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A numerical renormalization group approach to dissipative quantum impurity systems
(2011)
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David Roosen
- The miniaturization of electronics is reaching its limits.
Structures necessary to build integrated circuits from semiconductors are
shrinking and could reach the size of only a few atoms within the next few
years. It will be at the latest at this point in time that the physics of
nanostructures gains importance in our every day life.
This thesis deals with the physics of quantum impurity models.
All models of this class exhibit an identical structure: the simple and
small impurity only has few degrees of freedom. It can be built out of a
small number of atoms or a single molecule, for example. In the simplest
case it can be described by a single spin degree of freedom, in many
quantum impurity models, it can be treated exactly. The complexity of the
description arises from its coupling to a large number of fermionic or
bosonic degrees of freedom (large meaning that we have to deal with particle
numbers of the order of 10^{23}). An exact treatment thus remains
impossible. At the same time, physical effects which arise in quantum
impurity systems often cannot be described within a perturbative theory,
since multiple energy scales may play an important role. One example for
such an effect is the Kondo effect, where the free magnetic moment of the
impurity is screened by a "cloud" of fermionic particles of the quantum
bath.
The Kondo effect is only one example for the rich physics stemming from
correlation effects in many body systems. Quantum impurity models, and the
oftentimes related Kondo effect, have regained the attention of experimental
and theoretical physicists since the advent of quantum dots, which are
sometimes also referred to as as artificial atoms. Quantum dots offer a
unprecedented control and tunability of many system parameters. Hence, they
constitute a nice "playground" for fundamental research, while being
promising candidates for building blocks of future technological devices as
well.
Recently Loss' and DiVincenzo's proposal of a quantum computing scheme
based on spins in quantum dots, increased the efforts of
experimentalists to coherently manipulate and read out the spins of quantum
dots one by one.
In this context two topics are of paramount importance for future
quantum information processing:
since decoherence times have to be large enough to allow for good error
correction schemes, understanding the loss of phase coherence in quantum
impurity systems is a prerequisite for quantum computation in these
systems.
Nonequilibrium phenomena in quantum impurity systems also have to be
understood, before one may gain control of manipulating quantum bits.
As a first step towards more complicated nonequilibrium situations,
the reaction of a system to a quantum quench, i.e. a sudden change of
external fields or other parameters of the system can be investigated.
We give an introduction to a powerful numerical method used in this field
of research, the numerical renormalization group method, and apply this
method and its recent enhancements to various quantum impurity systems.
The main part of this thesis may be structured in the following way:
- Ferromagnetic Kondo Model,
- Spin-Dynamics in the Anisotropic Kondo and the Spin-Boson Model,
- Two Ising-coupled Spins in a Bosonic Bath,
- Decoherence in an Aharanov-Bohm Interferometer.
