紧束缚电子模型在Apollonian网络上的局域化性质
Localization properties of a tight-binding electronic model on the Apollonian network
摘要：
研究了紧束缚哈密顿量在阿波罗网络上的电子态性质。这种结构，这是基于阿波罗包装问题定义的，已被探索作为一个复杂的网络，并作为一个基板，在其上的物理模型可以定义。薛定谔方程的模型，其中只包括最近邻相互作用，是写在一个矩阵公式。在一致的情况下，所得到的哈密顿量与阿波罗网络的邻接矩阵成比例。电子本征态的表征是基于光谱的性质，其特征在于具有非常大的简并度。网络的$2π/3$旋转对称性和大量的等效位置反映在所有本征态中，这些本征态根据它们的宇称进行分类。通过评估参与率来确定扩展状态和局部状态。另外两个非均匀模型的阿波罗网络的结果也。在一种情况下，相互作用被认为是依赖于节点的程度，而在另一个，随机现场能量被认为是。
英文摘要：
An investigation on the properties of electronic states of a tight-binding Hamiltonian on the Apollonian network is presented. This structure, which is defined based on the Apollonian packing problem, has been explored both as a complex network, and as a substrate, on the top of which physical models can defined. The Schrodinger equation of the model, which includes only nearest neighbor interactions, is written in a matrix formulation. In the uniform case, the resulting Hamiltonian is proportional to the adjacency matrix of the Apollonian network. The characterization of the electronic eigenstates is based on the properties of the spectrum, which is characterized by a very large degeneracy. The $2π/3$ rotation symmetry of the network and large number of equivalent sites are reflected in all eigenstates, which are classified according to their parity. Extended and localized states are identified by evaluating the participation rate. Results for other two non-uniform models on the Apollonian network are also presented. In one case, interaction is considered to be dependent of the node degree, while in the other one, random on-site energies are considered.
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