椭圆型量子反磁效应的镜像
Elliptic mirror of the quantum Hall effect
AI总结：
通过镜像对称性，将量子反磁效应的椭圆模型与实验数据结合，揭示其临界行为和 universality 类。
摘要：
环形西格玛模型的磁输运被分析，其中整数和分数量子反磁效应通过一个holomorphic模对称性自动统一。通过利用称为镜像对称性的量子等价性，这些模型被映射到可处理的镜像模型（也称为椭圆模型）中，其中拓扑保护由更熟悉的缠绕数提供。椭圆模型的相图和标度性质与过去三十年积累的一些实验和数值数据进行了比较。从量子反磁实验中提取的标度流几何与模预测一致，包括许多量子临界点的位置。一个显眼的模型（可能是最简单和最自然的）具有临界去局域化指数ν_tor = 18 ln 2/(π² G⁴) = 2.6051…（G是高斯常数），与数值Chalker-Coddington模型计算出的值ν_num = 2.607±0.004一致，表明这些模型属于同一 universality 类。真实的去局域化指数可能在有限尺寸标度实验中与其它标度指数分离，给出实验值ν_exp = 2.3±0.2。模模型表明这些理论和实验结果如何调和，但为了确定这些理论模型是否真的属于量子反磁 universality 类，需要迫切改进有限尺寸标度实验。
英文摘要：
Toroidal sigma models of magneto-transport are analyzed, in which integer and fractional quantum Hall effects automatically are unified by a {holomorphic modular symmetry}. By exploiting a quantum equivalence called \emph{mirror symmetry}, these models are mapped to tractable mirror models (also elliptic), in which topological protection is provided by more familiar winding numbers. Phase diagrams and scaling properties of elliptic models are compared to some of the experimental and numerical data accumulated over the past three decades. The geometry of scaling flows extracted from quantum Hall experiments is in good agreement with modular predictions, including the location of many quantum critical points. One conspicuous model %(arguably the simplest and most natural one) has a critical delocalization exponent $ν_{\rm tor} = 18 \ln 2 /(π^2 G^4) = 2.6051\dots$ ($G$ is Gauss' constant) that is in excellent agreement with the value $ν_{\rm num} = 2.607\pm\,.004$ calculated in the numerical Chalker-Coddington model, suggesting that these models are in the same universality class. The real delocalization exponent may be disentangled from other scaling exponents in finite size scaling experiments, giving an experimental value $ν_{\rm exp} = 2.3\pm 0.2$. The modular model suggests how these theoretical and experimental results may be reconciled, but in order to determine if these theoretical models really are in the quantum Hall universality class, improved finite size scaling experiments are urgently needed.
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