一维无序准晶的非单调交叉和标度行为
Nonmonotonic crossover and scaling behaviors in a disordered 1D quasicrystal
摘要：
我们考虑弱无序区中的非相互作用无序一维准晶。我们表明，临界状态的纯模型的方法强本地化在显着不同的方式，这取决于他们的重整化性质。用有限尺寸标度分析了准晶的反参与比，发现它们可用几种标度函数描述。虽然大多数国家表现出逐步增加的IPR作为缩放变量的函数，其他国家表现出非单调的“再入”行为，其中IPR首先减少，并通过一个最小值，然后增加。这种令人惊讶的行为解释的框架内的微扰重整化群治疗，波函数可以计算分析作为一个函数的跳跃振幅比和无序，但它不是特定于这个模型。我们的结果应有助于澄清最近的研究结果，由于随机和准周期的潜力本地化。
英文摘要：
We consider a noninteracting disordered 1D quasicrystal in the weak disorder regime. We show that the critical states of the pure model approach strong localization in strikingly different ways, depending on their renormalization properties. A finite size scaling analysis of the inverse participation ratios of states (IPR) of the quasicrystal shows that they are described by several kinds of scaling functions. While most states show a progressively increasing IPR as a function of the scaling variable, other states exhibit a nonmonotonic `re-entrant' behavior wherein the IPR first decreases, and passes through a minimum, before increasing. This surprising behavior is explained in the framework of perturbation renormalization group treatment, where wavefunctions can be computed analytically as a function of the hopping amplitude ratio and the disorder, however it is not specific to this model. Our results should help to clarify results of recent studies of localization due to random and quasiperiodic potentials.
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