非厄米准周期修饰Lieb晶格中的精确迁移率环
Exact mobility rings in non-Hermitian quasiperiodically decorated Lieb lattices
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中文总结 AI 辅助
本文针对二维准周期修饰Lieb晶格，将其映射到非厄米广义Aubry-André-Harper模型，解析推导并数值验证了迁移率环的精确表达式，揭示了其随准周期势强度的演化规律，为高维非厄米系统研究提供了理论支持。
中文摘要 AI 辅助
迁移率环（MR）是复能平面上分隔扩展态与局域态的临界边界，是理解非厄米（NH）无序系统中安德森转变的基础。尽管一维（1D）非厄米准周期模型中的MR已被广泛研究，但超越一维的严格分析框架仍极度匮乏。本文研究一类二维（2D）准周期修饰Lieb晶格（QDLL），其特点是对晶格顶点选择性施加复非公度势。通过将这些二维结构精确映射到非厄米广义Aubry-André-Harper（AAH）模型，并利用扩展-局域转变点，我们解析推导了李雅普诺夫指数，得到MR的精确表达式。这些精确的理论边界通过波函数分形维数和实空间概率分布的数值计算得到了有力验证。此外，我们揭示了由准周期势强度驱动的MR的不同演化行为：κ=2的系统具有单个MR，而κ=3的系统会经历从单个整合环到两个独立环的动态连续演化。我们希望，本文关于二维MR的精确结果将有益于高维非厄米系统中安德森局域化和MR的研究。
英文摘要
The mobility ring (MR), a critical boundary in the complex energy plane separating extended and localized states, is fundamental to understanding the Anderson transition in non-Hermitian (NH) disordered systems. While MRs have been extensively studied in one-dimensional (1D) NH quasiperiodic models, rigorous analytical frameworks beyond 1D remain critically scarce. Here, we investigate a class of two-dimensional (2D) quasiperiodically decorated Lieb lattices (QDLLs) featuring complex incommensurate potentials selectively applied to the lattice vertices. By exactly mapping these 2D structures onto NH generalized Aubry-Andr{é}-Harper (AAH) models and leveraging extended-localized transition point, we analytically derive the Lyapunov exponents and obtain exact expressions for the MRs. These exact theoretical boundaries are strongly corroborated by numerical computations of wavefunction fractal dimensions and real-space probability distributions. Furthermore, we reveal distinct evolutionary behaviors of the MRs driven by the quasiperiodic potential strength: systems characterized by $κ=2$ possess a single MR, whereas systems with $κ=3$ undergo a dynamic sequential evolution from a single integrated ring into two independent rings. We hope that our exact results of MRs in 2D will benefit the study of Anderson localizations and MRs in high-dimensional NH systems.
