论文标题
Lyapunov指数，迁移率边缘和关键区域，具有无界的准潜能
Lyapunov exponent, mobility edges, and critical region in the generalized Aubry-Andre model with an unbounded quasiperiodic potential
论文作者
论文摘要
在这项工作中，我们使用无限制的quasi-periodic潜力研究了广义Aubry-André模型（Ganeshan-Pixley-Das Sarma的模型）的Anderson本地化问题，其中参数$ | |α| \ geq1 $。 Lyapunov指数$γ（e）$和移动性边缘$ e_c $是针对无界的准周期潜力获得的。使用Lyapunov指数，我们发现参数$λ-E $平面中存在一个关键区域。关键区域由关键国家组成。与局部和扩展状态相比，关键状态的空间扩展的波动更大。数值结果表明，关键状态$ x \ simeq0.5 $的反向参与率（IPR）的缩放指数。此外，发现有界长度的局部长度$ν= 1 $的关键指标（$ |α| <1 $）的情况和$ν= 1/2 $对于无约束（$ | |α| \ geq1 $）案例。上述不同的临界指标可用于区分本地化扩展与局部临界过渡。最后，我们表明，对于$ |α| <1 $和$ |α| \ geq1 $的$ e $的系统都可以由Lyapunov指数$γ（e）$和Avila的量化加速度$ω（e）进行分类。
In this work, we investigate the Anderson localization problems of the generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) with an unbounded quasi-periodic potential where the parameter $|α|\geq1$. The Lyapunov exponent $γ(E)$ and the mobility edges $E_c$ are exactly obtained for the unbounded quasi-periodic potential. With the Lyapunov exponent, we find that there exists a critical region in the parameter $λ-E$ plane. The critical region consists of critical states. In comparison with localized and extended states, the fluctuation of spatial extensions of the critical states is much larger. The numerical results show that the scaling exponent of inverse participation ratio (IPR) of critical states $x\simeq0.5$. Furthermore, it is found that the critical indices of localized length $ν=1$ for bounded ($|α|<1$) case and $ν=1/2$ for unbounded ($|α|\geq1$) case. The above distinct critical indices can be used to distinguish the localized-extended from localized-critical transitions. At the end, we show that the systems with different $E$ for both cases of $|α|<1$ and $|α|\geq1$ can be classified by the Lyapunov exponent $γ(E)$ and Avila's quantized acceleration $ω(E)$.
