Dynamical Mean-Field Theory of Electronic Correlations in Models and Materials

The concept of electronic correlations plays an important role in modern condensed matter physics. It refers to interaction effects which cannot be explained within a static mean-field picture as provided by Hartree-Fock theory. Electronic correlations can have a very strong influence on the properties of materials. For example, they may turn a metal into an insulator (Mott-Hubbard metal-insulator transition). In these lecture notes I (i) introduce basic notions of the physics of correlated electronic systems, (ii) discuss the construction of mean-field theories by taking the limit of high lattice dimensions, (iii) explain the simplifications of the many-body perturbation theory in this limit which provide the basis for the formulation of a comprehensive mean-field theory for correlated fermions, the dynamical mean-field theory (DMFT), (v) derive the DMFT self-consistency equations, and (vi) apply the DMFT to investigate electronic correlations in models and materials.Comment: Lecture Notes (65 pages, 26 figures), published version including corrections, published in "Lectures on the Physics of Strongly Correlated Systems XIV", eds. A. Avella and F. Mancini, AIP Conference Proceedings (2010

Mixtures of correlated bosons and fermions: Dynamical mean-field theory for normal and condensed phases

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 two different interaction models of correlated lattice bosons and fermions, one where all particles are spinless (model I) and one where fermions carry a spin one-half (model II). In model I the local, repulsive interaction between bosons and fermions can give rise to an attractive effective interaction between the bosons. In model II it can also lead to an attraction between the fermions.Comment: 11 pages, removed style-files for Greek letter

Exact many-electron ground states on diamond and triangle Hubbard chains

We construct exact ground states of interacting electrons on triangle and diamond Hubbard chains. The construction requires (i) a rewriting of the Hamiltonian into positive semidefinite form, (ii) the construction of a many-electron ground state of this Hamiltonian, and (iii) the proof of the uniqueness of the ground state. This approach works in any dimension, requires no integrability of the model, and only demands sufficiently many microscopic parameters in the Hamiltonian which have to fulfill certain relations. The scheme is first employed to construct exact ground state for the diamond Hubbard chain in a magnetic field. These ground states are found to exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior, which can be tuned by changing the magnetic flux, local potentials, or electron density. Detailed proofs of the uniqueness of the ground states are presented. By the same technique exact ground states are constructed for triangle Hubbard chains and a one-dimensional periodic Anderson model with nearest-neighbor hybridization. They permit direct comparison with results obtained by variational techniques for f-electron ferromagnetism due to a flat band in CeRh3B2.Comment: 21 pages, 9 figures. Will be published in the proceedings of YKIS2007 conference (November 2007, Kyoto) as a special issue of Progress of Theoretical Physics Supplement. Fig.6 correcte

Route to ferromagnetism in organic polymers

Employing a rigorous theoretical method for the construction of exact many-electron ground states we prove that interactions can be employed to tune a bare dispersive band structure such that it develops a flat band. Thereby we show that pentagon chain polymers with electron densities above half filling may be designed to become ferromagnetic or half metallic.Comment: 11 pages, 3 figure

Emergence of a common energy scale close to the orbital-selective Mott transition

We calculate the spectra and spin susceptibilities of a Hubbard model with two bands having different bandwidths but the same on-site interaction, with parameters close to the orbital-selective Mott transition, using dynamical mean-field theory. If the Hund's rule coupling is sufficiently strong, one common energy scale emerges which characterizes both the location of kinks in the self-energy and extrema of the diagonal spin susceptibilities. A physical explanation of this energy scale is derived from a Kondo-type model. We infer that for multi-band systems local spin dynamics rather than spectral functions determine the location of kinks in the effective band structure.Comment: 5 pages, 5 figure

Exact many-electron ground states on the diamond Hubbard chain

Exact ground states of interacting electrons on the diamond Hubbard chain in a magnetic field are constructed which exhibit a wide range of properties such as flat-band ferromagnetism and correlation induced metallic, half-metallic or insulating behavior. The properties of these ground states can be tuned by changing the magnetic flux, local potentials, or electron density.Comment: 4 pages, 2 figure