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Edge properties of principal fractional quantum Hall states in the cylinder geometry

机译：圆柱几何中主要分数量子霍尔态的边缘性质

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We study fractional quantum Hall states in the cylinder geometry with open boundaries. We focus on principal fermionic v = 1/3 and bosonic v = 1/2 fractions in the case of hard-core interactions. The gap behavior as a function of the cylinder radius is analyzed. By adding enough orbitals to allow for edge modes, we show that it is possible to measure the Luttinger parameter of the nonchiral liquid formed by the combination of the two counterpropagating edges when we add a small confining potential. Although we measure a Luttinger exponent consistent with the chiral Luttinger theory prediction for the full hard-core interaction, the exponent remains nontrivial in the Tao-Thouless limit as well as for simple truncated states that can be constructed on the cylinder. If the radius of the cylinder is taken to infinity, the problem becomes a Tonks-Girardeau one-dimensional interacting gas in Fermi and Bose cases. Finally, we show that the Tao-Thouless and truncated states have an edge electron propagator, which decays spatially with a Fermi-liquid exponent, even if the energy spectrum can still be described by a nontrivial Luttinger parameter.
机译：我们研究具有开放边界的圆柱几何体中的分数量子霍尔态。在硬核相互作用的情况下，我们专注于主要的铁离子v = 1/3和硼酸v = 1/2分数。分析了作为圆柱半径的函数的间隙行为。通过添加足够的轨道以允许边缘模式，我们证明了当我们添加较小的约束电位时，可以测量由两个反向传播的边缘组合而成的非手性液体的Luttinger参数。尽管我们测量的Luttinger指数与手性Luttinger理论预测的完全硬核相互作用相符，但在Tao-Thouless极限以及可在圆柱上构造的简单截断状态下，该指数仍然很重要。如果圆柱的半径取无穷大，那么在费米和玻色的情况下，问题就变成了Tonks-Girardeau一维相互作用的气体。最后，我们证明了道-不通和截断态具有边缘电子传播子，即使能谱仍然可以由非平凡的Luttinger参数来描述，该电子在费米液体指数的作用下也会在空间上衰减。

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