the local density approximation (LDA) with dynamical mean field theory (DMFT). With a fixed value of the Coulomb U=6.0 eV, we show how the abrupt pressure driven MIT is understood in a new picture: a pressure-induced decrease of the trigonal distortion within the strong correlation scenario (which is not obtained within LDA). We find good quantitative agreement with (i) switch of the orbital occupation of (a(1g),e(pi)(g1),e(pi)(g2)) and the spin state S=1 across the MIT, (ii) thermodynamics and dc resistivity, and (iii) the one-electron spectral function, within this new scenario.     

Origin of “Hot Spots” in the pseudogap regime of Nd1.85Ce0.15CuO4: An LDA + DMFT + Σk study

The material-specific electronic band structure of the electron-doped high- T _c cuprate Nd_1.85Ce_0.15CuO₄ (NCCO) is calculated in the pseudogap regime using the recently developed generalized LDA + DMFT + Σ _k scheme. The LDA/DFT (density-functional theory within local density approximation) provides model parameters (hopping integral values and local Coulomb interaction strength) for the one-band Hubbard model, which is solved by the DMFT (dynamical mean-field theory). To take pseudogap fluctuations into account, the LDA + DMFT is supplied with an “external” k-dependent self-energy Σ _k that describes interaction of correlated conducting electrons with nonlocal Heisenberg-like antiferromagnetic (AFM) spin fluctuations responsible for the pseudogap formation. Within this LDA + DMFT + Σ _k approach, we demonstrate the formation of pronounced hot spots on the Fermi surface (FS) map in NCCO, opposite to our recent calculations for Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212), which have produced a rather extended region of the FS “destruction.” There are several physical reasons for this fact: (i) the hot spots in NCCO are located closer to the Brillouin zone center; (ii) the correlation length ξ of AFM fluctuations is longer for NCCO; (iii) the pseudogap potential Δ is stronger than in Bi2212. Comparison of our theoretical data with recent bulk-sensitive high-energy angle-resolved photoemission (ARPES) data for NCCO provides good semiquantitative agreement. Based on that comparison, an alternative explanation of the van Hove singularity at −0.3 eV is proposed. Optical conductivity for both Bi2212 and NCCO is also calculated within the LDA + DMFT + Δ _k scheme and is compared with experimental results, demonstrating satisfactory agreement. The text was submitted by the authors in English.     

Pseudogap behavior in Bi<Subscript>2</Subscript>Ca<Subscript>2</Subscript>SrCu<Subscript>2</Subscript>O<Subscript>8</Subscript>: Results of the generalized dynamical mean-field approach

Pseudogap phenomena are observed for the normal underdoped phase of different high-T _c cuprates. Among others, the Bi₂Sr₂CaCu₂O_{8 − δ} (Bi2212) compound is one of the most studied experimentally. To describe the pseudogap regime in Bi2212, we use a novel generalized ab initio LDA + DMFT + Σ_k hybrid scheme. This scheme is based on the strategy of one of the most powerful computational tools for real correlated materials: the local density approximation (LDA) + dynamical mean-field theory (DMFT). Conventional LDA + DMFT equations are here supplied with an additional (momentum-dependent) self-energy Σ_k in the spirit of our recently proposed DMFT + Σ_k approach taking into account pseudogap fluctuations. In the present model, Σ_k describes nonlocal correlations induced by short-range collective Heisenberg-like antiferromagnetic spin fluctuations. The effective single-impurity problem of the DMFT is solved by the numerical renormalization group (NRG) method. Material-specific model parameters for the effective x ² − y ² orbital of Cu-3d shell of the Bi2212 compound, e.g., the values of intra-and interlayer hopping integrals between different Cu sites, the local Coulomb interaction U, and the pseudogap potential Δ were obtained within the LDA and LDA + DMFT schemes. Here, we report on the theoretical LDA + DMFT + Σ_k quasiparticle band dispersion and damping, Fermi surface renormalization, momentum anisotropy of (quasi)static scattering, densities of states, spectral densities, and angular-resolved photoemission (ARPES) spectra, taking into account pseudogap and bilayer splitting effects for normal (slightly) underdoped Bi2212 (δ = 0.15). We show that LDA + DMFT + Σ_k successfully describes strong (pseudogap) scattering close to Brillouin zone boundaries. Our calculated LDA + DMFT + Σ_k Fermi surfaces and ARPES spectra in the presence of pseudogap fluctuations are almost insensitive to the bilayer splitting strength. However, our LDA-calculated value of bilayer splitting is rather small to describe the experimentally observed peak-dip-hump structure. The results obtained are in good semiquantitative agreement with various recent ARPES experiments. The article was submitted by the authors in English.     

