Symmetry classes of disordered fermions
Symmetry classes of disordered fermions
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DOI：
10.1007/s00220-005-1330-9
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发表时间：
2005-08-01
影响因子：
2.4
通讯作者：
Zirnbauer, MR
中科院分区：
文献类型：
--
作者：
Heinzner, P;Huckleberry, A;Zirnbauer, MR
基于戴森1962年发表的随机矩阵理论中的三重方法的基本文章，我们将无序费米子系统与二次哈密顿系统按其酉和反酉对称性进行分类。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提供了重要的物理例子。分类的主要数据是费米子场算符的Nambu空间，它带有某种对称群的表示。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。约简后，指定一个线性空间的齐次相容哈密尔顿算子的块数据包括一个基本向量空间V，一个End（V圆加V*）中的自同态空间，一个对称或交替的V圆加V* 上的双线性形式，以及一个或两个可以混合V与V* 的反对酉对称。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。反之，每一个不可约的经典紧对称空间都是这样发生的，这证明了对称类与对称空间的对应关系。
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 physical 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 circle plus V*), a bilinear form on V circle plus 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.