Effective Hamiltonians for holes in antiferromagnets: a new approach to implement forbidden double occupancy

A coherent state representation for the electrons of ordered antiferromagnets is used to derive effective Hamiltonians for the dynamics of holes in such systems. By an appropriate choice of these states, the constraint of forbidden double occupancy can be implemented rigorously. Using these coherent states, one arrives at a path integral representation of the partition function of the systems, from which the effective Hamiltonians can be read off. We apply this method to the t-J model on the square lattice and on the triangular lattice. In the former case, we reproduce the well-known fermion-boson Hamiltonian for a hole in a collinear antiferromagnet. We demonstrate that our method also works for non-collinear antiferromagnets by calculating the spectrum of a hole in the triangular antiferromagnet in the self-consistent Born approximation and by comparing it with numerically exact results.Comment: 9 pages, Latex, 6 figure

Refactoring Legacy JavaScript Code to Use Classes: The Good, The Bad and The Ugly

JavaScript systems are becoming increasingly complex and large. To tackle the challenges involved in implementing these systems, the language is evolving to include several constructions for programming- in-the-large. For example, although the language is prototype-based, the latest JavaScript standard, named ECMAScript 6 (ES6), provides native support for implementing classes. Even though most modern web browsers support ES6, only a very few applications use the class syntax. In this paper, we analyze the process of migrating structures that emulate classes in legacy JavaScript code to adopt the new syntax for classes introduced by ES6. We apply a set of migration rules on eight legacy JavaScript systems. In our study, we document: (a) cases that are straightforward to migrate (the good parts); (b) cases that require manual and ad-hoc migration (the bad parts); and (c) cases that cannot be migrated due to limitations and restrictions of ES6 (the ugly parts). Six out of eight systems (75%) contain instances of bad and/or ugly cases. We also collect the perceptions of JavaScript developers about migrating their code to use the new syntax for classes.Comment: Paper accepted at 16th International Conference on Software Reuse (ICSR), 2017; 16 page

Heisenberg antiferromagnet with anisotropic exchange on the Kagome lattice: Description of the magnetic properties of volborthite

We study the properties of the Heisenberg antiferromagnet with spatially anisotropic nearest-neighbour exchange couplings on the kagome net, i.e. with coupling J in one lattice direction and couplings J' along the other two directions. For J/J' > 1, this model is believed to describe the magnetic properties of the mineral volborthite. In the classical limit, it exhibits two kinds of ground states: a ferrimagnetic state for J/J' < 1/2 and a large manifold of canted spin states for J/J' > 1/2. To include quantum effects self-consistently, we investigate the Sp(N) symmetric generalisation of the original SU(2) symmetric model in the large-N limit. In addition to the dependence on the anisotropy, the Sp(N) symmetric model depends on a parameter kappa that measures the importance of quantum effects. Our numerical calculations reveal that in the kappa-J/J' plane, the system shows a rich phase diagram containing a ferrimagnetic phase, an incommensurate phase, and a decoupled chain phase, the latter two with short- and long-range order. We corroborate these results by showing that the boundaries between the various phases and several other features of the Sp(N) phase diagram can be determined by analytical calculations. Finally, the application of a block-spin perturbation expansion to the trimerised version of the original spin-1/2 model leads us to suggest that in the limit of strong anisotropy, J/J' >> 1, the ground state of the original model is a collinearly ordered antiferromagnet, which is separated from the incommensurate state by a quantum phase transition.Comment: 21 pages, 22 figures. Final version, PRB in pres

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

Projecting flood hazard under climate change: an alternative approach to model chains

Flood hazard projections under climate change are typically derived by applying model chains consisting of the following elements: "emission scenario – global climate model – downscaling, possibly including bias correction – hydrological model – flood frequency analysis". To date, this approach yields very uncertain results, due to the difficulties of global and regional climate models to represent precipitation. The implementation of such model chains requires major efforts, and their complexity is high. <br><br> We propose for the Mekong River an alternative approach which is based on a shortened model chain: "emission scenario – global climate model – non-stationary flood frequency model". The underlying idea is to use a link between the Western Pacific monsoon and local flood characteristics: the variance of the monsoon drives a non-stationary flood frequency model, yielding a direct estimate of flood probabilities. This approach bypasses the uncertain precipitation, since the monsoon variance is derived from large-scale wind fields which are better represented by climate models. The simplicity of the monsoon–flood link allows deriving large ensembles of flood projections under climate change. We conclude that this is a worthwhile, complementary approach to the typical model chains in catchments where a substantial link between climate and floods is found

Flood risk assessment and associated uncertainty

International audienceFlood disaster mitigation strategies should be based on a comprehensive assessment of the flood risk combined with a thorough investigation of the uncertainties associated with the risk assessment procedure. Within the "German Research Network of Natural Disasters" (DFNK) the working group "Flood Risk Analysis" investigated the flood process chain from precipitation, runoff generation and concentration in the catchment, flood routing in the river network, possible failure of flood protection measures, inundation to economic damage. The working group represented each of these processes by deterministic, spatially distributed models at different scales. While these models provide the necessary understanding of the flood process chain, they are not suitable for risk and uncertainty analyses due to their complex nature and high CPU-time demand. We have therefore developed a stochastic flood risk model consisting of simplified model components associated with the components of the process chain. We parameterised these model components based on the results of the complex deterministic models and used them for the risk and uncertainty analysis in a Monte Carlo framework. The Monte Carlo framework is hierarchically structured in two layers representing two different sources of uncertainty, aleatory uncertainty (due to natural and anthropogenic variability) and epistemic uncertainty (due to incomplete knowledge of the system). The model allows us to calculate probabilities of occurrence for events of different magnitudes along with the expected economic damage in a target area in the first layer of the Monte Carlo framework, i.e. to assess the economic risks, and to derive uncertainty bounds associated with these risks in the second layer. It is also possible to identify the contributions of individual sources of uncertainty to the overall uncertainty. It could be shown that the uncertainty caused by epistemic sources significantly alters the results obtained with aleatory uncertainty alone. The model was applied to reaches of the river Rhine downstream of Cologne

Feedback Cooling of a Single Neutral Atom

We demonstrate feedback cooling of the motion of a single rubidium atom trapped in a high-finesse optical resonator to a temperature of about 160 \mu K. Time-dependent transmission and intensity-correlation measurements prove the reduction of the atomic position uncertainty. The feedback increases the 1/e storage time into the one second regime, 30 times longer than without feedback. Feedback cooling therefore rivals state-of-the-art laser cooling, but with the advantages that it requires less optical access and exhibits less optical pumping.Comment: 5 pages, 4 figure

The Heisenberg antiferromagnet on a triangular lattice: topological excitations

We study the topological defects in the classical Heisenberg antiferromagnet in two dimensions on a triangular lattice (HAFT). While the topological analysis of the order parameter space indicates that the defects are of $Z_2$ type, consideration of the energy leads us to a description of the low--energy stationary points of the action in terms of $\pm$ vortices, as in the planar XY model. Starting with the continuum description of the HAFT, we show analytically that its partition function can be reduced to that of a 2--dimensional Coulomb gas with logarithmic interaction. Thus, at low temperatures, the correlation length is determined by the spinwaves, while at higher temperatures we expect a crossover to a Kosterlitz--Thouless type behaviour. The results of recent Monte Carlo calculations of the correlation length are consistent with such a crossover.Comment: 9 pages, revtex, preprint: ITP-UH 03/9