Institute of Nanotechnology, Karlsruhe Institute of Technology, 76344 Eggenstein-Leopoldshafen, Germany.
Phys Rev Lett. 2012 Nov 16;109(20):206804. doi: 10.1103/PhysRevLett.109.206804.
We present a numerical finite-size scaling study of the localization length in long cylinders near the integer quantum Hall transition employing the Chalker-Coddington network model. Corrections to scaling that decay slowly with increasing system size make this analysis a very challenging numerical problem. In this work we develop a novel method of stability analysis that allows for a better estimate of error bars. Applying the new method we find consistent results when keeping second (or higher) order terms of the leading irrelevant scaling field. The knowledge of the associated (negative) irrelevant exponent y is crucial for a precise determination of other critical exponents, including multifractal spectra of wave functions. We estimate |y|>/~0.4, which is considerably larger than most recently reported values. Within this approach we obtain the localization length exponent 2.62±0.06 confirming recent results. Our stability analysis has broad applicability to other observables at integer quantum Hall transition, as well as other critical points where corrections to scaling are present.
我们提出了一种数值有限尺寸标度研究，研究了整数量子霍尔转变附近长圆柱中的局域长度，采用了 Chalker-Coddington 网络模型。随着系统尺寸的增加而缓慢衰减的标度修正使得这种分析成为一个非常具有挑战性的数值问题。在这项工作中，我们开发了一种新的稳定性分析方法，允许更好地估计误差。应用新方法，当保持领先的无关标度场的二阶（或更高阶）项时，我们得到了一致的结果。关联的（负）无关指数 y 的知识对于精确确定其他临界指数，包括波函数的多重分形谱，至关重要。我们估计 |y|>/~0.4，这比最近报道的值大得多。在这种方法中，我们得到了局域长度指数 2.62±0.06，证实了最近的结果。我们的稳定性分析具有广泛的适用性，可用于整数量子霍尔转变以及存在标度修正的其他临界点的其他观测值。
