233 research outputs found
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
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