We review the dynamical mean-field theory of strongly correlated electron systems which is based on a mapping of lattice models onto quantum impurity models subject to a self-consistency condition. This mapping is exact for models of correlated electrons in the limit of large lattice coordination (or infinite spatial dimensions). It extends the standard mean-field construction from classical statistical mechanics to quantum problems. We discuss the physical ideas underlying this theory and its mathematical derivation. Various analytic and numerical techniques that have been developed recently in order to analyze and solve the dynamical mean-field equations are reviewed and compared to each other. The method can be used for the determination of phase diagrams (by comparing the stability of various types of long-range order), and the calculation of thermodynamic properties, one-particle Green's functions, and response functions. We review in detail the recent progress in understanding the Hubbard model and the Mott metal-insulator transition within this approach, including some comparison to experiments on three-dimensional transition-metal oxides. We present an overview of the rapidly developing field of applications of this method to other systems. The present limitations of the approach, and possible extensions of the formalism are finally discussed. Computer programs for the numerical implementation of this method are also provided with this article.

Dynamical mean-field theory of strongly correlated fermion systems and the limit of infinite dimensions

Electronic excitations lie at the origin of most of the commonly measured spectra. However, the first-principles computation of excited states requires a larger effort than ground-state calculations, which can be very efficiently carried out within density-functional theory. On the other hand, two theoretical and computational tools have come to prominence for the description of electronic excitations. One of them, many-body perturbation theory, is based on a set of Green’s-function equations, starting with a one-electron propagator and considering the electron-hole Green’s function for the response. Key ingredients are the electron’s self-energy S and the electron-hole interaction. A good approximation for S is obtained with Hedin’s GW approach, using density-functional theory as a zero-order solution. First-principles GW calculations for real systems have been successfully carried out since the 1980s. Similarly, the electron-hole interaction is well described by the Bethe-Salpeter equation, via a functional derivative of S. An alternative approach to calculating electronic excitations is the time-dependent density-functional theory (TDDFT), which offers the important practical advantage of a dependence on density rather than on multivariable Green’s functions. This approach leads to a screening equation similar to the Bethe-Salpeter one, but with a two-point, rather than a four-point, interaction kernel. At present, the simple adiabatic local-density approximation has given promising results for finite systems, but has significant deficiencies in the description of absorption spectra in solids, leading to wrong excitation energies, the absence of bound excitonic states, and appreciable distortions of the spectral line shapes. The search for improved TDDFT potentials and kernels is hence a subject of increasing interest. It can be addressed within the framework of many-body perturbation theory: in fact, both the Green’s functions and the TDDFT approaches profit from mutual insight. This review compares the theoretical and practical aspects of the two approaches and their specific numerical implementations, and presents an overview of accomplishments and work in progress.

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Electronic excitations: density-functional versus many-body Green's-function approaches

http://sces.phys.utk.edu/mostcited/mc1_1114.pdf

Colossal Magnetoresistant Materials: The Key Role of Phase Separation

The purpose of this critical review is to give a representative and comprehensive overview of the arising developments in the field of magnetic metal–organic frameworks, in particular those containing cobalt(II). We examine the diversity of magnetic exchange interactions between nearest-neighbour moment carriers, covering from dimers to oligomers and discuss their implications in infinite chains, layers and networks, having a variety of topologies. We progress to the different forms of short-range magnetic ordering, giving rise to single-molecule-magnets and single-chain-magnets, to long-range ordering of two- and three-dimensional networks (323 references).

Magnetic metal-organic frameworks.

Recent technical advances in the atomic-scale synthesis of oxide heterostructures have provided a fertile new ground for creating novel states at their interfaces. Different symmetry constraints can be used to design structures exhibiting phenomena not found in the bulk constituents. A characteristic feature is the reconstruction of the charge, spin and orbital states at interfaces on the nanometre scale. Examples such as interface superconductivity, magneto-electric coupling, and the quantum Hall effect in oxide heterostructures are representative of the scientific and technological opportunities in this rapidly emerging field.

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Emergent phenomena at oxide interfaces

Superexchange interaction and symmetry properties of electron orbitals

The electron correlation in a narrow energy band is discussed taking into account the multiple scattering between two electrons. The discussion is an adaptation of Brueckner's theory of nuclear matter. It is assumed that electrons interact with each other only when they are at the same atom. The effect of the electron correlation depends in an intricate way on the energy spectrum of a given band. An approximate expression of the effective magnitude of the interaction is derived. The condition for the occurrence of ferromagnetism is investigated for various types of bands. The ferromagnetism of Ni and the paramagnetism of Pd can be understood reasonably through the present approach. The degeneracy of the d bands is taken into account in the discussion of these metals. (auth)

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Electron Correlation and Ferromagnetism of Transition Metals

A theoretical overview of the cooperative Jahn-Teller effect in the insulating phase is given. We obtain an effective Hamiltonian of an interaction between the orbital states of the Jahn-Teller ions through a canonical transformation, which associates each electronic state with a local lattice distortion, and by use of the mean field approximation. The effective Hamiltonian yields a simple unified picture of cooperative distortions of various types. The competing effect of the spin-orbit coupling is discussed also. Electron itinerancy is briefly discussed at the end.

Crystal Distortion in Magnetic Compounds

The magnetic properties of antiferromagnetics, FeO and CoO, are investigated from the standpoint of the one-ion approximation. In their crystalline field of cubic symmetry the orbital degeneracies of Fe++ and Co++ are not completely removed and the r<siduaJ orbital angular momenta play an im­ portant role through the presence of the spin-orbit coupling and through the direct effect of the orbital magnetic moments. After deriving the effective Hamiltonian for these degenerate cases, which corresponds to the Hamiltonian derived by Pryce for the non-degenerate case, we discuss the para­ magnetic susceptibility, the Nee! temperature and the state of each ion at absolute zero. We can give a reasonable quantitative interpretation of the susceptibility of CoO in paramagnetic state and obtain a good agreement with experiment for the magnetic moment of CoO in antiferromagnetic state. For FeO, sufficiently reliable data to compare with theory are not available at present, but a preliminary comparison is made. Further, in connection with the investigation of the validity of our theory, the origins of the crystalline field are discussed and it is pointed out that the covalent effect may make an appreciable contribution to the crystalline field.

Theory of the Magnetic Properties of Ferrous and Cobaltous Oxides, I

The electronic structure of Ni base ferromagnetic alloys with Co, Fe, Mn and Cr is discussed on the basis of the coherent potential approximation combined with the Hartree-Fock approximation for the electron-electron interaction. Calculations are carried out by use of a tight-binding single band model. With consistent choices of parameters the concentration dependences of the average magnetic moment of each constituent atom, the saturation magnetization, and the density of states at the Fermi level are calculated. The significance and limit of the coherent potential approximation for calculating the electronic structure of the ferromagnetic alloys are discussed in some detail.

Junjiro Kanamori

Papers

Superexchange interaction and symmetry properties of electron orbitals

Electron Correlation and Ferromagnetism of Transition Metals

Crystal Distortion in Magnetic Compounds

Theory of the Magnetic Properties of Ferrous and Cobaltous Oxides, I

Calculation of Electronic Structure of Fe Base bcc Ferromagnetic Alloys in the Coherent Potential Approximation