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Wir pr��sentieren einen Ansatz zur Behandlung von Quantenst��rstellensystemen, der die numerische Renormierungsgruppe (NRG) zu einem offenen-Quantensystem-Formalismus erweitert. Das kontinuierliche Leitungsband wird in eine beliebige Wilsonkette und einen Satz von Reservoirs aufgeteilt, ohne die lokale Badhybridisierungsfunktion zu beeinflussen. An jedes Kettenglied wird jeweils ein Reservoir ��ber den Bloch-Redfield Formalismus (BRF) angekoppelt, der eine Born-Markov-N��herung (BMN) impliziert. Dieser offene-Wilsonketten-Formalismus (OWF) garantiert eine echte Thermalisierung f��r lokale nicht-Gleichgewichtsdynamik, sowie eine endliche Lebenszeit f��r lokale Gleichgewichtsspektralfunktionen. Der Ansatz reproduziert die von der NRG vorhergesagten Gleichgewichtswerte f��r t ��� ��� und die korrekten Relaxationsraten f��r das Resonanzlevel-Modell. Durch Verl��ngerung der Wilsonkette wird die Genauigkeit der BMN, speziell f��r die Kurzzeitdynamik, erh��ht. Die Formierung der Hubbardh��gel und der Kondoresonanz k��nnen f��r das Einzelst��rstellen-Anderson-Modell reproduziert werden. Die BMN in zweiter Ordnung ist nicht in der Lage, die Oszillationen, die durch die Banddiskretisierung im Kontext der NRG entstehen, vollst��ndig zu d��mpfen, kann jedoch durch die wohlbekannte z-Mittelung konstruktiv erg��nzt werden. Es stellt sich heraus, dass der BRF ineffizient ist f��r wechselwirkende Systeme, in denen die lokale Wechselwirkung die Bandbreite ��bersteigt. Hierzu diskutieren wir mehrere alternative Optionen. Die Motivation dieser Arbeit ist rein methodologischer Natur, weshalb wir uns auf die einfachsten Quantenst��rstellenmodelle beschr��nken. Der OWF ist allerdings ebenso vielf��ltig einsetzbar wie die NRG selbst, und damit anwendbar auf z.B. Multi-St��rstellenmodelle oder lokalen Gleichgewichts- und Nicht-Gleichgewichts-Transport., We present an approach for quantum impurity systems that extends the numerical renormalization group (NRG) to an open quantum system formulation. The continuous conduction band is divided into an arbitrary Wilson chain and a set of reservoirs without affecting the local bath hybridization function. One reservoir is coupled to each chain site and is treated by the Bloch-Redfield formalism (BRF), which includes the Born-Markov approximation (BMA). This open chain formalism (OCF) yields true thermalization in local real-time non-equilibrium dynamics, as well as finite lifetime in local equilibrium spectral functions. It reproduces the t ��� ��� steady-state predicted by the NRG and the correct relaxation rates in the resonant level model. By enlarging the Wilson chain, the accuracy of the BMA, especially with respect to short-time dynamics, is increased. The formation of Hubbard-peaks and the Kondo-resonance are reproduced for the single-impurity Anderson model. The BMA in second order results in the persistence of finite-size oscillations to some degree, which can be damped by the well-established procedure of z-averaging. We find the BRF to be inadequate for interacting models, if the local Coulomb repulsion exceeds the conduction bandwidth, and discuss several options to improve the OCF for this parameter regime. Since the motivation for this thesis is of pure methodological nature, we restrict to the most simple quantum impurity models to benchmark our algorithm. However, the OCF is as versatilely applicable to more complex models as the pure NRG. Consequently, our approach can be adapted to e.g. multi-impurity models, as well as simulate local transport properties in and out of equilibrium.

In this dissertation, we present a detailed theoretical analysis of the spin dynam- ics in small antiferromagnetic systems in view of macroscopic quantum phenom- ena, possible applications in quantum information processing, and transport of the magnetization. Ferromagnetic and antiferromagnetic systems with a size on the nanometer scale such as nanoparticles or magnetic molecular clusters, show intriguing quantum e®ects which are in stark contrast to the behavior of a macroscopic magnetic moment. In recent years, the interest in small magnetic systems has been renewed due to the discovery of possible future technological applications such as data storage or quantum information processing. Fer- romagnetic molecular magnetic systems with a large net spin show incoherent tunneling of the magnetization on a long timescale. This quantum phenomenon is, by now, well established both experimentally and theoretically. Small an- tiferromagnetic systems have so far attracted less attention although quantum e®ects are even more pronounced than in their ferromagnetic counterparts. The main reason for this is that the predicted quantum phenomena such as coherent quantum tunneling of the N¶eel vector are not easily accessible in experiments. On a theoretical level, the description of an antiferromagnetic system is chal- lenging because of the pronounced quantum °uctuations of the spins. Several antiferromagnetic molecular ring molecules have been synthesized to date. The ferric wheels are the most prominent examples. These systems are promising candidates for macroscopic quantum coherence in the form of coherent N¶eel vector tunneling. Although the tunneling rate can be determined from the measurement of thermodynamic properties, a thorough understanding requires theoretical analysis and experimental observation of the spin dynamics. We calculate spin correlation functions using spin coherent state path integrals and ¯nd analytical expressions for the correlation functions of both the N¶eel vector and the total spin. Our results are in good agreement with numerical exact diagonalization for the small systems that are accessible numerically. From the correlation functions, we deduce that the observation of N¶eel vec- tor tunneling requires an experimental probe that couples to a single spin of the antiferromagnetic system only. Both nuclear magnetic resonance and elec- tron spin resonance on doped rings meet this criterion. Nuclear spins coupled only to single electron spins are ideal candidates for local probes because the nuclear spin susceptibiliy exhibits signatures of the coherent electron spin dy- namics. Alternatively, by doping of the ring molecule, an antiferromagnetic system emerges that has uncompensated sublattice spins. The resulting tracer spin would allow one to detect N¶eel vector tunneling with electron spin reso- nance or magnetic susceptibility measurements. Small antiferromagnetic systems with a ¯nite net spin are interesting in view of quantum information processing. Single electron spins are among the most promising candidates for qubits in a solid state system. However, quantum computing is also possible with a wide range of antiferromagnetic clusters which form an e®ective two-state system in the low energy sector. The main advantage of a qubit formed by a spin cluster is that initialization, quantum gate operation, error correction, and readout are possible with techniques applicable to single spins, while the requirements on local control are relaxed. Spin cluster qubits are very insensitive to the details of intracluster exchange interactions and spin placement. Quantum computing is only one of the exciting perspectives in the emerging ¯eld of spintronics in which the spin and charge degrees of freedom of an elec- tron are treated on an equal footing. We analyze transport of magnetization in insulating systems described by a spin Hamiltonian in which the magnetization current is not accompanied by a charge current. The magnetization current through a quasi one-dimensional magnetic wire of ¯nite length suspended be- tween two bulk magnets is determined by the spin conductance which remains ¯nite in the ballistic limit due to contact resistance. Magnetization currents produce an electric ¯eld and hence can be measured directly. For magnetiza- tion transport in an external electric ¯eld, phenomena analogous to the Hall e®ect emerge.