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Phase diagram of the strongly correlated Kane-Mele-Hubbard model

机译：高度相关的Kane-Mele-Hubbard模型的相图

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The phase diagram of the strongly correlated Hubbard model with intrinsic spin-orbit coupling on the honeycomb lattice is explored here. We obtain the low-energy effective model describing the spin degree of freedom. The resulting model is then studied by the Schwinger boson and Schwinger fermion approaches. The Schwinger boson method elucidates the boundary between the spin liquid phase and the magnetically ordered phases, Neel order, and incommensurate Neel order. Increasing the strength of the spin-orbit coupling is shown to narrow the width of the spin liquid region. The Schwinger fermion approach sheds further light on the nature of the spin liquid phase. We obtained three different candidates for the spin liquid phase within the mean-field approximation, namely, the gapless spin liquid, topological Mott insulator (fractionalized topological insulator), and chiral spin liquid phases. However, we argue that the gauge fluctuations and the instanton effect may suppress the first two spin liquids, while the chiral spin liquid is stable against gauge fluctuations due to its nontrivial topology.
机译：在此探索了在蜂窝晶格上具有固有自旋轨道耦合的强相关哈伯德模型的相图。我们获得了描述自旋自由度的低能量有效模型。然后，通过Schwinger玻色子和Schwinger费米子方法研究所得模型。 Schwinger玻色子方法阐明了自旋液相和磁有序相，尼尔级和不等尼尔级之间的边界。示出增加自旋轨道耦合的强度使自旋液体区域的宽度变窄。 Schwinger费米子方法进一步揭示了自旋液相的性质。我们在平均场近似内获得了三种不同的自旋液相候选物，即无间隙自旋液相，拓扑Mott绝缘体（分数化拓扑绝缘体）和手性自旋液相。但是，我们认为，表观波动和瞬时效应可能会抑制前两种自旋液体，而手性自旋液体由于其非平凡的拓扑结构而能够稳定地抵抗表观波动。

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