标题： 丰富的多分形迁移率边缘和里德伯原子阵列中的量子相的出现 显示英文标题

标题： Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays

摘要： 安德森局域描述了由无序引起的相变，区分了局域态和扩展态。 在准周期系统中，出现了一种第三类多分形态，其特征是独特的能量和波函数。 然而，用于区分这些态的临界指标，如李雅普诺夫指数（LEs）和逆参与比率（IPRs），尚未被实验检测到。 为了解决这些挑战，我们引入了具有平带的可精确求解的一维准周期晶格模型，使用阿维拉的全局定理解析地确定相变边界。 我们提出了使用里德伯原子阵列的实验实现，使得仅用18个量子比特就能区分局域态、扩展态和多分形态。 重要的是，我们开发了一种鲁棒的光谱方法，用于实验测量LEs和IPRs。 我们的工作为人工量子系统中安德森局域和多分形态的实验探索开辟了新途径。 显示英文摘要

摘要： Anderson localization describes disorder-induced phase transitions, distinguishing between localized and extended states. In quasiperiodic systems, a third multifractal state emerges, characterized by unique energy and wave functions. However, critical indicators for differentiating these states, such as Lyapunov exponents (LEs) and inverse participation ratios (IPRs), have yet to be experimentally detected. To address these challenges, we introduce exactly solvable one-dimensional quasiperiodic lattice models with flat bands, analytically determining phase boundaries using Avila's global theorem. We propose experimental realizations using Rydberg atom arrays, enabling the distinction of localized, extended, and multifractal states with as few as 18 qubits. Importantly, we develop a robust spectroscopic method for the experimental measurement of LEs and IPRs. Our work opens new avenues for the experimental exploration of Anderson localization and multifractal states in artificial quantum systems.