Anderson Localization in Nonlinear σ Model Representation
Anderson Localization in Nonlinear σ Model Representation
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非线性 σ 模型表示中的安德森定位
DOI：
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发表时间：
1981
期刊：
影响因子：
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通讯作者：
S. Hikami
中科院分区：
文献类型：
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作者：
S. Hikami
结果表明，电子杂质散射的安德森定域化问题可用一种特殊的场论模型来描述，这种场论模型称为非线性σ模型。在非线性σ模型中，图解的l/EFτ展开式与小耦合t展开式有一一对应的关系。安德森定域化中的重正化问题通过将这个问题等价于非线性σ模型来解决，σ模型是在小t和小e=d−2双展开意义下的二维和三维的可重正化理论。当系统具有时间反演和空间反演不变性时，β函数在二维空间表现出渐近自由行为。扩散常数D是频率ω的函数。酉和辛的情况下的结果也被提出。为了与一维电子散射问题的β函数进行比较，本文考虑了一维晶格非线性σ模型。
It is shown that the Anderson localization problem of electron impurity scattering is described by a special type of the field theoretical model, which is called a nonlinear σ model. The diagrammatic l/EFτ expansion has one-to-one correspondence with small coupling t-expansion in the nonlinear σ model. The renormalization problems in the Anderson localization are solved by the equivalence of this problem to the nonlinear σ model, which is a renormalizable theory in two and three dimensions in the sense of small t and small e=d−2 double expansions. The β-function is calculated up to three-loop order and it shows the asymptotic free behavior in two dimensions when the system has time-reversal and space-inversion invariance. The diffusion constant D is obtained as a function of frequency ω. The results of the unitary and the symplectic case are also presented. The lattice nonlinear σ model in one dimension is considered for the comparison with the β-function of the one dimension electron scattering problem.