Yan Kun, Wang Yixian, Zhan Yuwei, Zhang Zhiyong, Wu Xinglong
Collaborative Innovation Center of Advanced Microstructures, People's Republic of China.
National Laboratory of Solid State Microstructures and Key Laboratory of Modern Acoustics, MOE, People's Republic of China.
J Phys Condens Matter. 2022 Feb 21;34(16). doi: 10.1088/1361-648X/ac50dc.
The Anderson localization transition in a two-dimensional AIIsystem is studied by eigenvalue statistics and then confirmed by the multifractal analysis of the wave functions at the transition point. The system is modeled by a two-dimensional lattice structure with real-quaternion off-diagonal elements and complex on-site energies, whose real and imaginary parts are two independent random variables. Via finite-size scaling analysis of eigenvalue spacing ratios, we find the non-Hermiticity reduces the critical disorder and give an estimate of the critical exponent= 1.89, showing the system belongs to a new universal class other than the AII class and probably shares the same exponent with two-dimensional Hermitian DIII systems although they have different symmetries. The Anderson localization transition is further confirmed by checking the linearity in the parametric representation of the singularity strength and by checking the universality of the forms of the singularity spectra of different system sizes. The generalized dimensions are obtained asD1=1.80andD2=1.62.
通过特征值统计研究二维AII系统中的安德森局域化转变，然后通过对转变点处波函数的多重分形分析进行确认。该系统由具有实四元数非对角元素和复在位能的二维晶格结构建模，其实部和虚部是两个独立的随机变量。通过对特征值间距比的有限尺寸标度分析，我们发现非厄米性降低了临界无序度，并给出了临界指数(\nu = 1.89)的估计值，表明该系统属于不同于AII类的新普适类，尽管二维厄米DIII系统具有不同的对称性，但它们可能具有相同的指数。通过检查奇点强度的参数表示中的线性以及检查不同系统尺寸的奇点谱形式的普适性，进一步确认了安德森局域化转变。得到广义维数为(D_1 = 1.80)和(D_2 = 1.62)。
