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

• URL: http://arxiv.org/abs/2501.07866v2
• Date: Sun, 23 Feb 2025 12:19:47 GMT
• Title: Multifractal-enriched mobility edges and emergent quantum phases in Rydberg atomic arrays
• Authors: Shan-Zhong Li, Yi-Cai Zhang, Yucheng Wang, Shanchao Zhang, Shi-Liang Zhu, Zhi Li,
• Abstract summary: Anderson localization describes disorder-induced phase transitions, distinguishing between localized and extended states.<n> critical indicators for differentiating these states, such as Lyapunov exponents (LEs) and inverse participation ratios (IPRs) have yet to be experimentally detected.<n>We analytically determine phase boundaries using Avila's global theorem.<n>We propose experimental realizations using Rydberg atom arrays, enabling the distinction of localized, extended, and multifractal states with as few as 18 qubits.
• Score: 7.484984111497129
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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