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首页> 外文期刊>Annales Henri Poincare >Network Models for Chiral Symmetry Classes of Anderson Localisation
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Network Models for Chiral Symmetry Classes of Anderson Localisation

机译：Anderson本地化的手性对称类的网络模型

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We consider localisation problems belonging to the chiral symmetry classes, in which sublattice symmetry is responsible for singular behaviour at a band centre. As an account for the talk given in TH2002, we focus here on the chiral time-reversal invariant symmetry class. We formulate a model which has the relevant symmetries and which is a generalisation of the network model introduced previously in the context of the integer quantum Hall plateau transition. We show that this generalisation can be re-expressed as corresponding to the introduction of absorption and amplification into the original network model. This model represents a convenient starting point for analytic discussions and computational studies. It exhibits both localised and critical phases, and band-centre singularities in the critical phase approach more closely in small systems the expected asymptotic form than in other known realisations of the symmetry class. In addition, we demonstrate that by imposing appropriate constraints on disorder, a lattice version of the Dirac equation with a random vector potential can be obtained.
机译：我们考虑了属于手性对称性类别的局部化问题，其中，亚晶格对称性是谱带中心的奇异行为的原因。为了说明TH2002中的演讲，我们在这里集中讨论手性时间反转不变对称性类。我们制定了一个具有相关对称性的模型，该模型是先前在整数量子霍尔高原跃迁的背景下引入的网络模型的概括。我们表明，可以将这种概括重新表达为与将吸收和放大引入原始网络模型相对应。该模型代表了分析讨论和计算研究的便利起点。与对称类的其他已知实现方式相比，它在预期相位渐近形式的小型系统中表现出局部相和临界相以及临界相方法中的谱带中心奇点。此外，我们证明了通过对无序施加适当的约束，可以获得具有随机矢量势的狄拉克方程的晶格形式。

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