8 research outputs found
A junction of three quantum wires: restoring time-reversal symmetry by interaction
We investigate transport of correlated fermions through a junction of three
one-dimensional quantum wires pierced by a magnetic flux. We determine the flow
of the conductance as a function of a low-energy cutoff in the entire parameter
space. For attractive interactions and generic flux the fixed point with
maximal asymmetry of the conductance is the stable one, as conjectured
recently. For repulsive interactions and arbitrary flux we find a line of
stable fixed points with vanishing conductance as well as stable fixed points
with symmetric conductance (4/9)(e^2/h).Comment: 5 pages, 3 figures, version accepted for publication in Phys. Rev.
Let
Junctions of one-dimensional quantum wires - correlation effects in transport
We investigate transport of spinless fermions through a single site dot
junction of M one-dimensional quantum wires. The semi-infinite wires are
described by a tight-binding model. Each wire consists of two parts: the
non-interacting leads and a region of finite extent in which the fermions
interact via a nearest-neighbor interaction. The functional renormalization
group method is used to determine the flow of the linear conductance as a
function of a low-energy cutoff for a wide range of parameters. Several fixed
points are identified and their stability is analyzed. We determine the scaling
exponents governing the low-energy physics close to the fixed points. Some of
our results can already be derived using the non-self-consistent Hartree-Fock
approximation.Comment: version accepted for publication in Phys. Rev. B, 14 pages, 7 figures
include
Correlation effects on electronic transport through dots and wires
We investigate how two-particle interactions affect the electronic transport
through meso- and nanoscopic systems of two different types: quantum dots with
local Coulomb correlations and quasi one-dimensional quantum wires of
interacting electrons. A recently developed functional renormalization group
scheme is used that allows to investigate systems of complex geometry.
Considering simple setups we show that the method includes the essential
aspects of Luttinger liquid physics (one-dimensional wires) as well as of the
physics of local correlations, with the Kondo effect being an important
example. For more complex systems of coupled dots and Y-junctions of
interacting wires we find surprising new correlation effects.Comment: to appear in "Advances in Solid State Physics" Volume 46, Ed. R. Haug
(Springer, 2006
The nonperturbative functional renormalization group and its applications
The renormalization group plays an essential role in many areas of physics,
both conceptually and as a practical tool to determine the long-distance
low-energy properties of many systems on the one hand and on the other hand
search for viable ultraviolet completions in fundamental physics. It provides
us with a natural framework to study theoretical models where degrees of
freedom are correlated over long distances and that may exhibit very distinct
behavior on different energy scales. The nonperturbative functional
renormalization-group (FRG) approach is a modern implementation of Wilson's RG,
which allows one to set up nonperturbative approximation schemes that go beyond
the standard perturbative RG approaches. The FRG is based on an exact
functional flow equation of a coarse-grained effective action (or Gibbs free
energy in the language of statistical mechanics). We review the main
approximation schemes that are commonly used to solve this flow equation and
discuss applications in equilibrium and out-of-equilibrium statistical physics,
quantum many-particle systems, high-energy physics and quantum gravity.Comment: v2) Review article, 93 pages + bibliography, 35 figure