42 research outputs found

### Shot noise in tunneling transport through molecules and quantum dots

We consider electrical transport through single molecules coupled to metal
electrodes via tunneling barriers. Approximating the molecule by the Anderson
impurity model as the simplest model which includes Coulomb charging effects,
we extend the ``orthodox'' theory to expand current and shot noise
systematically order by order in the tunnel couplings. In particular, we show
that a combined measurement of current and shot noise reveals detailed
information of the system even in the weak-coupling limit, such as the ratio of
the tunnel-coupling strengths of the molecule to the left and right electrode,
and the presence of the Coulomb charging energy. Our analysis holds for
single-level quantum dots as well.Comment: 8 page

### A note on cluster methods for strongly correlated electron systems

We develop, clarify and test various aspects of cluster methods dynamical
mean field methods using a soluble toy model as a benchmark. We find that the
Cellular Dynamical Mean Field Theory (C-DMFT) converges very rapidly and
compare its convergence properties with those of the Dynamical Cluster
Approximation (DCA). We propose and test improved estimators for the lattice
self energy within C-DMFT.Comment: 5 pages, 3 figures; major change

### A novel FLEX supplemented QMC approach to the Hubbard model

This paper introduces a novel ansatz-based technique for solution of the
Hubbard model over two length scales. Short range correlations are treated
exactly using a dynamical cluster approximation QMC simulation, while
longer-length-scale physics requiring larger cluster sizes is incorporated
through the introduction of the fluctuation exchange (FLEX) approximation. The
properties of the resulting hybrid scheme are examined, and the description of
local moment formation is compared to exact results in 1D. The effects of
electron-electron coupling and electron doping on the shape of the
Fermi-surface are demonstrated in 2D. Causality is examined in both 1D and 2D.
We find that the scheme is successful if QMC clusters of $N_C\ge 4$ are used
(with sufficiently high temperatures in 1D), however very small QMC clusters of
$N_C=1$ lead to acausal results

### Towards analytical approaches to the dynamical-cluster approximation

I introduce several simplified schemes for the approximation of the
self-consistency condition of the dynamical cluster approximation. The
applicability of the schemes is tested numerically using the
fluctuation-exchange approximation as a cluster solver for the Hubbard model.
Thermodynamic properties are found to be practically indistinguishable from
those computed using the full self-consistent scheme in all cases where the
non-interacting partial density of states is replaced by simplified analytic
forms with matching 1st and 2nd moments. Green functions are also compared and
found to be in close agreement, and the density of states computed using
Pad\'{e} approximant analytic continuation shows that dynamical properties can
also be approximated effectively. Extensions to two-particle properties and
multiple bands are discussed. Simplified approaches to the dynamical cluster
approximation should lead to new analytic solutions of the Hubbard and other
models

### ARPES Spectra of the Hubbard model

We discuss spectra calculated for the 2D Hubbard model in the intermediate
coupling regime with the dynamical cluster approximation, which is a
non-perturbative approach. We find a crossover from a normal Fermi liquid with
a Fermi surface closed around the Brillouin zone center at large doping to a
non-Fermi liquid for small doping. The crossover is signalled by a splitting of
the Fermi surface around the $X$ point of the 2D Brillouin zone, which
eventually leads to a hole-like Fermi surface closed around the point M. The
topology of the Fermi surface at low doping indicates a violation of
Luttinger's theorem. We discuss different ways of presenting the spectral data
to extract information about the Fermi surface. A comparison to recent
experiments will be presented.Comment: 8 pages, 7 color figures, uses RevTeX

### Fictive Impurity Models: an Alternative Formulation of the Cluster Dynamical Mean Field Method

"Cluster" extensions of the dynamical mean field method to include longer
range correlations are discussed. It is argued that the clusters arising in
these methods are naturally interpreted not as actual subunits of a physical
lattice but as algorithms for computing coefficients in an orthogonal function
expansion of the momentum dependence of the electronic self-energy. The
difficulties with causality which have been found to plague cluster dynamical
mean field methods are shown to be related to the "ringing" phenomenon familiar
from Fourier analysis. The analogy is used to motivate proposals for simple
filtering methods to circumvent them. The formalism is tested by comparison to
low order perturbative calculations and self consistent solutions

### Dynamical 1/N approach to time-dependent currents through quantum dots

A systematic truncation of the many-body Hilbert space is implemented to
study how electrons in a quantum dot attached to conducting leads respond to
time-dependent biases. The method, which we call the dynamical 1/N approach, is
first tested in the most unfavorable case, the case of spinless fermions (N=1).
We recover the expected behavior, including transient ringing of the current in
response to an abrupt change of bias. We then apply the approach to the
physical case of spinning electrons, N=2, in the Kondo regime for the case of
infinite intradot Coulomb repulsion. In agreement with previous calculations
based on the non-crossing approximation (NCA), we find current oscillations
associated with transitions between Kondo resonances situated at the Fermi
levels of each lead. We show that this behavior persists for a more realistic
model of semiconducting quantum dots in which the Coulomb repulsion is finite.Comment: 18 pages, 7 eps figures, discussion extended for spinless electrons
and typo

### The Korringa-Kohn-Rostoker Non-Local Coherent Potential Approximation (KKR-NLCPA)

We introduce the Korringa-Kohn-Rostocker non-local coherent potential
approximation (KKR-NLCPA) for describing the electronic structure of disordered
systems. The KKR-NLCPA systematically provides a hierarchy of improvements upon
the widely used KKR-CPA approach and includes non-local correlations in the
disorder configurations by means of a self-consistently embedded cluster. The
KKR-NLCPA method satisfies all of the requirements for a successful cluster
generalization of the KKR-CPA; it remains fully causal, becomes exact in the
limit of large cluster sizes, reduces to the KKR-CPA for a single-site cluster,
is straightforward to implement numerically, and enables the effects of
short-range order upon the electronic structure to be investigated. In
particular, it is suitable for combination with electronic density functional
theory to give an ab-initio description of disordered systems. Future
applications to charge correlation and lattice displacement effects in alloys
and spin fluctuations in magnets amongst others are very promising. We
illustrate the method by application to a simple one-dimensional model.Comment: Revised versio