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.

• Received 13 January 2020
• Revised 17 May 2020
• Accepted 11 June 2020

DOI:https://doi.org/10.1103/PhysRevA.102.013301