近日，西北大学王一平团队研究了一维腔磁晶格中的霍夫施塔特蝴蝶和拓扑边缘态。2025年10月28日出版的《物理评论A》杂志发表了这项成果。

分形能谱是两个周期参数在不同尺度上相互作用的结果。在合成维度上具有非平凡拓扑特征的人工晶格可以模拟这种相互作用，表现出类似霍夫施塔特蝴蝶的拓扑边界对应和分形结构。然而，霍夫施塔特蝴蝶光谱在腔磁晶格中的实现受到的关注有限。

在这项工作中，研究组提出了一种一维腔磁振晶格，其中每个单元晶胞将一个腔光子与一个磁振子耦合。通过调整系统参数来实现合成磁通，研究组证明了霍夫施塔特蝴蝶能谱的出现和不同边缘态模式的形成。这些边缘状态表现出翻转行为，使量子信息的受控存储和传输成为可能。研究组进一步分析了光谱结构，并计算了拓扑不变量来表征系统的相图。研究了随机缺陷的影响。虽然小的缺陷对拓扑性质的影响很小，但较大的缺陷可能会破坏边缘模式，因此在实际实现中需要抑制缺陷以保持拓扑的稳定性。

附：英文原文

Title: Hofstadter butterfly and topological edge states in a one-dimensional cavity magnonic lattice

Author: Ling Li, Yi-Ping Wang, Ai-Xi Chen

Issue&Volume: 2025/10/28

Abstract: Fractal energy spectra arise from the interplay between two periodic parameters at different scales. Artificial lattices with nontrivial topological features in synthetic dimensions can emulate such interplay, exhibiting topological boundary correspondence and fractal structures resembling the Hofstadter butterfly. However, the realization of Hofstadter butterfly spectra in cavity magnonic lattices has received limited attention. In this work, we propose a one-dimensional cavity magnonic lattice in which each unit cell couples a cavity photon with a magnon. By tuning the system parameters to implement a synthetic magnetic flux, we demonstrate the emergence of a Hofstadter butterflylike energy spectrum and the formation of distinct edge-state modes. These edge states exhibit flipping behavior, enabling controlled storage and transmission of quantum information. We further analyze the spectral structure and compute thetopological invariants to characterize the system's phase diagram. The influence of random defects is also investigated. While small imperfections have minimal impact on topological properties, larger defects may disrupt the edge modes, highlighting the need for defect suppression to preserve topological robustness in practical implementations.

DOI: 10.1103/cc91-n6b3

Source: https://journals.aps.org/pra/abstract/10.1103/cc91-n6b3