We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer classification, we show that our system hosts a symmetry-protected phase protected by a magnetic group symmetry ($\mathcal{M}$) and characterized by a $Z_2$ topological invariant. In single-particle spectra, we show that the topological nontrivial phase supports two kinds of edge states, which include two (four) zero-energy edge modes in the absence (presence) of two-photon detuning. We further study the bulk-edge correspondence in a non-Hermitian model by taking into account the particle dissipation. It is shown that the non-Hermitian system preserves the bulk-edge correspondence under the $\mathcal{M}$ symmetry but exhibits the non-Hermitian skin effect with breaking the $\mathcal{M}$ symmetry at nonzero magnetic flux. This work provides insights in understanding the exotic topological quantum states of high-spin systems and facilitating their experimental explorations.

中文翻译：

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自旋张量动量耦合的超冷原子的对称保护拓扑相

我们提出了一个可实现的实验方案，以构造具有自旋-张量-动量耦合的spin-1原子的一维合成磁通晶格，并探索其奇异的拓扑状态。与Altland-Zirnbauer分类不同，我们表明我们的系统具有受磁基对称性保护的对称保护相（$\mathcal{中号}$）并以 ${ž}_2$拓扑不变。在单粒子光谱中，我们表明拓扑非平凡相位支持两种边缘状态，包括在没有（存在）两光子失谐的情况下的两个（四个）零能边缘模式。通过考虑粒子耗散，我们进一步研究了非Hermitian模型中的体积边缘对应关系。结果表明，非Hermitian系统保留了在$\mathcal{中号}$ 对称但显示非赫密特皮肤效果，破坏了 $\mathcal{中号}$非零磁通时的对称性。这项工作为了解高旋转系统的奇异拓扑量子态提供了见识，并有助于他们的实验探索。