Vanoni Carlo, Altshuler Boris L, Kravtsov Vladimir E, Scardicchio Antonello
International School for Advanced Studies, Trieste 34136, Italy.
Istituto Nazionale di Fisica Nucleare Sezione di Trieste, Trieste 34127, Italy.
Proc Natl Acad Sci U S A. 2024 Jul 16;121(29):e2401955121. doi: 10.1073/pnas.2401955121. Epub 2024 Jul 11.
We present a renormalization group (RG) analysis of the problem of Anderson localization on a random regular graph (RRG) which generalizes the RG of Abrahams, Anderson, Licciardello, and Ramakrishnan to infinite-dimensional graphs. The RG equations necessarily involve two parameters (one being the changing connectivity of subtrees), but we show that the one-parameter scaling hypothesis is recovered for sufficiently large system sizes for both eigenstates and spectrum observables. We also explain the nonmonotonic behavior of dynamical and spectral quantities as a function of the system size for values of disorder close to the transition, by identifying two terms in the beta function of the running fractal dimension of different signs and functional dependence. Our theory provides a simple and coherent explanation for the unusual scaling behavior observed in numerical data of the Anderson model on RRG and of many-body localization.
我们给出了一个关于随机正则图（RRG）上安德森局域化问题的重整化群（RG）分析，它将亚伯拉罕斯、安德森、利恰尔代洛和拉马克里什南的RG推广到了无限维图。RG方程必然涉及两个参数（其中一个是子树不断变化的连通性），但我们表明，对于足够大的系统尺寸，本征态和能谱可观测量都恢复了单参数标度假设。我们还通过识别不同符号和函数依赖关系的跑动分形维数的β函数中的两项，解释了在接近转变的无序值下，动力学和能谱量作为系统尺寸函数的非单调行为。我们的理论为在RRG上的安德森模型以及多体局域化的数值数据中观察到的异常标度行为提供了一个简单而连贯的解释。
