Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model
Toward a theory of the integer quantum Hall transition: Continuum limit of the Chalker–Coddington model
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走向整数量子霍尔跃迁理论：Chalker-Coddington 模型的连续极限
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发表时间：
1997
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通讯作者：
M. Zirnbauer
中科院分区：
文献类型：
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作者：
M. Zirnbauer
考虑了Chalker和科丁顿网络模型的N通道推广。已知N=1的模型描述了表现出整数量子霍尔效应的系统在平台转变处的临界行为。利用最近发现的一个积分等式，将网络模型转化为定义在具有酉对称性的Efetov σ模型空间上的格场论。变换对所有N都是精确的，没有鞍点近似，也没有大质量模需要消除。格点理论的朴素连续极限是Pruisken的非线性σ模型的超对称形式，在对称点上耦合为σxx=N/4和σxy=N/2.由此可见，描述自旋简并朗道能级和随机通量问题的N=2的模型是非临界的。基于对称性的考虑和对哈密顿极限的检验，提出了一种改进的网络模型，它仍然属于量子Hall普适类。前景...
An N-channel generalization of the network model of Chalker and Coddington is considered. The model for N=1 is known to describe the critical behavior at the plateau transition in systems exhibiting the integer quantum Hall effect. Using a recently discovered equality of integrals, the network model is transformed into a lattice field theory defined over Efetov’s σ model space with unitary symmetry. The transformation is exact for all N, no saddle-point approximation is made, and no massive modes have to be eliminated. The naive continuum limit of the lattice theory is shown to be a supersymmetric version of Pruisken’s nonlinear σ model with couplings σxx=N/4 and σxy=N/2 at the symmetric point. It follows that the model for N=2, which describes a spin degenerate Landau level and the random flux problem, is noncritical. On the basis of symmetry considerations and inspection of the Hamiltonian limit, a modified network model is formulated, which still lies in the quantum Hall universality class. The prospec...