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Logarithmic correlations in quantum Hall plateau transitions

机译：量子霍尔高原跃迁中的对数相关

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摘要

The critical behavior of quantum Hall transitions in two-dimensional disordered electronic systems can be described by a class of complicated, nonunitary conformal field theories with logarithmic correlations. The nature and the physical origin of these logarithmic correlation functions remain, however, mysterious. Using the replica trick and the underlying symmetries of these quantum critical points, we show here how to construct nonperturbatively disorder-averaged observables in terms of Green's functions that scale logarithmically at criticality. In the case of the spin quantum Hall transition, which may occur in disordered superconductors with spin-rotation symmetry and broken time reversal invariance, we argue that our results are compatible with an alternative approach based on supersymmetry. The generalization to the integer quantum Hall plateau transition is also discussed.
机译：二维无序电子系统中的量子霍尔跃迁的临界行为可以用一类具有对数相关性的复杂非non形共形场理论来描述。这些对数相关函数的性质和物理起源仍然是神秘的。使用复制技巧和这些量子临界点的潜在对称性，我们在此处展示如何根据格林函数在临界点对数尺度上构造非扰动平均的可观察物。在自旋量子霍尔跃迁的情况下，它可能发生在具有自旋旋转对称性和断裂时间反转不变性的无序超导体中，我们认为我们的结果与基于超对称性的另一种方法兼容。还讨论了对整数量子霍尔平稳跃迁的推广。

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