标题： 对偶性破坏、迁移率边以及原子链中费米子在拓扑 Aubry-André 和量子霍尔绝缘体之间的联系 显示英文标题

标题： Duality breaking, mobility edges, and the connection between topological Aubry-André and quantum Hall insulators in atomic wires with fermions

摘要： 众所周知，由于其能量无关的自对偶性，Aubry-André模型缺乏迁移率边缘，但可能表现出边缘态。 当对偶性被破坏时，我们表明会形成迁移率区域，并出现非平凡的拓扑相。 通过改变对偶性破坏的程度，我们确定了迁移率区域，并建立了Aubry-André原子线与费米子和依赖于激光场相对相位的哈密顿量家族之间的联系，该相位被视为合成维度。 根据填充因子和对偶性破坏的程度，我们发现了三类非平凡相：常规拓扑绝缘体、常规拓扑Aubry-André绝缘体和非常规（混合）拓扑Aubry-André绝缘体。 最后，我们讨论了适当的陈数，这些陈数说明了原子线中局域费米子拓扑相的分类。 显示英文摘要

摘要： It is well known that the Aubry-Andr{\'e} model lacks mobility edges due to its energy-independent self-duality but may exhibit edge states. When duality is broken, we show that mobility regions arise and non-trivial topological phases emerge. By varying the degree of duality breaking, we identify mobility regions and establish a connection between Aubry-Andr{\'e} atomic wires with fermions and quantum Hall systems for a family of Hamiltonians that depends on the relative phase of laser fields, viewed as a synthetic dimension. Depending on the filling factor and the degree of duality breaking, we find three classes of non-trivial phases: conventional topological insulator, conventional topological Aubry-Andr{\'e} insulator, and unconventional (hybrid) topological Aubry-Andr{\'e} insulator. Finally, we discuss appropriate Chern numbers that illustrate the classification of topological phases of localized fermions in atomic wires.