5,514 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
Conservation laws in disordered electron systems: Thermodynamic limit and configurational averaging
We discuss conservation of probability in noniteracting disordered electron
systems. We argue that although the norm of the electron wave function is
conserved in individual realizations of the random potential, we cannot extend
this conservation law easily to configurationally averaged systems in the
thermodynamic limit. A direct generalization of the norm conservation to
averaged functions is hindered by the existence of localized states breaking
translational invariance. Such states are elusive to the description with
periodic Bloch waves. Mathematically this difficulty is manifested through the
diffusion pole in the electron-hole irreducible vertex. The pole leads to a
clash with analyticity of the self-energy, reflecting causality of the theory,
when norm conservation is enforced by the Ward identity between one- and
two-particle averaged Green functions.Comment: REVTeX4, 8 pages, no figure
Canted Antiferromagnetic Order of Imbalanced Fermi-Fermi mixtures in Optical Lattices by Dynamical Mean-Field Theory
We investigate antiferromagnetic order of repulsively interacting fermionic
atoms in an optical lattice by means of Dynamical Mean-Field Theory (DMFT).
Special attention is paid to the case of an imbalanced mixture. We take into
account the presence of an underlying harmonic trap, both in a local density
approximation and by performing full Real-Space DMFT calculations. We consider
the case that the particle density in the trap center is at half filling,
leading to an antiferromagnetic region in the center, surrounded by a Fermi
liquid region at the edge. In the case of an imbalanced mixture, the
antiferromagnetism is directed perpendicular to the ferromagnetic polarization
and canted. We pay special attention to the boundary structure between the
antiferromagnetic and the Fermi liquid phase. For the moderately strong
interactions considered here, no Stoner instability toward a ferromagnetic
phase is found. Phase separation is only observed for strong imbalance and
sufficiently large repulsion.Comment: 7 pages, 5 figures, published versio
Self-Consistent Theory of Anderson Localization: General Formalism and Applications
The self-consistent theory of Anderson localization of quantum particles or
classical waves in disordered media is reviewed. After presenting the basic
concepts of the theory of Anderson localization in the case of electrons in
disordered solids, the regimes of weak and strong localization are discussed.
Then the scaling theory of the Anderson localization transition is reviewed.
The renormalization group theory is introduced and results and consequences are
presented. It is shown how scale-dependent terms in the renormalized
perturbation theory of the inverse diffusion coefficient lead in a natural way
to a self-consistent equation for the diffusion coefficient. The latter
accounts quantitatively for the static and dynamic transport properties except
for a region near the critical point. Several recent applications and
extensions of the self-consistent theory, in particular for classical waves,
are discussed.Comment: 25 pages, 2 figures; published version including correction
Microscopic conditions favoring itinerant ferromagnetism: Hund's rule coupling and orbital degeneracy
The importance of Hund's rule coupling for the stabilization of itinerant
ferromagnetism is investigated within a two-band Hubbard model. The magnetic
phase diagram is calculated by finite-temperature quantum Monte Carlo
simulations within the dynamical mean-field theory. Ferromagnetism is found in
a broad range of electron fillings whereas antiferromagnetism exists only near
half filling. The possibility of orbital ordering at quarter filling is also
analyzed.Comment: 5 pages, 6 figures, RevTeX, final version contains an additional
phase diagram for smaller Hund's rule coupling. to appear in Eur. Phys. J. B
(1998
Superfluid Helium 3: Link between Condensed Matter Physics and Particle Physics
The discovery of the superfluid phases of Helium 3 in 1971 opened the door to
one of the most fascinating systems known in condensed matter physics.
Superfluidity of Helium 3, originating from pair condensation of Helium 3
atoms, turned out to be the ideal testground for many fundamental concepts of
modern physics, such as macroscopic quantum phenomena, (gauge-)symmetries and
their spontaneous breakdown, topological defects, etc. Thereby the superfluid
phases of Helium 3 enriched condensed matter physics enormously. In particular,
they contributed significantly - and continue to do so - to our understanding
of various other physical systems, from heavy fermion and high-Tc
superconductors all the way to neutron stars, particle physics, gravity and the
early universe. A simple introduction into the basic concepts and questions is
presented.Comment: 11 pages, 2 figures; to be published in Acta Physica Polonica B
[Proceedings of the XL Jubilee Cracow School of Theoretical Physics on
"Quantum Phase Transitions in High Energy and Condensed Matter Physics"; 3-11
June, 2000, Zakopane, Poland
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
Ferromagnetism and non-local correlations in the Hubbard model
We study the possibility and stability of band-ferromagnetism in the
single-band Hubbard model for the simple cubic (SC) lattice. A non-local
self-energy is derived within a modified perturbation theory. Results for the
spectral density and quasiparticle density of states are shown with special
attention to the effects of k-dependence. The importance of non-local
correlations for the fulfillment of the Mermin-Wagner theorem is our main
result. A phase digram showing regions of ferromagnetic order is calculated for
the three dimensional lattice. Besides, we show results for the optical
conductivity and prove that already the renormalized one-loop contribution to
the conductivity cancels the Drude peak exactly in case of a local self-energy
which is not anymore true for a non-local self-energy.Comment: 11 pages, 10 figures, accepted for publication in PR
Anderson localization as position-dependent diffusion in disordered waveguides
We show that the recently developed self-consistent theory of Anderson
localization with a position-dependent diffusion coefficient is in quantitative
agreement with the supersymmetry approach up to terms of the order of
(with the dimensionless conductance in the absence of interference
effects) and with large-scale {\it ab-initio} simulations of the classical wave
transport in disordered waveguides, at least for . In the
latter case, agreement is found even in the presence of absorption. Our
numerical results confirm that in open disordered media, the onset of Anderson
localization can be viewed as position-dependent diffusion.Comment: 6 pages, 3 figure
- …