Topological phase transitions involving intrinsic topological orders are usually characterized by qualitative changes of ground state quantum entanglement, which cannot be described by conventional mean-field theories with local order parameters. Here, we apply the lattice Chern-Simons theory to study frustrated quantum magnets and show that the conventional concepts, such as the order parameter and symmetry breaking, can still play a crucial role in certain topological phase transitions. The lattice Chern-Simons representation establishes a nonlocal mapping from quantum spin models to interacting spinless Dirac fermions. We show that breaking certain emergent symmetries of the fermionic theory could provide a unified approach to describing both magnetic and topological orders, as well as the topological phase transitions between them. We apply this method to the perturbed spin-1/2 $J_1-J_2$ XY model on the honeycomb lattice and predict a nonuniform chiral spin liquid ground state in the strong frustration region. This is further verified by our high-precision tensor network calculations. These results suggest that the lattice Chern-Simons theory can simplify the complicated topological phase transitions to effective mean-field theories in terms of fermionic degrees of freedom, which lead to different understandings that help to understand the frustrated quantum magnets.

中文翻译：

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量子磁体晶格 Chern-Simons 理论中的涌现拓扑顺序和相变

涉及本征拓扑序的拓扑相变通常以基态量子纠缠的质变为特征，这是传统的具有局部序参数的平均场理论无法描述的。在这里，我们应用晶格 Chern-Simons 理论来研究受挫量子磁体，并表明常规概念，如有序参数和对称破缺，仍然可以在某些拓扑相变中发挥关键作用。晶格 Chern-Simons 表示建立了从量子自旋模型到相互作用的无自旋狄拉克费米子的非局部映射。我们表明，打破费米子理论的某些新兴对称性可以提供一种统一的方法来描述磁序和拓扑序，以及它们之间的拓扑相变。${Ĵ}_1-{Ĵ}_2$蜂窝晶格上的 XY 模型，并预测强挫折区域中的非均匀手性自旋液态基态。我们的高精度张量网络计算进一步验证了这一点。这些结果表明，晶格 Chern-Simons 理论可以将复杂的拓扑相变简化为费米子自由度方面的有效平均场理论，这导致了有助于理解受挫量子磁体的不同理解。