Zhang Yi-Cai
School of Physics and Materials Science, Guangzhou University, Guangzhou, 510006, People's Republic of China.
Sci Rep. 2024 Aug 2;14(1):17921. doi: 10.1038/s41598-024-68851-4.
In our previous work, the concept of critical region in a generalized Aubry-André model (Ganeshan-Pixley-Das Sarma's model) has been established. In this work, we find that the critical region can be realized in a one-dimensional flat band lattice with a quasi-periodic potential. It is found that the above flat band lattice model can be reduced to an effective Ganeshan-Pixley-Das Sarma's model. Depending on various parameter ranges, the effective quasi-periodic potential may be bounded or unbounded. In these two cases, the Lyapunov exponent, mobility edge, and critical indices of localized length are obtained exactly. In this flat band model, the localized-extended, localized-critical and critical-extended transitions can coexist. Furthermore, we find that near the transitions between the bound and unbounded cases, the derivative of Lyapunov exponent of localized states with respect to energy is discontinuous. At the end, the localized states in bounded and unbounded cases can be distinguished from each other by Avila's acceleration.
在我们之前的工作中，已经在广义奥布里 - 安德烈模型（加内山 - 皮克斯利 - 达斯·萨尔马模型）中建立了临界区域的概念。在这项工作中，我们发现临界区域可以在具有准周期势的一维平带晶格中实现。研究发现，上述平带晶格模型可以简化为一个有效的加内山 - 皮克斯利 - 达斯·萨尔马模型。根据各种参数范围，有效的准周期势可能是有界的或无界的。在这两种情况下，精确地得到了李雅普诺夫指数、迁移率边和局域长度的临界指数。在这个平带模型中，局域 - 扩展、局域 - 临界和临界 - 扩展转变可以共存。此外，我们发现在有界和无界情况之间的转变附近，局域态的李雅普诺夫指数关于能量的导数是不连续的。最后，有界和无界情况下的局域态可以通过阿维拉加速度相互区分。
