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首页> 外文会议>Transactions of the KONWIHR Result Workshop on High Performance Computing in Science and Engineering; 20041014-15; Garching(DE) >HQS@HPC: Comparative numerical study of Anderson localisation in disordered electron systems
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HQS@HPC: Comparative numerical study of Anderson localisation in disordered electron systems

机译：HQS @ HPC：无序电子系统中安德森定位的比较数值研究

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摘要

Taking into account that a proper description of disordered systems should focus on distribution functions, the authors develop a powerful numerical scheme for the determination of the probability distribution of the local density of states (LDOS), which is based on a Chebyshev expansion with kernel polynomial refinement and allows the study of large finite clusters (up to 100~3). For the three-dimensional Anderson model it is demonstrated that the distribution of the LDOS shows a significant change at the disorder induced delocalisation-localisation transition. Consequently, the so-called typical density of states, defined as the geometric mean of the LDOS, emerges as a natural order parameter. The calculation of the phase diagram of the Anderson model proves the efficiency and reliability of the proposed approach in comparison to other localisation criteria, which rely, e.g., on the decay of the wavefunction or the inverse participation number.
机译：考虑到对无序系统的正确描述应集中在分布函数上，因此作者开发了一种强大的数值方案，用于确定状态局部密度（LDOS）的概率分布，该方案基于具有核多项式的Chebyshev展开改进并允许研究大型有限簇（最大100〜3）。对于三维安德森模型，证明了LDOS的分布在无序诱导的离域-定位转变上显示出显着变化。因此，所谓的典型状态密度（定义为LDOS的几何平均值）作为自然阶参数出现。与其他定位标准相比，安德森模型相图的计算证明了该方法的效率和可靠性，其他定位标准依赖于例如波函数的衰减或逆参与数。

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