1,099 research outputs found

### Dynamical Mean-Field Theory - from Quantum Impurity Physics to Lattice Problems

Since the first investigation of the Hubbard model in the limit of infinite
dimensions by Metzner and Vollhardt, dynamical mean-field theory (DMFT) has
become a very powerful tool for the investigation of lattice models of
correlated electrons. In DMFT the lattice model is mapped on an effective
quantum impurity model in a bath which has to be determined self-consistently.
This approach lead to a significant progress in our understanding of typical
correlation problems such as the Mott transition; furthermore, the combination
of DMFT with ab-initio methods now allows for a realistic treatment of
correlated materials. The focus of these lecture notes is on the relation
between quantum impurity physics and the physics of lattice models within DMFT.
Issues such as the observability of impurity quantum phase transitions in the
corresponding lattice models are discussed in detail.Comment: 18 pages, 5 figures, invited paper for the Proceedings of the "3rd
International Summer School on Strongly Correlated Systems, Debrecen, 2004

### ``Linearized'' Dynamical Mean-Field Theory for the Mott-Hubbard transition

The Mott-Hubbard metal-insulator transition is studied within a simplified
version of the Dynamical Mean-Field Theory (DMFT) in which the coupling between
the impurity level and the conduction band is approximated by a single pole at
the Fermi energy. In this approach, the DMFT equations are linearized, and the
value for the critical Coulomb repulsion U_{\rm c} can be calculated
analytically. For the symmetric single-band Hubbard model at zero temperature,
the critical value is found to be given by 6 times the square root of the
second moment of the free (U=0) density of states. This result is in good
agreement with the numerical value obtained from the Projective Selfconsistent
Method and recent Numerical Renormalization Group calculations for the Bethe
and the hypercubic lattice in infinite dimensions. The generalization to more
complicated lattices is discussed. The ``linearized DMFT'' yields plausible
results for the complete geometry dependence of the critical interaction.Comment: 8 page

### Magnetism and Phase Separation in the Ground State of the Hubbard Model

We discuss the ground state magnetic phase diagram of the Hubbard model off
half filling within the dynamical mean-field theory. The effective
single-impurity Anderson model is solved by Wilson's numerical renormalization
group calculations, adapted to symmetry broken phases. We find a phase
separated, antiferromagnetic state up to a critical doping for small and
intermediate values of U, but could not stabilise a Neel state for large U and
finite doping. At very large U, the phase diagram exhibits an island with a
ferromagnetic ground state. Spectral properties in the ordered phases are
discussed.Comment: 9 pages, 11 figure

### Modeling molecular conduction in DNA wires: Charge transfer theories and dissipative quantum transport

Measurements of electron transfer rates as well as of charge transport
characteristics in DNA produced a number of seemingly contradictory results,
ranging from insulating behaviour to the suggestion that DNA is an efficient
medium for charge transport. Among other factors, environmental effects appear
to play a crucial role in determining the effectivity of charge propagation
along the double helix. This chapter gives an overview over charge transfer
theories and their implication for addressing the interaction of a molecular
conductor with a dissipative environment. Further, we focus on possible
applications of these approaches for charge transport through DNA-based
molecular wires

### Quantum Critical Points in Quantum Impurity Systems

The numerical renormalization group method is used to investigate zero
temperature phase transitions in quantum impurity systems, in particular in the
soft-gap Anderson model, where an impurity couples to a non-trivial fermionic
bath. In this case, zero temperature phase transitions occur between two
different phases whose fixed points can be built up of non-interacting
single-particle states. However, the quantum critical point cannot be described
by non-interacting fermionic or bosonic excitations.Comment: 2 pages, 3 figures, submitted to SCES'0

