霍夫施塔特蝴蝶中隐藏的准晶体
Hidden Quasicrystal in Hofstadter Butterfly
摘要：
霍夫施塔特蝴蝶的光谱间隙的层次集的拓扑描述被发现是编码在准晶体中，其中磁通量起着一个相位因子的作用，移动的准周期秩序的起源。揭示了一个内在的挫折在最小的能量尺度，描述为$ζ=2-\sqrt{3}$，这个无理数的特点，普遍的蝴蝶和相关的两个量子数，其中包括陈数的量子霍尔态。随着周期性的驱动，诱导系统中的相变，蝴蝶的精细结构被放大，使大拓扑不变量的实验访问状态。
英文摘要：
Topological description of hierarchical sets of spectral gaps of Hofstadter butterfly is found to be encoded in a quasicrystal where magnetic flux plays the role of a phase factor that shifts the origin of the quasiperiodic order. Revealing an intrinsic frustration at smallest energy scale, described by $ζ=2-\sqrt{3}$, this irrational number characterizes the universal butterfly and is related to two quantum numbers that includes the Chern number of quantum Hall states. With a periodic drive that induces phase transitions in the system, the fine structure of the butterfly is shown to be amplified making states with large topological invariants accessible experimentally .
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