非互惠非ermitian 系统中安德森定位转换的统一单参数缩放函数

C. Wang, Wenxue He, X. R. Wang, Hechen Ren
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引用次数: 0

摘要

通过使用无量纲电导作为缩放变量,传统的一参数局部化缩放理论对于诸如哈纳托-纳尔逊模型这样的非互易非赫米提系统是失效的。在此,我们提出了一种使用参与比作为缩放变量的单参数缩放函数。通过基于精确对角的高精度数值计算过程,我们证明了这个一参数缩放函数可以描述对称类 AI 和 A 的一维和二维非互惠非ermitian 系统的安德森定位转换。此外,我们还推导出基于自洽玻恩近似的复隙方程,它可以确定点隙关闭时的无序度。得到的无序度与单参数缩放函数中安德森局域化转换的临界无序度完全吻合。最后,我们证明了单参数缩放函数对于对等非赫米提系统(如二维 AII 类$^\dagger$)中的安德森定位转换也是有效的,因此可以作为无序非赫米提系统的统一缩放函数。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Unified one-parameter scaling function for Anderson localization transitions in non-reciprocal non-Hermitian systems
By using dimensionless conductances as scaling variables, the conventional one-parameter scaling theory of localization fails for non-reciprocal non-Hermitian systems such as the Hanato-Nelson model. Here, we propose a one-parameter scaling function using the participation ratio as the scaling variable. Employing a highly accurate numerical procedure based on exact diagonalization, we demonstrate that this one-parameter scaling function can describe Anderson localization transitions of non-reciprocal non-Hermitian systems in one and two dimensions of symmetry classes AI and A. The critical exponents of correlation lengths depend on symmetries and dimensionality only, a typical feature of universality. Moreover, we derive a complex-gap equation based on the self-consistent Born approximation that can determine the disorder at which the point gap closes. The obtained disorders match perfectly the critical disorders of Anderson localization transitions from the one-parameter scaling function. Finally, we show that the one-parameter scaling function is also valid for Anderson localization transitions in reciprocal non-Hermitian systems such as two-dimensional class AII$^\dagger$ and can, thus, serve as a unified scaling function for disordered non-Hermitian systems.
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