### Numerical Renormalization Group for Impurity Quantum Phase Transitions: Structure of Critical Fixed Points

The numerical renormalization group method is used to investigate zero
temperature phase transitions in quantum impurity systems, in particular in the
particle-hole symmetric soft-gap Anderson model. The model displays two stable
phases whose fixed points can be built up of non-interacting single-particle
states. In contrast, the quantum phase transitions turn out to be described by
interacting fixed points, and their excitations cannot be described in terms of
free particles. We show that the structure of the many-body spectrum of these
critical fixed points can be understood using renormalized perturbation theory
close to certain values of the bath exponents which play the role of critical
dimensions. Contact is made with perturbative renormalization group
calculations for the soft-gap Anderson and Kondo models. A complete description
of the quantum critical many-particle spectra is achieved using suitable
marginal operators; technically this can be understood as epsilon-expansion for
full many-body spectra.Comment: 14 pages, 12 figure

### Anderson impurity in a correlated conduction band

We investigate the physics of a magnetic impurity with spin 1/2 in a
correlated metallic host. Describing the band by a Hubbard Hamiltonian, the
problem is analyzed using dynamical mean-field-theory in combination with
Wilson's nonperturbative numerical renormalization group. We present results
for the single-particle density of states and the dynamical spin susceptibility
at zero temperature. New spectral features (side peaks) are found which should
be observable experimentally. In addition, we find a general enhancement of the
Kondo scale due to correlations. Nevertheless, in the metallic phase, the Kondo
scale always vanishes exponentially in the limit of small hybridization.Comment: Final version, 4 pages RevTeX, 8 eps figures include

### Phase diagram of the frustrated Hubbard model

The Mott-Hubbard metal-insulator transition in the paramagnetic phase of the
one-band Hubbard model has long been used to describe similar features in real
materials like V$_2$O$_3$. Here we show that this transition is hidden inside a
rather robust antiferromagnetic insulator even in the presence of comparatively
strong magnetic frustration. This result raises the question of the relevance
of the Mott-Hubbard metal-insulator transition for the generic phase diagram of
the one-band Hubbard model.Comment: 4 pages, 6 figure

### On X-ray-singularities in the f-electron spectral function of the Falicov-Kimball model

The f-electron spectral function of the Falicov-Kimball model is calculated
within the dynamical mean-field theory using the numerical renormalization
group method as the impurity solver. Both the Bethe lattice and the hypercubic
lattice are considered at half filling. For small U we obtain a single-peaked
f-electron spectral function, which --for zero temperature-- exhibits an
algebraic (X-ray) singularity ($|\omega|^{-\alpha}$) for $\omega \to 0$. The
characteristic exponent $\alpha$ depends on the Coulomb (Hubbard) correlation
U. This X-ray singularity cannot be observed when using alternative
(Keldysh-based) many-body approaches. With increasing U, $\alpha$ decreases and
vanishes for sufficiently large U when the f-electron spectral function
develops a gap and a two-peak structure (metal-insulator transition).Comment: 8 pages, 8 figures, revte

### Numerical renormalization group study of the symmetric Anderson-Holstein model: phonon and electron spectral functions

We study the symmetric Anderson-Holstein (AH) model at zero temperature with
Wilson's numerical renormalization group (NRG) technique to study the interplay
between the electron-electron and electron-phonon interactions. An improved
method for calculating the phonon propagator using the NRG technique is
presented, which turns out to be more accurate and reliable than the previous
works in that it calculates the phonon renormalization explicitly and satisfies
the boson sum rule better. The method is applied to calculate the renormalized
phonon propagators along with the electron propagators as the onsite Coulomb
repulsion $U$ and electron-phonon coupling constant $g$ are varied. As $g$ is
increased, the phonon mode is successively renormalized, and for $g \gtrsim
g_{co}$ crosses over to the regime where the mode splits into two components,
one of which approaches back to the bare frequency and the other develops into
a soft mode. The initial renormalization of the phonon mode, as $g$ is
increased from 0, depends on $U$ and the hybridization $\Delta$; it gets
softened (hardened) for $U \gtrsim (\lesssim) U_s (\Delta)$. Correlated with
the emergence of the soft mode is the central peak of the electron spectral
function severely suppressed. These NRG calculations will be compared with the
standard Green's function results for the weak coupling regime to understand
the phonon renormalization and soft mode.Comment: 18 pages, 4 figures. Submitted to Phys. Rev.

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