从相同准周期结构导出的不同电子位点构型中的广义类布洛赫基态
Generalized Bloch-like ground states in distinct electron-site configurations derived from the same quasiperiodic structure
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中文总结 AI 辅助
研究在准周期系统中构建广义类布洛赫态（SKK态）的方法，基于紧束缚模型中产生算符的广义傅里叶变换开发构造方法，应用于AB平铺的顶点和对偶模型，重现并揭示了相应SKK态，表明其不依赖特定电子位点选择。
中文摘要 AI 辅助
在准周期系统中，由于缺乏平移对称性，布洛赫定理无法应用，因此提出了Sutherland-Kalugin-Katz (SKK) 态作为广义类布洛赫态。然而，以往的研究很大程度上依赖于基于假设的论证，从指定哈密顿量构建SKK态的系统程序仍不明确。在这项工作中，我们基于紧束缚模型中产生算符的广义傅里叶变换开发了一种构造方法。然后，我们将这个框架应用于Ammann-Beenker (AB) 平铺的顶点模型和对偶模型，它们源于相同的准周期性，但电子位点构型不同。我们的构造在顶点模型的基态中重现了先前报道的SKK态，并在对偶模型的基态中高保真地揭示了相应的SKK态。这两个SKK态之间的结构对应表明，这些态不依赖于电子位点的特定选择，反映了AB平铺的潜在准周期性。
英文摘要
Sutherland-Kalugin-Katz (SKK) states have been proposed as generalized Bloch-like states in quasiperiodic systems where the absence of translational symmetry prevents the application of Bloch's theorem. However, previous studies have largely relied on ansatz-based arguments, and a systematic procedure for constructing the SKK state from a specified Hamiltonian has remained unclear. In this work, we develop a constructive approach based on a generalized Fourier transform of creation operators in tight-binding models. We then apply this framework to vertex and dual models on the Ammann-Beenker (AB) tiling that stem from the same quasiperiodicity but differ in their electron-site configurations. Our construction reproduces the previously reported SKK state in the ground state of the vertex model and reveals a corresponding SKK state in the ground state of the dual model with high fidelity. The structural correspondence between the two SKK states indicates that such states are not tied to a particular choice of electron sites and reflect the underlying quasiperiodicity of the AB tiling.
