Quantum Hall Ferromagnets: Induced Topological term and electromagnetic interactions

The $\nu = 1$ quantum Hall ground state in materials like GaAs is well known to be ferromagnetic in nature. The exchange part of the Coulomb interaction provides the necessary attractive force to align the electron spins spontaneously. The gapless Goldstone modes are the angular deviations of the magnetisation vector from its fixed ground state orientation. Furthermore, the system is known to support electrically charged spin skyrmion configurations. It has been claimed in the literature that these skyrmions are fermionic owing to an induced topological Hopf term in the effective action governing the Goldstone modes. However, objections have been raised against the method by which this term has been obtained from the microscopics of the system. In this article, we use the technique of the derivative expansion to derive, in an unambiguous manner, the effective action of the angular degrees of freedom, including the Hopf term. Furthermore, we have coupled perturbative electromagnetic fields to the microscopic fermionic system in order to study their effect on the spin excitations. We have obtained an elegant expression for the electromagnetic coupling of the angular variables describing these spin excitations.Comment: 23 pages, Plain TeX, no figure

Renormalization-group analysis of the one-dimensional extended Hubbard model with a single impurity

We analyze the one-dimensional extended Hubbard model with a single static impurity by using a computational technique based on the functional renormalization group. This extends previous work for spinless fermions to spin-1/2 fermions. The underlying approximations are devised for weak interactions and arbitrary impurity strengths, and have been checked by comparing with density-matrix renormalization-group data. We present results for the density of states, the density profile and the linear conductance. Two-particle backscattering leads to striking effects, which are not captured if the bulk system is approximated by its low-energy fixed point, the Luttinger model. In particular, the expected decrease of spectral weight near the impurity and of the conductance at low energy scales is often preceded by a pronounced increase, and the asymptotic power laws are modified by logarithmic corrections.Comment: 36 pages, 13 figures, revised version as publishe

Spatially anisotropic Heisenberg Kagome antiferromagnet

In the search for spin-1/2 kagome antiferromagnets, the mineral volborthite has recently been the subject of experimental studies [Hiroi et al.,2001]. It has been suggested that the magnetic properties of this material are described by a spin-1/2 Heisenberg model on the kagome lattice with spatially anisotropic exchange couplings. We report on investigations of the Sp(N) symmetric generalisation of this model in the large N limit. We obtain a detailed description of the dependence of possible ground states on the anisotropy and on the spin length S. A fairly rich phase diagram with a ferrimagnetic phase, incommensurate phases with and without long range order and a decoupled chain phase emerges.Comment: 6 pages, 6 figures, proceedings of the HFM2006 conference, to appear in a special issue of J. Phys.: Condens. Matte

Monte Carlo Simulation of the Heisenberg Antiferromagnet on a Triangular Lattice: Topological Excitations

We have simulated the classical Heisenberg antiferromagnet on a triangular lattice using a local Monte Carlo algorithm. The behavior of the correlation length $\xi$, the susceptibility at the ordering wavevector $\chi(\bf Q)$, and the spin stiffness $\rho$ clearly reflects the existence of two temperature regimes -- a high temperature regime $T > T_{th}$, in which the disordering effect of vortices is dominant, and a low temperature regime $T < T_{th}$, where correlations are controlled by small amplitude spin fluctuations. As has previously been shown, in the last regime, the behavior of the above quantities agrees well with the predictions of a renormalization group treatment of the appropriate nonlinear sigma model. For $T > T_{th}$, a satisfactory fit of the data is achieved, if the temperature dependence of $\xi$ and $\chi(\bf Q)$ is assumed to be of the form predicted by the Kosterlitz--Thouless theory. Surprisingly, the crossover between the two regimes appears to happen in a very narrow temperature interval around $T_{th} \simeq 0.28$.Comment: 13 pages, 8 Postscript figure

Absolute calibration of the LOPES antenna system

Radio emission in extensive air showers arises from an interaction with the geomagnetic field and is subject of theoretical studies. This radio emission has advantages for the detection of high energy cosmic rays compared to secondary particle or fluorescence measurement methods. Radio antennas like the LOPES30 antenna system are suited to investigate this emission process by detecting the radio pulses. The characteristic observable parameters like electric field strength and pulse length require a calibration which was done with a reference radio source resulting in an amplification factor representing the system behavior in the environment of the KASCADE-Grande experiment. Knowing the amplification factor and the gain of the LOPES antennas LOPES30 is calibrated absolutely for systematic analyses of the radio emission.Comment: 5 pages, Proceedings of International Workshop on Acoustic and Radio EeV Neutrino detection Activities: ARENA, May 17-19, 2005, DESY Zeuthe

The LOPES experiment - recent results, status and perspectives

The LOPES experiment at the Karlsruhe Institute of Technology has been taking radio data in the frequency range from 40 to 80 MHz in coincidence with the KASCADE-Grande air shower detector since 2003. Various experimental configurations have been employed to study aspects such as the energy scaling, geomagnetic dependence, lateral distribution, and polarization of the radio emission from cosmic rays. The high quality per-event air shower information provided by KASCADE-Grande has been the key to many of these studies and has even allowed us to perform detailed per-event comparisons with simulations of the radio emission. In this article, we give an overview of results obtained by LOPES, and present the status and perspectives of the ever-evolving experiment.Comment: Proceedings of the ARENA2010 conference, Nantes, Franc

Investigation of the Properties of Galactic Cosmic Rays with the KASCADE-Grande Experiment

The properties of galactic cosmic rays are investigated with the KASCADE-Grande experiment in the energy range between $10^{14}$ and $10^{18}$ eV. Recent results are discussed. They concern mainly the all-particle energy spectrum and the elemental composition of cosmic rays.Comment: Proc. RICAP 09, Nucl. Instr. and Meth. in pres

A new methodology for anisotropic mesh refinement based upon error gradients

We introduce a new strategy for controlling the use of anisotropic mesh refinement based upon the gradients of an a posteriori approximation of the error in a computed finite element solution. The efficiency of this strategy is demonstrated using a simple anisotropic mesh adaption algorithm and the quality of a number of potential a posteriori error estimates is considered

The spectrum of high-energy cosmic rays measured with KASCADE-Grande

The energy spectrum of cosmic rays between 10**16 eV and 10**18 eV, derived from measurements of the shower size (total number of charged particles) and the total muon number of extensive air showers by the KASCADE-Grande experiment, is described. The resulting all-particle energy spectrum exhibits strong hints for a hardening of the spectrum at approximately 2x10**16 eV and a significant steepening at c. 8x10**16 eV. These observations challenge the view that the spectrum is a single power law between knee and ankle. Possible scenarios generating such features are discussed in terms of astrophysical processes that may explain the transition region from galactic to extragalactic origin of cosmic rays.Comment: accepted by Astroparticle Physics June 201