Motivated by a recent experiment [J. H. Han, {et. al.}, Phys. Rev. Lett.~122, 065303 (2019)], we investigate many-body physics of interacting fermions in a synthetic Hall tube, using state-of-the-art density-matrix renormalization-group numerical method. Since the inter-leg couplings of this synthetic Hall tube generate an interesting spin-tensor Zeeman field, exotic topological and magnetic properties occur. Especially, four new quantum phases, such as nontopological spin-vector and -tensor paramagnetic insulators, and topological and nontopological spin-mixed paramagnetic insulators, are predicted by calculating entanglement spectrum, entanglement entropies, energy gaps, and local magnetic orders with 3 spin-vectors and 5 spin-tensors. Moreover, the topologically magnetic phase transitions induced by the interaction as well as the inter-leg couplings are also revealed. Our results pave a new way to explore many-body (topological) states induced by both the spiral spin-vector and -tensor Zeeman fields.

中文翻译：

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相互作用费米子的合成霍尔管

受最近的实验启发[JH Han，{et。al。}，物理学。Rev. Lett。〜122，065303（2019）]，我们使用最新的密度矩阵重归一化组数值方法研究了合成霍尔管中相互作用的费米子的多体物理学。由于这种合成霍尔管的腿间耦合会产生有趣的自旋张量塞曼场，因此会产生奇特的拓扑和磁性。特别是，通过计算纠缠谱，纠缠熵，能隙和具有3个自旋能级的局部磁阶，预测了四个新的量子相，例如非拓扑自旋矢量和-张量顺磁绝缘子，以及拓扑和非拓扑自旋混合顺磁绝缘子。向量和5个自旋张量。此外，还揭示了由相互作用以及腿间耦合引起的拓扑磁性相变。我们的结果为探索由螺旋自旋矢量场和-张量塞曼场引起的多体（拓扑）状态开辟了新途径。