量子无序系统模型的改进Lanczos对角化
Advanced Lanczos diagonalization for models of quantum disordered systems
摘要：
本文讨论了一种有效的数值算法在求解量子无序系统电子性质模型中出现的本征值问题中的应用。在Anderson晶格模型的框架下，研究了由随机势引起的定域-离域跃迁的电子态。对于尺寸超过10^6 x 10^6的非常稀疏的厄米矩阵，谱的内部和相应的波函数的计算是通过Lanczos型方法进行的，该方法特别修改用于研究能级和本征函数振幅的统计特性。
英文摘要：
An application of an effective numerical algorithm for solving eigenvalue problems which arise in modelling electronic properties of quantum disordered systems is considered. We study the electron states at the localization-delocalization transition induced by a random potential in the framework of the Anderson lattice model. The computation of the interior of the spectrum and corresponding wavefunctions for very sparse, hermitian matrices of sizes exceeding 10^6 x 10^6 is performed by the Lanczos-type method especially modified for investigating statistical properties of energy levels and eigenfunction amplitudes.
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