Multifractal-enriched mobility edges and emergent quantum phases in one-dimensional exactly solvable lattice models

• URL: http://arxiv.org/abs/2501.07866v1
• Date: Tue, 14 Jan 2025 06:07:44 GMT
• Title: Multifractal-enriched mobility edges and emergent quantum phases in one-dimensional exactly solvable lattice models
• Authors: Shan-Zhong Li, Yi-Cai Zhang, Yucheng Wang, Shanchao Zhang, Shi-Liang Zhu, Zhi Li,
• Abstract summary: We propose a class of exactly solvable flat-band quasiperiodic lattice models. We derive exact expressions of the Lyapunov exponents in both lattice and dual spaces. We numerically compute the inverse participation ratios of the eigenstates in both real and dual spaces.
• Score: 7.484984111497129
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• Abstract: We propose a class of exactly solvable flat-band quasiperiodic lattice models that encompass a variety of multifractal-enriched mobility edges and multi-state coexisting quantum phases. Utilizing Avila's global theory, we derive exact expressions of the Lyapunov exponents in both lattice and dual spaces, providing an analytical expression and phase diagram for the multifractal-enriched mobility edges. Additionally, we numerically compute the inverse participation ratios of the eigenstates in both real and dual spaces to further characterize these phases. Furthermore, we demonstrate that these models can be realized using Rydberg atomic arrays, enabling the observation of Lyapunov exponents and inverse participation ratios through a powerful spectroscopy approach.

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