具有 onsite 增益和损耗的非厄米 Aubry-André 模型中局域化相变的平衡与非平衡标度行为
Equilibrium and nonequlibrium scaling behaviors of localization transition in a non-Hermitian Aubry-André model with onsite gain and loss
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中文总结 AI 辅助
本文研究具有 onsite 增益损耗的非厄米 Aubry-André 模型的局域化相变，提取了独特的临界指数，验证了有限时间标度框架对该模型的适用性，确立其为新普适类并扩展了 FTS 框架的适用范围。
中文摘要 AI 辅助
非厄米性与局域化的相互作用已引起大量关注，但具有 onsite 增益和损耗的非厄米系统中局域化相变的驱动动力学仍未得到充分探索。本文研究了具有 onsite 增益和损耗的非厄米 Aubry-André（AA）模型的临界标度行为和驱动动力学。通过对局域化长度、参与度倒数（IPR）和能隙进行有限尺寸标度分析，我们提取了临界指数 ν = 1.00(2)、s = 0.7965(2) 和 z = 1.999(2)。这些指数与厄米 AA 模型及非互易跳跃 AA 模型的指数不同，尤其是 IPR 指数 s，表明增益-损耗机制属于一个独特的普适类。对于驱动动力学，我们关注系统初始制备为无隙扩展态并线性驱动越过临界点的情况。我们验证了有限时间标度（FTS）框架在满足准则 z' < r 时仍适用，其中 z' = 1.999(2) 表征扩展相中的能隙闭合，r = z + 1/ν ≈ 2.999。我们在宽范围的系统尺寸和驱动速率下数值验证了 IPR 的预测 FTS 标度形式，证明统一标度描述可成功推广到增益-损耗型非厄米 AA 模型。本工作不仅确立了增益-损耗 AA 模型为局域化相变的新普适类，还扩展了 FTS 框架对具有无隙初始态的非厄米系统的适用性。
英文摘要
The interplay between non-Hermiticity and localization has attracted considerable interest, yet the driven dynamics of localization transitions in non-Hermitian systems with on-site gain and loss remains largely unexplored. Here we investigate the critical scaling behavior and driven dynamics of the non-Hermitian Aubry-André (AA) model with on-site gain and loss. Through finite-size scaling analyses of the localization length, the inverse participation ratio (IPR), and the energy gap, we extract the critical exponents $ν= 1.00(2)$, $s = 0.7965(2)$, and $z = 1.999(2)$. These exponents are different from those of both the Hermitian AA model and the nonreciprocal hopping AA model, particularly the IPR exponent $s$, demonstrating that the gain-loss mechanism belongs to a distinct universality class. For the driven dynamics, we focus on the case where the system is initially prepared in a gapless extended state and linearly driven across the critical point. We verify that the finite-time scaling (FTS) framework remains applicable provided that the criterion $z' < r$ is satisfied, where $z' = 1.999(2)$ characterizes the gap closure in the extended phase and $r = z + 1/ν\approx 2.999$. The predicted FTS scaling forms for the IPR are numerically validated across a wide range of system sizes and driving rates, demonstrating that the unified scaling description can be successfully generalized to the gain-loss type non-Hermitian AA model. Our work not only establishes the gain-loss AA model as a new universality class of localization transitions but also extends the applicability of the FTS framework to non-Hermitian systems with gapless initial states.
