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Symmetry-Protected Topological Phase for Spin-Tensor-Momentum-Coupled Ultracold Atoms

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 symmetryprotected phase protected by a magnetic group symmetry (M) and characterized by a Z2 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 M symmetry but exhibits the non-Hermitian skin effect with breaking the 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.