Ganeshan Sriram, Pixley J H, Das Sarma S
Condensed Matter Theory Center and Joint Quantum Institute, Department of Physics, University of Maryland, College Park, Maryland 20742, USA.
Phys Rev Lett. 2015 Apr 10;114(14):146601. doi: 10.1103/PhysRevLett.114.146601. Epub 2015 Apr 9.
We investigate localization properties in a family of deterministic (i.e., no disorder) nearest neighbor tight binding models with quasiperiodic on site modulation. We prove that this family is self-dual under a generalized duality transformation. The self-dual condition for this general model turns out to be a simple closed form function of the model parameters and energy. We introduce the typical density of states as an order parameter for localization in quasiperiodic systems. By direct calculations of the inverse participation ratio and the typical density of states we numerically verify that this self-dual line indeed defines a mobility edge in energy separating localized and extended states. Our model is a first example of a nearest neighbor tight binding model manifesting a mobility edge protected by a duality symmetry. We propose a realistic experimental scheme to realize our results in atomic optical lattices and photonic waveguides.
我们研究了一族具有准周期在位调制的确定性（即无无序）最近邻紧束缚模型中的局域化性质。我们证明了该族模型在广义对偶变换下是自对偶的。这个一般模型的自对偶条件结果是模型参数和能量的一个简单封闭形式函数。我们引入典型态密度作为准周期系统中局域化的一个序参量。通过直接计算逆参与率和典型态密度，我们从数值上验证了这条自对偶线确实在能量中定义了一个迁移率边缘，将局域态和扩展态分开。我们的模型是第一个表现出由对偶对称性保护的迁移率边缘的最近邻紧束缚模型的例子。我们提出了一个现实的实验方案，以在原子光学晶格和光子波导中实现我们的结果。
