Bott Periodicity for Z2 Symmetric Ground States of Gapped Free-Fermion Systems
Bott Periodicity for Z2 Symmetric Ground States of Gapped Free-Fermion Systems
复制标题
带隙自由费米子系统 Z2 对称基态的 Bott 周期
DOI：
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发表时间：
2015
期刊：
影响因子：
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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：
R. Kennedy;M. Zirnbauer
在无序费米子对称性分类的基础上，证明了Kitaev等人提出的具有对称性的有隙系统自由费米子基态的“Bott Clock”拓扑分类.我们的方法与以前的方法不同之处在于：(I)我们在复数上的厄米量子力学的标准框架下工作，(Ii)我们直接建立基态的数学模型，而不是光谱平坦的哈密顿量，(Iii)我们使用同伦理论工具，而不是K理论。我们证明的关键是一个自然变换，它与标准的Bott映象平方，并将对称类S中d维系统的基态与对称类S+1中(d+1)维系统的基态联系起来。这种关系为拓扑绝缘体和超导体提供了一个新的有利条件。
Building on the symmetry classification of disordered fermions, we give a proof of the proposal by Kitaev, and others, for a “Bott clock” topological classification of free-fermion ground states of gapped systems with symmetries. Our approach differs from previous ones in that (i) we work in the standard framework of Hermitian quantum mechanics over the complex numbers, (ii) we directly formulate a mathematical model for ground states rather than spectrally flattened Hamiltonians, and (iii) we use homotopy-theoretic tools rather than K -theory. Key to our proof is a natural transformation that squares to the standard Bott map and relates the ground state of a d-dimensional system in symmetry class s to the ground state of a (d + 1)-dimensional system in symmetry class s + 1. This relation gives a new vantage point on topological insulators and superconductors.
影响因子：
2.4
作者：
Heinzner, P;Huckleberry, A;Zirnbauer, MR
通讯作者：
Zirnbauer, MR