Chen Anffany, Maciejko Joseph, Boettcher Igor
Theoretical Physics Institute, <a href="https://ror.org/0160cpw27">University of Alberta</a>, Edmonton, Alberta T6G 2E1, Canada and Department of Physics, <a href="https://ror.org/0160cpw27">University of Alberta</a>, Edmonton, Alberta T6G 2E1, Canada.
Phys Rev Lett. 2024 Aug 9;133(6):066101. doi: 10.1103/PhysRevLett.133.066101.
We study Anderson localization in disordered tight-binding models on hyperbolic lattices. Such lattices are geometries intermediate between ordinary two-dimensional crystalline lattices, which localize at infinitesimal disorder, and Bethe lattices, which localize at strong disorder. Using state-of-the-art computational group theory methods to create large systems, we approximate the thermodynamic limit through appropriate periodic boundary conditions and numerically demonstrate the existence of an Anderson localization transition on the {8,3} and {8,8} lattices. We find unusually large critical disorder strengths, determine critical exponents, and observe a strong finite-size effect in the level statistics.
我们研究了双曲晶格上无序紧束缚模型中的安德森局域化。此类晶格是介于普通二维晶体晶格（在无穷小无序下局域化）和贝塞晶格（在强无序下局域化）之间的几何结构。利用最先进的计算群论方法创建大型系统，我们通过适当的周期性边界条件来近似热力学极限，并通过数值方法证明了在{8,3}和{8,8}晶格上存在安德森局域化转变。我们发现了异常大的临界无序强度，确定了临界指数，并在能级统计中观察到了强烈的有限尺寸效应。