First-principles approach to the electronic structure of strongly correlated systems: combining the GW approximation and dynamical mean-field theory

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.     

Pseudogap behavior in the emery model for the electron-doped superconductor Nd2 − x Ce x CuO4: Multiband LDA + DMFT + Σk approach

We propose a generalization of the LDA + DMFT + Σ _k approach to the multiband case, in which correlated and uncorrelated states are present in the model simultaneously. Using the multiband version of the LDA + DMFT + Σ _k approach, we calculate the density of states and spectral functions for the Emery model in a wide energy interval around the Fermi level. We also obtain the Fermi surfaces for the electron-doped high-temperature superconductor Nd_{2 ? x} Ce _x CuO₄ in the pseudogap phase. The self-energy part Σ _k introduced additionally to take into account pseudogap fluctuations describes the nonlocal interaction of correlated electrons with collective Heisenberg short-range spin fluctuations. To solve the effective impurity model, the numerical renorm-group (NRG) method is used for the DMFT equations. Good qualitative agreement of the Fermi surfaces calculated using the LDA + DMFT + Σ _k approach and experimental angle-resolved photoemission spectroscopic data is attained. The stability of the dielectric solution with charge transfer in the Emery model with correction for double counting is analyzed in the Appendix.     

Electronic Structure of InCo2As2 and KInCo4As4: LDA + DMFT

JETP Letters - A comparative analysis of the electronic structure obtained in the DFT/LDA and LDA + DMFT approaches of the possible isostructural analogues of iron superconductors InCo2As2 and...     

Dynamical mean-field approach to materials with strong electronic correlations

We review recent results on the properties of materials with correlated electrons obtained within the LDA+DMFT approach, a combination of a conventional band structure approach based on the local density approximation (LDA) and the dynamical mean-field theory (DMFT). The application to four outstanding problems in this field is discussed: (i) we compute the full valence band structure of the charge-transfer insulator NiO by explicitly including the p-d hybridization, (ii) we explain the origin for the simultaneously occuring metal-insulator transition and collapse of the magnetic moment in MnO and Fe₂O₃, (iii) we describe a novel GGA+DMFT scheme in terms of plane-wave pseudopotentials which allows us to compute the orbital order and cooperative Jahn-Teller distortion in KCuF₃ and LaMnO₃, and (iv) we provide a general explanation for the appearance of kinks in the effective dispersion of correlated electrons in systems with a pronounced three-peak spectral function without having to resort to the coupling of electrons to bosonic excitations. These results provide a considerable progress in the fully microscopic investigations of correlated electron materials.     

Effect of correlation on electronic properties of NiO: A study from dynamical mean field theory

In order to describe a typical strongly correlated insulator NiO at electronic level, we perform a first principles calculation for temperature effect on electronic properties of NiO using a many-body method merging local density approximation (LDA) with dynamical mean field theory, so called the LDA+DMFT scheme. Band gap and density of states (DOS) are in good agreement with available experimental data and theoretical calculations, and Ni d-e_g and d-t_2g components both exhibit insulating character. Calculated hybridization functions indicate that Ni d-e_g states strongly hybrid with O p states at T = 58 K, 116 K, 145 K, 232 K and 464 K. In order to compare with experimental angle-resolved photoemission spectrum (ARPES), we also calculate momentum-resolved electronic spectrum function, which is established that obvious electronic excitation mainly arises from Ni d-t_2g states at temperature T = 232 K, and the spectrum functions between −0.5 eV and 0.0 eV are almost symmetric about certain k points. Finally, we analyze the effect of temperature on electronic properties of NiO by carrying out LDA+DMFT calculations at T = 58 K, 116 K, 145 K, 232 K and 464 K, respectively. Results show that temperature mainly influences the valence states of spectrum function and hybridization function, in particular high-lying states close to Fermi level. Electronic excitation distributions and spectrum characters in electronic spectrum function are also discussed.     

Nonlocal Coulomb interactions and metal-insulator transition in Ti2O3: a cluster LDA+DMFT approach

We present an ab initio quantum theory of the metal-insulator transition in Ti2O3. 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 nonlocal Coulomb interactions and the strong chemical bonding within the Ti-Ti pair is the origin of the small gap insulating ground state of Ti2O3.