动力学形变一维Aubry-André模型中的局域化转变
Localization Transition in Kinetically Deformed one-dimensional Aubry-André Model
- Indian Institute of Technology Tirupati（蒂鲁帕蒂印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
我们提出在动能中引入$q$-形变的一维Aubry-André模型，通过打破自对偶性改变局域化转变，使部分态在临界点后仍离域，并出现局域与扩展态共存的中间区域。
AI中文摘要：
我们提出在单粒子动能中引入$q$-形变，并研究其如何改变一维Aubry-André (AA)模型中的局域化性质。我们构造了一个厄米的$q$-形变动能算符，作为晶格平移算符的非线性函数，该算符保持均匀晶格不变，并在无形变极限$q\to1$下连续恢复传统的AA哈密顿量。该形变产生一组由单一参数$q$控制的无限集关联奇程动能过程，而非现象学地引入长程跳跃。在对偶变换下，这种长程跳跃表现为对偶准周期势的高次谐波，为打破AA模型的精确自对偶性提供了一条受控途径，其中$q$作为控制参数，从而在$q\neq1$时改变局域化结构。与传统AA模型（所有本征态在$\lambda_c=2$处同时局域化）相反，形变模型即使在$\lambda_c=2$之外仍存在一部分离域态。在$q-\lambda$平面上还出现了一个中间区域，其中局域化和扩展本征态在整个能谱中共存。我们还提出了在周期驱动的AA模型中实现$q$-形变动能设置中产生的层级结构的可能实验方案。
英文摘要：
We propose a $q$-deformation in the single-particle kinetic energy and investigate how it modifies the localization in the one-dimensional Aubry-André (AA) model. We construct a Hermitian $q$-deformed kinetic operator as a nonlinear function of the lattice translation operator, preserving the uniform lattice and recovering the conventional AA Hamiltonian continuously in the undeformed limit $q\to1$. The deformation generates an infinite set of correlated odd-range kinetic processes, controlled by a single parameter q, rather than phenomenologically involving long-range hopping. Under the dual transformation, this long-range hopping appears as higher harmonics of the dual quasiperiodic potential, providing a controlled route for breaking the exact self-duality of the AA model, with $q$ as the control parameter, consequently modifying the localization structure for $q\neq1$. In contrast to the conventional AA model, where all eigenstates localize simultaneously at $λ_c=2$, the deformed model exhibits a fraction of delocalized states even beyond $λ_c =2$. An intermediate regime also emerges in the $q-λ$ plane where localized and extended eigenstates coexist across the spectrum. We also propose a possible experimental realization of the hierarchy produced in the $q$-deformed kinetic setting in a periodically driven AA model.
