分数阶Chern绝缘子中的拓扑电流
Topological Current in Fractional Chern Insulators
摘要：
本文研究了周期边界条件下二维格点上磁场中相互作用费米子。为了测量霍尔电流，我们使用一个带有紧凑支撑的电势。然后，由于洛伦兹力，霍尔电流沿等位线出现。在电势的边缘引入一个局部电流算符，我们导出了霍尔电导的线性响应系数。对于广泛的一类模型，我们证明了，如果存在一个频谱间隙以上的简并基态，然后霍尔电导的基态分数量子化，而不平均的通量。这是格点上非相互作用费米子系统中积分量子化霍尔电导的拓扑论证的一个推广。
英文摘要：
We consider interacting fermions in a magnetic field on a two-dimensional lattice with the periodic boundary conditions. In order to measure the Hall current, we apply an electric potential with a compact support. Then, due to the Lorentz force, the Hall current appears along the equipotential line. Introducing a local current operator at the edge of the potential, we derive the Hall conductance as a linear response coefficient. For a wide class of the models, we prove that if there exists a spectral gap above the degenerate ground state, then the Hall conductance of the ground state is fractionally quantized without averaging over the fluxes. This is an extension of the topological argument for the integrally quantized Hall conductance in noninteracting fermion systems on lattices.
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