Low-energy transport in quantum Hall states is carried through edge modes and is dictated by bulk topological invariants and possibly microscopic Boltzmann kinetics at the edge. Here, we show how the presence or breaking of symmetries of the edge Hamiltonian underlie transport properties, specifically dc conductance and noise. We demonstrate this through the analysis of hole-conjugate states of the quantum Hall effect, specifically the $\nu =2/3$ case in a quantum point-contact geometry. We identify two symmetries, a continuous SU(3) symmetry and a discrete $Z_3$ symmetry, whose presence or absence (different symmetry scenarios) dictate qualitatively different types of behavior of conductance and shot noise. While recent measurements are consistent with one of these symmetry scenarios, others can be realized in future experiments.

中文翻译：

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分数量子霍尔边缘上与对称有关的传输

量子霍尔态中的低能输运通过边缘模式进行，并由整体拓扑不变量以及边缘处的微观玻尔兹曼动力学决定。在这里，我们显示了边缘哈密顿量的对称性的存在或破坏是传输特性（尤其是直流电导和噪声）的基础。我们通过分析量子霍尔效应的空穴共轭态来证明这一点，特别是$\nu =\mathrm{2个}/3$点接触几何中的情况。我们确定两个对称，一个连续的SU（3）对称和一个离散${ž}_3$对称性，其存在与否（不同的对称性场景）在性质上决定了电导和散粒噪声的行为类型。尽管最近的测量结果与这些对称情况之一一致，但其他测量结果仍可以在以后的实验中实现。