Lehrstuhl für Theoretische Physik III

-Elektronische Korrelationen und Magnetismus-

Priv.-Doz. Dr. Stefan Kehrein

Phone: 0821-5983714

E-mail: Stefan.Kehrein@Physik.Uni-Augsburg.DE

Main Research Interests

Flow Equation Approach to Many-Particle Systems

Flow equations are a new non-perturbative approximation method for many-particle systems. The method consists of applying a continuous sequence of infinitesimal unitary transformations to a given many-particle Hamiltonian. This scheme can be seen as an extension of traditional renormalization group and scaling ideas. My main interest is the application of the flow equation method to strong-coupling problems for correlated electron systems. For certain models (like e.g. the sine-Gordon model and the Kondo model) I could show that this approach allows a controlled systematic approximation in an expansion parameter that remains small throughout the entire crossover flow from weak to strong coupling. This observation can e.g. be used to analytically study more complex strong-coupling models, where one otherwise has to resort largely to numerical methods (see e.g. Phys. Rev. B 69, 214413 (2004)).
For more information on the flow equation approach see my Habilitation thesis and other publications. (Click here for related work at the University of Heidelberg ).

Non-Equilibrium Phenomena in Many-Particle Systems

My main current research interest is to explore non-equilibrium phenomena in many-body systems, both in statistical physics and in condensed matter theory. This research direction is motivated by recent experimental advances, e.g. in quantum dot experiments, and by fundamental theoretical questions as most of our theoretical understanding of many-body systems is limited to equilibrium or near-to-equilibrium behavior. The flow equation method turns out to be a very suitable approach for non-equilibrium problems since it retains all energy scales, which is important for systems driven out of their equilibrium ground state. Using flow equations and other methods, my current research activities are focused on strongly correlated electron systems with applied voltage bias ( cond-mat/0410341), on time-dependent Hamiltonians ( cond-mat/0405193 and cond-mat/0504373), and on generally developing a better understanding of scaling concepts in non-equilibrium situations.

Most Recent Publications

Violation of the Fluctuation-Dissipation Theorem and Heating Effects in the Time-Dependent Kondo Model [Preprint cond-mat/0504373]
D. Lobaskin and S. Kehrein

The fluctuation-dissipation theorem (FDT) plays a fundamental role in understanding quantum many-body problems. However, its applicability is limited to equilibrium systems and it does in general not hold in nonequilibrium situations. This violation of the FDT is an important tool for studying nonequilibrium physics. In this paper we present results for the violation of the FDT in the Kondo model where the impurity spin is frozen for all negative times, and set free to relax at positive times. We derive exact analytical results at the Toulouse point, and results within a controlled approximation in the Kondo limit, which allow us to study the FDT violation on all time scales. A measure of the FDT violation is provided by the effective temperature, which shows initial heating effects after switching on the perturbation, and then exponential cooling to zero temperature as the Kondo system reaches equilibrium.

Scaling and Decoherence in the Nonequilibrium Kondo Model [Preprint cond-mat/0410341]
S. Kehrein

We study the Kondo effect in quantum dots in an out-of-equilibrium state due to an applied dc-voltage bias. Using the method of infinitesimal unitary transformations ("flow equations"), we develop a perturbative scaling picture that naturally contains both equilibrium coherent and non-equilibrium decoherence effects. This allows one to study the competition between Kondo effect and current-induced decoherence, and e.g. establishes a large single-channel Kondo physics dominated regime for asymmetrically coupled quantum dots.

Crossover from Non-Equilibrium to Equilibrium Behavior in the Time-Dependent Kondo Model [cond-mat/0405193, accepted for publication in Phys. Rev. B]
D. Lobaskin and S. Kehrein

We investigate the equilibration of a Kondo model that is initially prepared in a non-equilibrium state towards its equilibrium behavior. Such initial non-equilibrium states can e.g. be realized in quantum dot experiments with time-dependent gate voltages. We evaluate the non-equilibrium spin-spin correlation function at the Toulouse point of the Kondo model exactly and analyze the crossover between non-equilibrium and equilibrium behavior as the non-equilibrium initial state evolves as a function of the waiting time for the first spin measurement. Using the flow equation method we extend these results to the experimentally relevant limit of small Kondo couplings.


Quantum phase transition of Ising-coupled Kondo impurities [Phys. Rev. B 69, 214413 (2004)]
Markus Garst, Stefan Kehrein, Thomas Pruschke, Achim Rosch, and Matthias Vojta

We investigate a model of two Kondo impurities coupled via an Ising interaction. Exploiting the mapping to a generalized single-impurity Anderson model, we establish that the model has a singlet and a (pseudospin) doublet phase separated by a Kosterlitz-Thouless quantum phase transition. Based on a strong-coupling analysis and renormalization group arguments, we show that at this transition the conductance G through the system either displays a zero-bias anomaly, G ~ |V|^{-2(\sqrt{2}-1)}, or takes a universal value, G = e^2/(\pi\hbar) cos^2[\pi/(2\sqrt{2})], depending on the experimental setup. Close to the Toulouse point of the individual Kondo impurities, the strong-coupling analysis allows to obtain the location of the phase boundary analytically. For general model parameters, we determine the phase diagram and investigate the thermodynamics using numerical renormalization group calculations. In the singlet phase close to the quantum phase transtion, the entropy is quenched in two steps: first the two Ising-coupled spins form a magnetic mini-domain which is, in a second step, screened by a Kondoesque collective resonance in an effective solitonic Fermi sea. In addition, we present a flow equation analysis which provides a different mapping of the two-impurity model to a generalized single-impurity Anderson model in terms of fully renormalized couplings, which is applicable for the whole range of model parameters.


Unusual Single-Ion Non-Fermi Liquid Behavior in Ce_(1-x)La_xNi_9Ge_4 [Phys. Rev. Lett. 93, 216404 (2004)]
U. Killer, E.-W. Scheidt, G. Eickerling, H. Michor, J. Sereni, Th. Pruschke, and S. Kehrein

We report on specific heat and magnetic susceptibility measurements on the compound Ce_(1-x)La_xNi_9Ge_4 for various concentrations ranging from the stoichiometric system with x=0 to the dilute limit x=0.95. Our data reveals single-ion scaling with the Ce-concentration and the largest ever recorded value of the electronic specific heat c/T approximately 5.5 J K^(-2)mol^(-1) at T=0.08K for the stoichiometric compound x=0 without any trace of magnetic order. While in the doped samples c/T increases logarithmically below 3K down to 50mK, their magnetic susceptibility behaves Fermi liquid like below 1K. These properties make the compound Ce_(1-x)La_xNi_9Ge_4 a unique system on the borderline between Fermi liquid and non-Fermi liquid physics.

Habilitation thesis

List of publications