H. Fehske

The kernel polynomial method

Efficient and stable algorithms for the calculation of spectral quantities and correlation functions are some of the key tools in computational condensed matter physics. In this article we review basic properties and recent developments of Chebyshev expansion based algorithms and the Kernel Polynomial Method. Characterized by a resource consumption that scales linearly with the problem dimension these methods enjoyed growing popularity over the last decade and found broad application not only in physics. Representative examples from the fields of disordered systems, strongly correlated electrons, electron-phonon interaction, and quantum spin systems we discuss in detail. In addition, we illustrate how the Kernel Polynomial Method is successfully embedded into other numerical techniques, such as Cluster Perturbation Theory or Monte Carlo simulation.

Stability of edge states and edge magnetism in graphene nanoribbons

We critically discuss the stability of edge states and edge magnetism in zigzag edge graphene nanoribbons (ZGNRs). We point out that magnetic edge states might not exist in real systems and show that there are at least three very natural mechanisms - edge reconstruction, edge passivation, and edge closure - which dramatically reduce the effect of edge states in ZGNRs or even totally eliminate them. Even if systems with magnetic edge states could be made, the intrinsic magnetism would not be stable at room temperature. Charge doping and the presence of edge defects further destabilize the intrinsic magnetism of such systems.

Efficient Temporal Blocking for Stencil Computations by Multicore-Aware Wavefront Parallelization

We present a pipelined wavefront parallelization approach for stencil-based computations. Within a fixed spatial domain successive wavefronts are executed by threads scheduled to a multicore processor chip with a shared outer level cache. By re-using data from cache in the successive wavefronts this multicore-aware parallelization strategy employs temporal blocking in a simple and efficient way. We use the Jacobi algorithm in three dimensions as a prototype or stencil-based computations and prove the efficiency of our approach on the latest generations of Intels x86 quad- and hexa-core processors.

A Unified Sparse Matrix Data Format for Efficient General Sparse Matrix-Vector Multiplication on Modern Processors with Wide SIMD Units

Sparse matrix-vector multiplication (spMVM) is the most time-consuming kernel in many numerical algorithms and has been studied extensively on all modern processor and accelerator architectures. However, the optimal sparse matrix data storage format is highly hardware-specific, which could become an obstacle when using heterogeneous systems. Also, it is as yet unclear how the wide single instruction multiple data (SIMD) units in current multi- and many-core processors should be used most efficiently if there is no structure in the sparsity pattern of the matrix. We suggest SELL-

Polarons and bipolarons in strongly interacting electron-phonon systems

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Entanglement and correlation in anisotropic quantum spin systems

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Polaron band formation in the Holstein model

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Classical and quantum Coulomb crystals

, a variant of Sliced ELLPACK, as a SIMD-friendly data format which combines long-standing ideas from general-purpose graphics processing units and vector computer programming. We discuss the advantages of SELL-

High-order commutator-free exponential time-propagation of driven quantum systems

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Crystallization in two-component Coulomb systems

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