Critical Exponent of the Anderson Transition Using Massively Parallel Supercomputing
Critical Exponent of the Anderson Transition Using Massively Parallel Supercomputing
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DOI：
10.7566/jpsj.87.094703
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发表时间：
2018-09-15
影响因子：
1.7
通讯作者：
Ohtsuki, Tomi
中科院分区：
文献类型：
--
作者：
Slevin, Keith;Ohtsuki, Tomi
迄今为止，对安德森跃迁的临界指数的最精确估计是用传递矩阵法得到的。该方法涉及对极长准一维系统的模拟。该方法本质上是串行的，不太适合现代大规模并行超级计算机。一个明显的替代方案是模拟超立方系统和平均系统的大集合。虽然这允许在大规模并行超级计算机上充分利用OpenMP和MPI，但直接的实现导致数据无法扩展。我们证明了可以通过生成具有适当平稳概率分布的正交初始向量的随机集来避免这个问题。我们将该方法应用于三维正交普适类中的Anderson转换，并能够将模拟的最大L x L截面从L= 24 [New J. Phys. 16, 015012(2014)]增加到L= 64。这允许以更高的精度估计临界指数，而不需要引入无关的缩放变量。此外，这种方法更适合于具有相关随机势的模拟，如在量子霍尔或冷原子系统中所需要的模拟。
To date the most precise estimations of the critical exponent for the Anderson transition have been made using the transfer matrix method. This method involves the simulation of extremely long quasi one-dimensional systems. The method is inherently serial and is not well suited to modern massively parallel supercomputers. The obvious alternative is to simulate a large ensemble of hypercubic systems and average. While this permits taking full advantage of both OpenMP and MPI on massively parallel supercomputers, a straight forward implementation results in data that does not scale. We show that this problem can be avoided by generating random sets of orthogonal initial vectors with an appropriate stationary probability distribution. We have applied this method to the Anderson transition in the three-dimensional orthogonal universality class and been able to increase the largest L x L cross section simulated from L= 24 [New J. Phys. 16, 015012 (2014)] to L= 64 here. This permits an estimation of the critical exponent with improved precision and without the necessity of introducing an irrelevant scaling variable. In addition, this approach is better suited to simulations with correlated random potentials such as is needed in quantum Hall or cold atom systems.