无序费米子的对称类
Symmetry classes of disordered fermions
摘要：
戴森的基础上1962年的文章称为随机矩阵理论的“三重方式”，我们分类无序费米子系统与二次哈密顿由他们的酉和反酉对称性。无序金属和超导体中的非相互作用准粒子，以及随机规范场背景中的相对论费米子，都提供了重要的例子。分类的主要数据是一个Nambu空间的费米子场运营商进行表示的一些对称群。我们的方法是消除所有的酉对称从图片转移到一个不可约块的等变同态。在约简之后，指定一个线性空间的齐次相容哈密尔顿算子的块数据由基本向量空间V、End（V+V*）中的自同态空间、V+V* 上的对称或交替的双线性形式以及一个或两个可以混合V与V* 的反对酉对称组成。每一个这样的块数据集，以确定一个不可约的经典紧对称空间。相反，每个不可约的经典紧致对称空间都以这种方式出现。这证明了前一段时间所讨论的对称类和对称空间之间的对应关系。
英文摘要：
Building upon Dyson's fundamental 1962 article known in random-matrix theory as 'the threefold way', we classify disordered fermion systems with quadratic Hamiltonians by their unitary and antiunitary symmetries. Important examples are afforded by noninteracting quasiparticles in disordered metals and superconductors, and by relativistic fermions in random gauge field backgrounds. The primary data of the classification are a Nambu space of fermionic field operators which carry a representation of some symmetry group. Our approach is to eliminate all of the unitary symmetries from the picture by transferring to an irreducible block of equivariant homomorphisms. After reduction, the block data specifying a linear space of symmetry-compatible Hamiltonians consist of a basic vector space V, a space of endomorphisms in End(V+V*), a bilinear form on V+V* which is either symmetric or alternating, and one or two antiunitary symmetries that may mix V with V*. Every such set of block data is shown to determine an irreducible classical compact symmetric space. Conversely, every irreducible classical compact symmetric space occurs in this way. This proves the correspondence between symmetry classes and symmetric spaces conjectured some time ago.
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